WPCL 2BJ|x! x   @ Њ`Gazetteer p. ! x @` Њ 7. MONUMENTS IN FRANCE.  Note. French orthography is confused for several reasons. Accents are often omitted on capital letters and the usage of accents has changed over the last few centuries. Modern French writers often use modern forms, while nonFrench writers often omit the accents entirely. E.g. N=tre is often given as Notre, even in France. In place names, there is a tendency to combine words with hyphens, e.g. StGermaindesPr)s, but this is not consistently done. The words Rue, Avenue, Place, etc. are sometimes capitalised and sometimes not. In Paris, I will indicate the arrondissements by e.g. 5e, except the first is 1er. The French post codes for Paris begin 75 and then have the arrondissement number given as three digits, e.g. the 5th arr. has code 75005. I have generally put the house number before the street name, though the French often do it the other way.  7A. PARIS. 7A1. INSTITUTIONS.  CEMETERIES. Many details come from [Culbertson & Randall (3)]. See also the Panth)on below. MONTMARTRE CEMETERY is at 20 Avenue Rachel, 18e. A free list/map is provided by the Mairie de Paris at the entrance. Jean Bernard L)on FOUCAULT (18191868) is buried in Division 7 [Culbertson & Randall(3), pp.112-114]. Andr) Marie AMP.RE (17751836) is in Division 30 [Culbertson & Randall (3), pp.112113 & 127], with his son, a notable linguist. Andreas Hinz reports that he found LUCAS's grave here, near to Offenbach, but it is mostly illegible Lucas is not on the list/map and when I visited in 1998, I found that the main lists are in the cemetery office which is not open on weekends. I was unable to find it in Jan 2002, but Hinz later told me it is across the path from Offenbach, where I did not look. [Hare(2), p. 488] says De Bougainville's tomb is here, but I have now found that he had been in the cemetery of St. Pierre, on the top of Montmartre, just west of Sacr) Coeur, and this is only open on 1 Nov. He has been removed to the Panth)on, qv, but [ MGG ] says his heart remains at St. Pierre. The list/map mentions a Charles Fourier (philosopher and economist), but I don't know if he is any relation to the mathematician. GALOIS was buried in a common grave in MONTPARNASSE CEMETERY, 3 Boulevard Edgar Quinet, 14e, in 1832, but no trace of it remains [Solovyov]. Alexander ALEKHINE (18921946), World Chess Champion in 19271935 and 19371946, is buried in Montparnasse Cemetery with an appropriate statue [Schonberg, p. 171]. Urbain Jean Joseph LEVERRIER (1811-1877) is buried in Division 11 [Culbertson & Randall (3), p. 171]. Henri POINCAR( (18541912) is here [ MGG ]. Nicolas CONT( (17551805), inventor of the pencil, is buried in Division 25 [Culbertson & Randall (3), p. 181]. P.RE LACHAISE CEMETERY, 16 rue de Repos (or Boulevard M)nilmontant), 20e, is the largest in Paris, established in 1804 when the city was overflowing with corpses. Maps of the famous graves are obtainable near the entrances, but they don't list all of the following. Gustave FROMENT (18151865), inventor of the gyroscope (but see under Panth)on, below, and Foucault in Section 7A2) and a telegraph, is buried in Division 1 [Culbertson & Randall (3), p. 10]. Fran'ois ARAGO (17861853) is in Division 4 [Culbertson & Randall (3), pp. 8 & 10; MGG ]. Edward BRANLY (1844-1940), inventor of the Branly decoherer used in early radio, is in Division 10 [Culbertson & Randall (3), p. 23]. Augustin Jean FRESNEL (17881827) is in Division 14 [Culbertson & Randall (3), p.31]. JeanBaptiste DELAMBRE is in Division 10. Michel CHASLES (17931880) is in Division 17 [Culbertson & Randall (3), p.33]. Auguste COMTE (17981857), the philosopher, is in Division 17 [Culbertson & Randall (3), pp. 3336; MGG ]. Jean Fran'ois CHAMPOLLION (1790-1832), the decipherer of hieroglyphics, is in Division 18 [Culbertson&Randall (3), p.36; MGG ]. MONGE was also buried here in Division 18 facing the Grand Carrefour [ MGG ]. The tomb is shown in the Open University program Paris and the New Mathematics, part of the course on History of Mathematics. In 1989, the remains were translated to the Panth)on, qv below. J.N. HACHETTE, Monge's assistant, is beside the Monge tomb and FOURIER is nearby. Joseph Louis GAYLUSSAC (17781850) is in Division 26 [Culbertson & Randall (3), p. 34; MGG ]. Allan KARDEC (previously L)on RIVAIL) (18041869) began as a mathematician, then wrote on education and grammar, before becoming the leading spokesman for spiritualism! He is now in Division44 [Culbertson & Randall (3), pp. 5354], having previously been in Montmartre. There is a LALANDE tomb in Division 46 but I don't know if the mathematician/astronomer is buried there. Th)ophile GRAMME (16261901), Belgian inventor of a dynamo in 1869, is in Division 94 [Culbertson & Randall (3), p.85]. [Hare(2), pp. 244245] says Louis POINSOT (1777-1859) is buried to the left of the main path, near Rossini. LAPLACE was buried here, but in 1888 he was translated to Mailloc, near Beaumont, qv in Section 7B, and the tomb was moved to Beaumont. The remains of AB(LARD and H)lo5se were transferred to P/re Lachaise cemetery in 1817, where the graves are a shrine for unhappy lovers [Okey, pp. 9093]. Andreas Hinz reports that Camille JORDAN is here, near Victor Hugo. Both CURIEs were buried at SCEAUX [Wymer, p. 6:32], but in 1995, they were translated to the Panth)on she is the first woman there. The Montparnasse area lies over a complex of old quarries and tunnels known as the Catacombs and stacked with bones removed from old cemeteries in 1785 entrance in Place DenfertRochereau, 14e, on the east side of the approach to Av. G)n)ralLeclerc. LAVOISIER was buried here. ACAD(MIE DES SCIENCES. [ MGG France ] considers the 1635 founding of the Acad)mie Fran'aise as also the foundation of the Acad)mie des Sciences, but others consider it began about 1664 as a series of meetings of scientists, notably Pascal, Descartes, Gassendi, Huygens and Mersenne. In 1666, Colbert invited them to meet in the Royal Library and their first meeting was on 22 Dec 1666. In 1669 they adopted the name Acad)mie Royale des Sciences and transferred to meeting in the Louvre. Colbert got HUYGENS to come as the founding Director, living in the building from 1666 to 1681. It was suppressed by the Convention on 21 Dec 1792 and its functions were vested in a branch of the Institut National. In 1816, the original name was readopted and the Institut was renamed the Institut de France. Arago, Bailly, Biot, Borel, Buffon, L. Carnot, Cauchy, Clairaut (elected at age 18), Condorcet, d'Ocagne, D'Alembert, Fourier, Lacroix, Lagrange, Lalande, Langevin, Laplace, Legendre, Lemonnier, Libri, Monge, Navier, Ozanam, Poinsot, Poisson, Prony were members. Monge & Carnot were expelled in 1816. Fontenelle was the first Secretary. Delambre was Permanent Secretary and was succeeded by Fourier in 18221830. Arago succeeded Fourier. Clairaut was elected at age 12 in 1725. Borel was President in 1934. Vaucanson was Inspector of Mechanical Inventions in the mid 18C. DARBOUX was perpetual secretary in the early 20C. The Acad)mie occasionally awards a gold medal "Henri Poincar)" in mathematics. The recipients have been: Hadamard (1962); Deligne (1974); J.G.Thompson (1992). It is presently at Place de l'Institut, 23 Quai de Conti, 6e see below. [Pengelley & Pengelley, p.128] say you can ask to look around it and there is a quantity of busts and portraits. In 1665, the first scientific journal (at least in a vernacular language), the Journal des s'avans was started. It soon became the organ of the Acad)mie Royale des Sciences. (The Philosophical Transactions also started in 1665, and seems to just precede this. The Accademia dei Lincei had a short lived journal sometime in the 17C. The Acad)mie formally began its own journal with the Histoire de l'Acad)mie Royale des Sciences in 1729, which summarised the proceedings from 1666.) At a joint meeting of the Acad)mie des Sciences and the Acad)mie des BeauxArts on 19 Aug 1839, Arago first presented Daguerre's photographic process, the first practical method. Within four months, thirty editions of Daguerre's booklet had appeared. Arago immediately made suggestions for applications to astronomy. [Darius, pp. 1011.] In the early 17C, nine lovers of literature established a regular meeting. In 1635, Richelieu organized them into an Acad)mie Libre or ACAD(MIE FRAN&AIS. [Hare(2), pp. 512513] says the idea was due to Chancellor S)guier. It met in the PalaisRoyal, though [ MGG ] says early meetings were across the road at 6 Rue de Valois, but this may then have been an outbuilding of the palace. Bachet and Pascal's father were founder members. [Culbertson & Randall (3), p. 105. Okey, p. 213.] Hare adds that after Richelieu's death in 1642, S)guier became President for 30 years and the Acad)mie met in the H=tel S)guier, which was in the Cour des Fermes, 1er, between Rue du Bouloi and Rue du Louvre, but was demolished after S)guier's death in 1672. Its main function has been to regulate the French language. In 1762, it regularized the spelling of some 5000 words, about a quarter of those in common use. Estre became +tre, roy became roi, etc. This Acad)mie suffered interruption and reorganization in 17931816, similar to the Acad)mie des Sciences. Fontenelle, Buffon, D'Alembert, Bailly, Voltaire, Laplace and Fourier were members. The third great academy is the Acad)mie des Inscriptions et BellesLettres, sometimes called the Petite Acad)mie, dating from 1663. Fontenelle and Bailly were the first two persons to be members of all three great academies [Arago, p. 156]. Since Napol)on's time, all the Acad)mies have been housed in the INSTITUT DE FRANCE, founded in 1795, at Place de l'Institut, 23 Quai de Conti, 6e, facing the Pont des Artes. The building was founded by Mazarin's will of 1661 as the College of the Four Nations, opened in 1688 but expropriated by the Convention in 1795 [Okey, p. 222] or 1790 [ MGG ]. The Institut has a famous statue of VOLTAIRE in the nude by Jean Baptiste Pigalle (eponym of Place Pigalle) [Cronin, p.246], but I have recently seen it (or a copy?) in the Louvre, qv below. There is another statue of Voltaire in the small Place Honore Champion, behind the Institut at the end of Rue de Seine. AVIATION has significant origins in Paris. The brothers Joseph (17401810) and Jacques (tienne (1745-1799) Montgolfier sent up three hot air balloons at Annonay, near Lyon, the last on 5 Jun 1783. They then travelled to Paris to build larger balloons. The Acad)mie des Sciences heard of this and decided to build their own balloon, but they didn't know how the Montgolfiers had obtained lift so they decided to use hydrogen, recently discovered by Cavendish. J.A.C. Charles was commissioned to create a hydrogen generator and the brothers Robert created a rubberised fabric. They launched an unmanned balloon from the Champs de Mars on 27 Aug 1783. Supposedly someone asked Benjamin Franklin what use this might be and he made the reply "And what use is a newborn baby?" Meanwhile, on 19 Sep the Montgolfiers sent up a sheep, a duck and a rooster and they later even sent up some people in tethered balloons, including the physicist Piltre de Rozier in Oct 1783, from the factory of R)veillon at 31 Rue de Montreuil, Faubourg St. Antoine, 11e. On 21 Nov 1783, they launched the first balloon flight, from the Chteau de la Muette in the Bois de Boulogne. There were two persons on board: the pilot, Piltre de Rozier and a passenger, the Marquis d'Arlandes. ([ MGG ] says they started from the adjacent Jardin Ranelagh, 16e, where the All)e PiltredeRozier commemorates the launch site.) They went for 25 minutes, covering five miles, and landed unharmed at La ButteauxCailles, 13e. On 1 Dec 1783 (1782??), Charles and one of the Roberts ascended from the Tuileries Gardens and travelled 27 miles to Nesle this balloon was the ancestor of all later gas balloons. [C. H. GibbsSmith; Aeronautics 1: Early Flying up to the Reims Meeting ; HMSO for Science Museum, 1966, items 1 & 2. MGG .] A late 18C account says they went about 20 miles and landed, but then Charles went up on his own, ascending 3052 yards and recording the pressure and temperature and came down some four or five miles further on. On 6 Sep 1804, GayLussac ascended at Paris to 23,400 ft and later made several longer ascents, taking samples of the air which proved to have the same composition at all heights. The BIBLIOTH.QUE NATIONALE, 58 Rue de Richelieu, 2e, was the palace of Mazarin, where his library of 35,000 volumes was open to scholars [Okey, p. 222]. The collections date back to Charles V in the 14C, whose collection was in La Tour de Louvre. In the 15C, these collections were moved to the Chteau d'Amboise, but came back to Paris in the 16C. A copyright act was made in 1537 requiring a copy of every printed book to be given to the library. It has one of the five (or two) known Roman hand abaci (cf British Museum in Section 2B). Stewart Culin [ Chess and playing cards. Catalogue of games and implements for divination exhibited by the United States National Museum in connection with the Department of Arch%ology and Paleontology of the University of Pennsylvania at the Cotton States and International Exposition, Atlanta, Georgia, 1895 . IN: Report of the U. S. National Museum, year ending June 30, 1896 . Government Printing Office, Washington, 1898, pp. 665942 [there is a reprint by Ayer Co., Salem, Mass., c1990], p. 863] says that the oldest European chessmen have been in the Biblioth/que Nationale since the Revolution. These are six ivory pieces, reputedly given to the Abbey of St. Denis by Charlemagne. The dress and ornaments on the pieces are 9C Greek. [I wonder if this is because they were a gift from Byzantium?] The library includes two Gutenberg Bibles, MSS by Pascal, Voltaire, Rousseau, Diderot, and the original plaster for Houdon's bust of Voltaire [cf Voltaire in Section 7A2]. [ MGG . Hare(2), p. 508.] The library has 10 to 12 million books. In 19881996, a new building, the Biblioth/que Fran'ois Mitterand, was erected near the Gare d'Austerlitz to house all the books. It was opened on 17 Dec 1996. The BIBLIOTH.QUE STE. GENEVI.VE, 10 Place du Panth)on, 5e, is a large library for students at the Sorbonne. The reading room is a fine example of late 19C ironwork. There are busts in the entrance hall, including Buffon, Descartes, L'Hopital, Laplace, Pascal, Voltaire. The BUREAU DES LONGITUDES was founded in 1795 to administer the observatories and coordinate astronomy. In 1803, the conservation of the metric standards was entrusted to it, so it is probably the ancestor of the BUREAU INTERNATIONAL DES POIDS ET MESURES, in the SW suburb of S.VRES, though I find the Bureau still exists at 3 Rue Mazarine, 6e. [ MGG ] says it is in the Breteuil Pavilion on All)e de Mail in Parc St. Cloud, near the S/vres factory, which is a bit N of S/vres. Though the standards of length and time are now determined atomically, the most precise measurements of mass still depend on comparative weighing based on the standard kilogram kept here. The Assembly ordered the Acad)mie des Sciences to standardize weights and measures on 8 May 1790. The Acad)mie appointed a Commission of Lagrange, Borda, Condorcet, Laplace and Tillet to compare the decimal and duodecimal systems. Another Commission, with Monge instead of Tillet, was to examine how to make a standard of length. The Commissions continued functioning through the Revolution. A law of 17 Apr 1795 formally established the metric system. 16 marble standard metres (m/tres )talons) were erected in the most frequented parts of Paris between Feb 1796 and Dec 1797. The only survivor in its original place is in a courtyard at 36 rue de Vaugirard, across from the gates of the Palais du Luxembourg, 6e. This is intact, with a large inscription METRE. It shows a metre on the marble, subdivided into decimetres and some centimetres. There are brass ends of the metre. There is a descriptive plaque beside it. The only other surviving example was moved to the facade of the Ministry of Justice, 11/13 Place Vend=me, 1er, in 1848. It is in a poor state one of the end marks has been broken off. [DBS. Baillie&Salmon, p.122.] Delambre and M)chain measured the meridian from Dunkirk (qv in Section 7B) to Barcelona (qv under Spain in Section 10), completing their work in 1799 and leading to the formal definition of the metre on 10 Dec 1799. In 1812, it was decreed that a hybrid 'systeme usuelle' could be used. The metric system became the only legal system on 1 Jan 1840. [Thanks to Norman Biggs for sorting this out for me.] The CAF( DE LA R(GENCE was a centre for chess players in the 1819C. BONAPARTE, D'ALEMBERT, DIDEROT, ROUSSEAU, VOLTAIRE were regular habitues. [Okey, pp. 426427] says its prominence stopped when it removed from the Place du Palais Royal in 1852, though the Caf) continues at 161Rue St. Honor), 1er. The CAF( PROCOPE, Boulevard Ste Germain, 6e, by the Od)on Metro station, was the resort of VOLTAIRE and the other intellectuals of the Age of Reason. The modern (1986) CIT( DES SCIENCES ET DE L'INDUSTRIE at La Villette (30 Ave. CorentinCariou, 19e) is perhaps the largest popular science museum in the world. As with most such museums, there is little actual historical material on display, but has lots of interactive exhibits. There are some computer based displays, but not so many as to be boring. It has a nice exhibition section on mathematics, with some quite sophisticated mathematics, e.g. triangulations of Delaunay and a rotating chamber (inertial merrygoround) which one can ride in and see the effects on trajectories of thrown balls, etc. There is a turbulent fountain which displays chaotic behaviour. It is one of the few places where I actually learned something from the computer terminal exhibits. There are also some videos of discussions with mathematicians including JeanPierre Kahane and Adrian Douady. I also saw a large Jacquard loom. The computing exhibition is also nice and has a nice video on the Whirlwind and SAGE projects which led to the development of core memory. The section on light games has some nice perspective rooms. WARNING the Museum is vast and the exhibit on any one subject can occupy one for several hours; allow a long day or several short days to see it thoroughly. There is a Mini Guide available is several languages, but some exhibits have changed since it appeared. There is a spherical cinema, called La G)ode, nearby. The Metro station of CLUNYSORBONNE (corner of Boulevard St. Michel and Boulevard St. Germain, 5e) has its roof decorated with mosaic facsimiles of the signatures of noted Parisians, including Bachelard, Bergson, Champollion, Marie Curie, Descartes, Gay Lussac, Pascal, Poincare (given without the accent), Rousseau, Voltaire. The COLL.GE ROYAL (des Trois Langues) was founded by Fran'ois I in 1529 or 1530 as an antithesis or antagonist to the narrow scholasticism of the University (= Sorbonne). [Okey, p. 163] says this was an institutionalization of a number of schools or masters which had started teaching Greek. ERASMUS was offered the Directorship in 1517, but declined. The idea was repromoted by the king's confessor, Guillaume Parvi, and Guillaume Bud), who became the first director in 1530. Initially there were 12 professors, including mathematics and philosophy, who gave free lectures. Construction of a building did not start until 1610 and was completed in 1842. [Okey, pp. 163164.] [Pengelley & Pengelley, p.116] say that the Coll/ge was founded in its present form by Louis XV in 1732. It is now the COLL.GE DE FRANCE at 11 Place M. Bertholet, 5e, in the Rue des (coles, beside the Sorbonne. There were 28 professors, c1887 [Hare (2), p. 366]. It is independent of the University, with 50 Professors who still deliver free lectures. There are no classes and the Coll/ge gives no degrees. AMP.RE, BERGSON, BERTHOLET, BIOT, CAUCHY, CHAMPOLLION, Oronce FINE (= Orontius Finaeus) (from 1532), FORCADEL, FOURIER(?), GASSENDI, HADAMARD, JOLIOTCURIE, LACROIX, LEBESGUE, LIOUVILLE (during 1851-1882), PERRIN, POISSON(?), Petrus RAMUS (1515-1572, author of a popular arithmetic in 1555 and a logic which displaced Aristotle), ROBERVAL were here. CHAMPOLLION was a student and later was Professor of Archaeology in 18301832. DIRICHLET was a student. Camille JORDAN (18381922) taught here. Szolem MANDELBROJT (18991983) was professor from 1938. SERRE was here from 1956. In the courtyard were lists of all the Professors from the foundation to the present, and a statue of Bud). [Cronin, p. 92.] However, when I visited in 2002, the lists and the statue of Bud) were gone and there was a statue of Champollion. (Perhaps the missing items are in another courtyard??) Fr)d)ric JoliotCurie was here and built a cyclotron to test his theory of nuclear fission in 1948 [ MGG ]. The CONCIERGERIE is part of the Palais de la Cit) and is generally visited jointly with the Sainte-Chapelle. It is notorious as the place where the condemned of the Revolution, especially the Terror, were kept for trial and then taken out for execution. The historical placards include pictures of BAILLY and LAVOISIER who were victims. There is a large list of the victims of the Terror in 17921793 which has an entry for Bailli (sic) but doesn't include Lavoisier or any of the other mathematical victims who were killed at later dates. The Guardroom on the lower floor has a central pillar whose capital includes a carving thought to be AB(LARD and Heloise. See also Tour de l'Horologe, which is the NE corner of the building. The CONSERVATOIRE NATIONAL DES ARTS ET M(TIERS, 292 Rue Saint Martin, 3e, contains the MUS(E NATIONAL DE TECHNIQUES (apparently now called the Mus)e du Conservatoire National des Arts et M)tiers). This is the oldest technical museum in the world, created by the Convention in 1794 and installed in 1799. It was founded on the initiative of Abbot Gr)goire. It occupies the buildings of the priory of St. Martin des Champs, founded in 1060. It is the best preserved monastic establishment in Paris, with some of the 11C building preserved. The library occupies the former refectory, built in the 13C, with its pulpit intact. [Hare (2), pp.136-138.] Jacques de VAUCANSON (17091782) left his extensive collections to the King in 1783 and this led to the formation of the Conservatoire and Mus)e. [Danilov, pp. 14 & 16.] There are busts of Painlev)(?) and Coulomb on the facade and a statue of Papin to the side. DUPIN was professor of Mechanics here from 1819. The whole museum was being extensively restored in 19921997 and many exhibits were closed. Also they are building a depot at St. Denis and much of the material may go there. Rue Vaucanson is just to the east of the site. It contains an early version of FOUCAULT's pendulum and the later version used by Flammarion (see under the Panth)on, below), PASCAL's first adding machine, LAVOISIER's laboratory (including his balances, thermometers, etc.), an early VOLTAic pile, instruments belonging to the physicist CHARLES, the transmitting station from the Eiffel Tower, cameras of Niepce, Daguerre and Edison, the magic lantern of the Lumi/re brothers, astrolabes, clocks, microscopes, and other instruments, etc., etc. The ball of Foucault's 1851 pendulum is preserved here and the 1855 support and drive mechanism is in daily use [photos in Foiret et al., pp. 9 & 18 and colour plates 5 & 6]. SYLVESTER suggested and Foucault created a mechanism to show how the pendulum behaves at different latitudes and this is here, having been presented by Foucault's widow [Foiret et al., pp. 2324 & colour plate 7]. POINSOT suggested and Foucault created the gyroscope, which also demonstrates the rotation of the earth an 1851 version is here [Foiret et al., pp. 811 & 27]. (However, J. G. D. Bohnenberger described such a device for demonstrating precession in 1817, but he may not have realised that it showed the rotation of the earth [Henk J. M. Bos; Descriptive Catalogue Mechanical Instruments in the Utrecht University Museum ; Utrecht University Museum, 1968, p. 59]. A version of Vaucanson's famous automaton duck, which even ate and excreted, is supposed to be here, though it is unclear if this is the original of 1738 [Reichardt, p. 13, with photo; drawing in Hillier, p. 45]. However, it wasn't there when I visited in 1992. [Hillier, p. 46] says its whereabouts is unknown, though other makers made similar ducks, and that the Conservatoire has none of Vaucanson's automata. Vaucanson also made a flute player and a pipe and tabor player all these were exhibited in 1738. [Byard, plate 7] is a 1738 illustration of the three on exhibition. [Byard, p. 67] says they no longer exist and their fate is uncertain. [ MGG ] says that Marie Antoinette's dulcimer playing puppet of 1784 is here. The historic automata of RobertHoudin were acquired by Georges Melies, the cinema pioneer, and given to the Conservatoire in the 1920s. Due to neglect, they were stored in an attic which collapsed during a heavy rain and were all destroyed. [Hillier, p. 69.] [ MGG France ] says it has MarieAntoinette's automaton Dulcimer Player. I have seen a picture of a 1750 Vaucanson loom with instructions on a perforated cylinder, which is currently here. The Mus)e also has an early JACQUARD loom. I believe the Mus)e also has the earliest FALCON loom, etc.(??) VANDERMONDE was a Director. The Mus)e has two original examples of the Tower of Hanoi presented and inscribed by LUCAS in 1888. This is the only place where he is known to have definitely acknowledged his invention of the Tower of Hanoi. A. SAINTLAGU,, who wrote several recreational mathematics books including an early book on graph theory, was Professor here around 1927. A few nonmathematical items in the Mus)e are: Cugnot's 1771 steam carriage; Thimonnier's 1825 sewing machine; the Lumi/re brothers cinema apparatus of 1895; the airplane that Bleriot flew on the first crossChannel flight. The short-lived first (COLE NORMALE (SUP(RIEURE) had lectures in the Amphitheatre of the Jardin des Plantes, 5e. This is shown in the Open University program Paris and the New Mathematics, part of the course on History of Mathematics. The (cole was formed early in the Revolution, c1794, to provide teachers for the schools all the teachers having gone into the army. Here LAPLACE, LAGRANGE, LEGENDRE(?), MONGE, LACROIX, etc. would lecture to 1200 students (Arago [p. 386] says 1500) and the idea of its successor, the (COLE POLYTECHNIQUE, was formed. Monge is generally credited with being the principal founder of both (coles. FOURIER was a student about 1794. It was here that Monge first publicly lectured on his descriptive geometry in the Year 3 (1795) the lectures were edited by J. N. HACHETTE and published as a book in 1799 while Monge was in Egypt. Lagrange lectured from 1795. The (cole Normale constituted a revolution in teaching the foremost researchers were appointed to lecture (previously research and teaching were separate) and they were required to lecture more or less extemporaneously i.e. they were not to recite written lectures. Shorthand writers made transcripts of the lectures, which were distributed to all the students (and have recently been republished!). Napol)on even attended lectures here. [Arago, pp. 386391]. The (cole Normale was closed in 1822, but it was reopened as the PREPARATORY SCHOOL in 1826, where GALOIS was a student in 1830 (or 1829) until he was expelled in the following year. BONNET taught here. PASTEUR was a student of chemistry in 18431848 and began the studies of crystals that led to his discovery of stereoisomerism. He received a doctorate in crystallography in 1847. He returned as Director of Scientific Studies in 18571867. [Wymer, p. 2:7, 10, 15.] HERMITE was Professor at the later (COLE NORMALE (SUP(RIEURE) in c1867. LUCAS was a student in 18611864. PAINLEV( was a student, getting his doctorate in 1887. Jules TANNERY (18481910) was Deputy Director in charge of science from 1884 to 1901. (Jean) Gaston DARBOUX (18421917 (or 1912?)) was a student and taught here, attracting BOREL as a student in 18891893. (lie CARTAN entered in 1888. Borel returned in 1897 and remained for the rest of his life. In 1910, he succeeded TANNERY as Deputy Director in charge of science, and the Borels then lived in the (cole. BAIRE was a student in 18921895. GOURSAT taught here from 1885. LEBESGUE was a student in 18941899. PICARD and APPELL were teachers in the late 19C. CHEVALLEY, WEIL (19221925, [Cartan] says he read Riemann and did all his examinations in his first year, thesis in 1928), H. CARTAN (19231926, thesis in 1928), DELSARTE (entered 1922), van HEIJENOORT, PAD( were students. H. CARTAN was professor. FR(CHET was here in the 1930s. The (cole has been at 45 Rue d'Ulm, 5e, south of the Panth)on, from 1847, but has expanded its building and parts have since moved out of Paris. For years, it was the most elite college in France, admitting only 55 students per year. In the courtyard are busts of Amp/re, Descartes, GayLussac, Lavoisier, Voltaire, etc. On the right is the building where Pasteur worked and is now the school's infirmary. The room where he carried out the experiments that disproved spontaneous generation is now a cupboard for children's toys, with a plaque outside it. [Pengelley & Pengelley, pp.119120.] The (COLE POLYTECHNIQUE, founded in the Year 3 (1794/1795), continuation of the (cole Normale, originally named the (cole Centrale des Travaux Publics, moved in 1805 to a site on the Place Monge, a bit to the east of the University quarter indeed it was on the site of the 14C College of Navarre. It has now removed to the suburb of Palaiseau and the square is now the Square Langevin, 5e, and the name Place Monge has been moved south on the Rue Monge. A large back gate with the name faces onto the minisquare where Rue Descartes and Rue de l'(cole Polytechnique meet Rue de la Montagne SteGenevi/ve; there are busts of Lagrange, Laplace and, probably, Monge (the name has worn away leaving only the final e). In the minisquare is a cafe/restaurant named 'La M)thode', probably the only restaurant anywhere named for a mathematics book. At 1 rue de l'(cole Polytechnique is another restaurant named 'Bar de l'X', probably the only restaurant anywhere named for an algebraic symbol! (Both restaurants are good.) The building is now the Ministry of Research and Technology; one can go into the garden but I saw nothing of mathematical interest in it. MONGE was a main founder of the (cole and a professor from 1795. LAPLACE, LAGRANGE, LEGENDRE, FOURIER, CARNOT, VANDERMONDE, etc. were professors. Lagrange began lecturing in 1797. LACROIX assisted Monge. POINSOT was a student in the first class, 17941797. GAYLUSSAC was a student from 1797 and later was a teacher. G. PLANA was a student in 18001803. ARAGO was a student from 1803 and succeeded Monge in 1809 until 1830. CAUCHY was a student in 1805-1807 and a professor in 1815-1830. AMP.RE was professor of mathematics from 1809. NAVIER, CORIOLIS, MANNHEIM were professors. DUPIN was a student. LIOUVILLE was a student in 1825-1827. He was a r)p)titeur in 1831-1838 and Professor of Analysis in 1838-1851. [Stander.] He founded his Journal de Math)matiques pures et appliqu)es in 1836. He discovered transcendental numbers in 1844. STURM was here in the same period. COMTE was a student and a teacher. Gaspard De PRONY (17551839) was the first Professor of Analysis, 1794-1815. POISSON was a student, then assistant professor in 1802 and succeeded Fourier in 1806, when he was 25. GALOIS was rejected twice, c1829 supposedly he threw a blackboard eraser at an examiner for asking a simple question. Sylvestre Fran'ois LACROIX (17651843) succeeded Lagrange. POINSOT was Professor of Analysis and Mechanics in 1809-1816, but another source says he was the first such professor in 18161825. NAVIER was Professor of Analysis and Mechanics from 1819. CHASLES taught geodesy, astronomy and applied mathematics here in 18411851. HERMITE was a student for one year in c1840 but was sent away because his lame leg made him unfit for military service. He was later a lecturer from c1862. [Stander (2).] BONNET taught here. PONCELET was Commandant in 1848-1850. Camille JORDAN (18381922) studied engineering here, learning mathematics in his spare time. He taught here in 18731912. Paul TANNERY (c18431904) was a student. BECQUEREL was a student and then Professor of Physics from 1895. Matthieu Paul Hermann LAURENT (18411908) was here. GOURSAT taught here from 1885. HADAMARD was a professor. Philbert Maurice D'OCAGNE (1862-1938) was Professor of Geometry. Paul L(VY (18861971) was Professor of Analysis in 1920-1959. Gaston (Maurice) JULIA (18931978) was a professor. MANDELBROT was a student. The (cole was the model for most later technical schools, particularly in the USA e.g. West Point, MIT. The (COLE NATIONALE DES PONTS ET CHAUSS(ES is at 28 Rue des SaintsP/res, 7e. The Corps des Ponts et Chauss)es was established in 1716. The (cole was founded in 1747 it was the world's first engineering school. Claude Louis Marie Henri NAVIER (17851836) was a student and later a professor. CAUCHY was a student in 1807-1809. LIOUVILLE was a student in 1827-1831. Gaspard De PRONY (17551839) was Director from 1799 until his death. The (COLE SUP(RIEURE DE PHYSIQUE ET DE CHIMIE INDUSTRIELLES DE LA VILLE DE PARIS was at 10 Rue Vauquelin, 5e, adjacent to the (cole Normale Sup)rieure. Pierre CURIE was a Professor here when Marie Sklodovska came in 1894, seeking a doctoral project. They were married in 1895. It was in a vanished shed in the courtyard that Marie and Pierre CURIE processed several tons of material to obtain samples of radium and polonium [photo in Wymer, p.6:22]. [ MGG France ] says the outline of the shed is shown in the paving pattern of the courtyard of the School. She received her doctorate and they received the Nobel Prize in Physics, shared with Becquerel, in 1903. The Institut Curie was built for her in 1914 at 26 Rue d'Ulm, 5e, (apparently now entered from 11 Rue PierreetMarieCurie), near the (cole Normale Sup)rieure. (My 1986 MGG shows the Institut de Radium also on the Rue d'Ulm, but my 1991 map shows the site as part of the (cole Nationale Sup)rieure de Chimie.) [Pengelley & Pengelley, pp. 120122] say little of the old school survives except the original portico and there is a plaque outside commemorating the discovery. Outside the Director's office is a case with some of the Curies' apparatus and notes you have to ask to see this. The EIFFEL TOWER, 7e, was built in 26 months and opened in Mar 1889 for the Universal Exposition. it is 320.75 m (1051 ft) high and only weighs 7000 tons less than the air around it! In LES HALLES, 1er, the Bourse du Commerce is on the site of the H=tel de Soissons, built by Queen Catherine de Medicis in the late 16C. She had an observatory here and an astrologer. [Hare (2), pp. 113114; MGG ] say the only surviving part is a 30 m high fluted column erected for the observatory in 1572 and now attached to the side wall south of the Bourse. Hare says it bears a sundial, but I didn't notice it on a recent visit. The H<TEL DE VILLE (= City Hall), 4e, includes many allegorical paintings e.g. 'Meteorology' and 'Electricity' perhaps there is some Mathematics?? [Cronin, p. 204]. Institut de France see under Acad)mie Fran'ais, above. The INSTITUT DU MONDE ARABE, 1 rue des Foss)sSaintBernard, 5e, has a museum and an active program of exhibitions. A 1995 guide shows an astrolabe and says the Museum owns one of the oldest examples. The INSTITUT HENRI POINCAR( was founded by BOREL in 1927. He served as Director or Joint Director until his death in 1956. Prince LouisVictor de BROGLIE was here and at the Sorbonne when he received the Nobel Prize in Physics in 1929 for his discovery that matter had wave properties. FR(CHET was here in the 1930s. MANDELBROT taught here. It is part of the (cole Pratique des Hautes (tudes, 11 Rue PierreetMarie Curie, 5e. Institut Pasteur see under Pasteur in Section 7A2. The JARDIN DES PLANTES, 5e, was essentially a herb and exotic plant garden, then called Le Jardin Royal, until George Louis Leclerc BUFFON was appointed director in 1739. He laid out the gardens from 1739, which include a pleasant labyrinth around a hill. and turned the institution into one of the great botanical and natural history research establishments. There is a monument or plaque to Buffon near the corner of Rue Buffon and Rue Geoffroy Saint Hilaire. In the Jardin are also the Amphitheatre see under (cole Normale, above and Buffon's house cf Section 7A2. Also in the Jardin is the Mus)e National d'Histoire Naturelle, where BECQUEREL was born and worked his father was a professor of physics here. A plaque on the building in rue Cuvier records that it was here that Becquerel discovered radioactivity (a term later coined by Marie Curie) on 1 March 1896. The LEFT BANK area around the universities and polytechnics, mostly in the 5e, has a number of streets and squares named for mathematicians and related scientists: ARAGO, Pierre et Marie CURIE, DESCARTES, GAYLUSSAC, LAGRANGE, LANGEVIN, LAPLACE, LEVERRIER, MONGE and PASCAL [Alexanderson]. Elsewhere (not always on the Left Bank) are streets named for: AMP.RE, BAILLY, BIOT, Maurice et Louis de BROGLIE, CASSINI, CAUCHY, CHAMPOLLION, CLAIRAUT, CONDORCET, D'ALEMBERT, DELAMBRE, D'OCAGNE, DUPIN, ERASMUS, EULER, FERMAT, FOUCAULT, FRESNEL, GASSENDI, HUYGENS, LACROIX, LALANDE, LEGENDRE, LEIBNIZ, M(CHAIN, NEWTON, OZANAM, PAINLEV(, POINSOT, ROBERVAL, ROUSSEAU [Alexanderson; Michelin map of Paris; Hare (2)]. I had remembered seeing a park or square named for PERRIN, but it was not in the index of my map. However, in 1998, I relocated it it is the space in front of the Champs (lys)es entrance of the Grand Palais, actually on the Ave. du General Eisenhower, 8e, and it is labelled in small print on my map. There is a bas relief monument to Perrin on the south side. On the Right Bank, near the Louvre, are a Place and a Rue des Pyramides, as well as a Pyramides Metro station, all 1er, but these are named for the Napoleonic Battle of the Pyramids, rather than from any geometric reason [Hare, p.8]. LAGRANGE, BERTHOLET, LAPLACE and MONGE were early members of the LEGION OF HONOUR in 1803. Lagrange was made a Grand officer in 1804. There is a Museum of the Legion of Honour at 2 Rue de Bellechasse, 7e, by the Mus)e d'Orsay, but I don't know if it has anything of interest. The MUS(E DU LOUVRE, 1er, has a modern monumental entrance through a glass pyramid designed by I. M. Pei. It contains some of LEONARDO DA VINCI's most famous works. One of Paolo UCCELLO's panels of 'The Battle of San Romano', displaying his mastery of perspective, is here (the others are in the National Gallery, London (Section 2B) and the Uffizi Gallery, Florence (Section 9A2)). Holbein's 1528 portrait of Nicolas KRATZER showing him constructing a dial and with numerous mathematical instruments is here, as is Holbein's portrait of ERASMUS. DFRER's self portrait at age 22 is here. The Richelieu wing was reorganized in 1997 and many items have been relocated. Area 29 of French Sculptures has become a Salle des Grandes Hommes and contains statues of a number of scientists. There is a version of the famous Houdon bust of VOLTAIRE [cf Voltaire in Section 7A2] as well as a Houdon statue of him (if I read my notes correctly). There are also a Houdon bust of ROUSSEAU and his terra cotta models for the busts of DIDEROT and FRANKLIN. These are very familiar images as Houdon made many replicas of his works to avoid starvation during the Revolution [Okey, p. 348]. The statue of Voltaire nude, by Jean Baptiste Pigalle (eponym of Place Pigalle), is here, though he is tactfully draped with a 'philosopher's sash'. (This was in the Institut de France, qv above, or they have another version.) The series of Grandes Hommes includes PASCAL and D'ALEMBERT. There are other busts or portraits of ARAGO and DESCARTES (attributed to Hals or Bourdon [Hare, p.49]). There is a sculpture of Geometry by Legros [Hare(2), p. 97] I recently saw a (different??) sculpture of Geometry in the hall of 1619C Italian Sculptures. There are tombs of a Roberte Legendre and her husband Louis Poncher, from 1522, in the Louvre [Okey, p. 343; Hare (2), p. 94], but I don't know if there is any connection with the mathematician. Room 6 of the Arts of Islam has some astrolabes, a proportional compass and several celestial spheres, including ones from 1145 and 1285. Rooms 1113 have some wonderful Iznik pottery. Room 23 has a game box from c1500 with boards for chess, m)relles (ninemen's morris), fox and hens, glic(?) and backgammon. there are also chessmen and backgammon pieces from 11C to 16C and a bone cubooctahedral die from the early 11C. In the Assyrian Art galleries are some of the colossal winged bulls and one of these has a Royal Game of Ur board scratched on the base cf British Museum in Section 2B. The LYC(E CHARLEMAGNE is on Rue Charlemagne, 4e, near the Metro stop St. Paul. BURDON and LUCAS taught here in 18761879 and 18901891. The LYC(E HENRI IV is just east of the Panth)on, 5e, comprising much of the abbey of Ste. Genevi/ve. It was also called the Lyc)e Napol)on (or Bonaparte) for a while and is sometimes called a coll/ge. Zerah COLBURN was a student briefly in c1815. BOURDON was a professor here. Louis POINSOT (17771859) was professor here from 1819, but another source says he was here until 1816. The LYC(E LOUIS LE GRAND, Rue Cujas, 5e, between the Sorbonne and the Panth)on, was supported by Louis XIV. It was originally the College of Clermont. It was a school run by the Jesuits for many years. In the 1718C, it was the leading college of the university. After the expulsion of the Jesuits in 1763, it became the seat of the university and the main college, with 26 small colleges being suppressed and only ten left. VOLTAIRE was a student from 1704. During the Revolution, it was used as a prison, then became the Lyc)e Imperiale before reverting to its earlier name. In later years, GALOIS and BOREL were students. Some of the original buildings survive. [Cronin, p. 103. Okey, pp. 105106. Hare (2), pp. 365366.] The MUS(E DE CLUNY (= Mus)e National du Moyen Age, 8 Place Paul Painlev), 5e) is a wonderful museum of medieval material, containing the six justly famous tapestries of the Lady and the Unicorn. It is an unlikely place to find mathematics, but there is handsome sundial dated 1674 on the side of the staircase tower in the courtyard and a simpler sundial a bit to the right. In room X is a 15C card from some sort of educational game (I don't know of any earlier European example of an extant card). Also in Room X, at the staircase, is a tapestry of Arithmetic, from a series of the Liberal Arts, made c1520. Several people are standing around a table doing accounts, both with counters and in writing. In Room 20, the Chapel, dating from c1500, is a fine carved example of the three rabbits pattern. In Room 22 is a stained glass window of c1435 showing two people playing chess. The Mus)e National d'Histoire Naturelle is located in the Jardin des Plantes, qv. Mus)e Pasteur see under Pasteur in Section 7A2. The Cathedral Square (the Place du Parvis) in front of NOTREDAME, 4e, is the zero point for distances from Paris there is a bronze star marking the centre of Paris, from which all road distances are measured. The Cloister of Notre Dame, on the north side of the church, was the earliest academic area in Paris, where Anselm debated Roscelin and Ab)lard (qv in Section 7A2) debated St. Bernard. Nothing remains except some street names: Rue du Clo3tre Notre Dame, Rue des Chanoinesses, Rue des Chantres. [Hare(2), p. 314.] See also the University, below. The church of Saint Jean-le-Rond, where d'Alembert was abandoned, was the baptistery of NotreDame, against the north tower at the end of Rue du Clo3tre Notre Dame, and was destroyed in 1748. Under the figure of Christ on the central pillar of the centre portal are basreliefs of the seven liberal arts arithmetic, geometry and astronomy are among these. The portal of the Virgin under the north tower includes reliefs of the zodiac and the seasons. During the Revolution, it was proposed to destroy the superstitious images on the west doors, but it was argued that they were images relating to astronomy, philosophy and the arts. The astronomer Dupuis was asked to advise and the carvings were reprieved. [Okey, p. 299]. Several persons of mathematical interest have been connected with the Paris OBSERVATORY, 61 Ave. de l'Observatoire, 14e, to the south of the Luxembourg Gardens. Colbert persuaded Louis XIV to establish this in 1667 and then got CASSINI to become first Director, making it the second national observatory the one in Copenhagen opened in 1637 but later burnt down [P. Moore (4), p. 15]. It was built in 16671672 to designs of Claude Perrault (brother of the collector of fairy tales, he was also designer of part of the Louvre and died from a disease contracted while dissecting a camel! [Cronin, pp. 183 & 226227]). While awaiting the completion of the building, Louis installed Cassini in a tower of the Chteau of StGermainenLaye [ MGG ], west of Paris. Unfortunately, the construction of the Observatory was designed for appearance rather than use and Cassini found that its turret restricted observing so much that he set up his telescopes in the garden [P. Moore (4), p. 16]. The Observatory occupies over a third of the former Luxembourg Gardens and [Okey, p. 322] laments this loss about 250 years afterward! The building contains no iron, in order to avoid deflecting compasses. Four CASSINIs, ARAGO and LEVERRIER (or Le Verrier or LeVerrier) were directors. Giovanni (or Gian) Domenico (= Jean Dominique) Cassini (16251712) came to Paris as the first Director in 1667. He discovered four moons of Saturn in 16711684 and, in 1675, the division in the rings of Saturn named for him. He proposed the 'ovals of Cassini' as alternatives to Kepler's ellipses. He made the first reasonable calculation of the distance from the earth to the sun, getting, getting 86,000,000 miles (s140,000,000km) [P. Moore (4), p. 25]. Died at the Observatory. Olaus ROEMER (or Ole R?mer) (16441710) was Cassini's assistant and first determined the speed of light here in 1675, by observing differences in times for the moons of Jupiter depending on whether the earth was near or far from Jupiter, getting about 3.2x108Ġm/sec. (However, another source says he didn't compute the speed, merely noted that there was a difference, which showed that light had a finite speed. Others did the calculation, using various values for the distance of the earth from the sun and obtained results ranging from 2.6to5.6x108 m/sec, all of which are attributed to Roemer. [Sobel, pp. 2930] says he calculated the speed in 1676 and got a slight underestimate. [Don Glass, ed.; Why You Can Never Get to the End of the Rainbow and Other Moments of Science ; Indiana Univ Press, Bloomington, Indiana, 1993, p. 102] says Roemer announced his results to the Acad)mie des Sciences in Sep 1676, correctly predicting the eclipse of Io on 9 Nov would be 10minutes late and says Roemer got a speed of light about 2.3 x 108 m/sec.) In 1669, Jean Picard (16201682) surveyed a degree of the meridian near Paris (but cf Maupertuis in Section 7A2). This result was so successful that it influenced Newton and led to a project of accurately mapping the coast of France. This was done in 1681 with La Hire and Picard making measurements at French ports while Cassini made corresponding measurements at Paris. The resulting map was presented to Louis XIV in 1682, when Louis is said to have remarked that the astronomers had reduced his kingdom more than his wars had, and published in 1693. An annual almanac or ephemeris was started in 1679, nearly a century before the English version, with Picard as first editor. In 1671, Jean RICHER went to Cayenne, French Guiana (now Guyane), 5o north of the equator, while Cassini (I) remained in Paris they made simultaneous observations and determined the parallax of Mars and hence the size of the solar system was first determined to reasonable accuracy. They got 86,000,000 miles for the distance from the sun to the earth. Jacques Cassini (16771756), son of the above Cassini, was born at the Observatory and succeeded his father as Director in 1712. In 1697, he travelled to England and determined the relative longitude of Greenwich, by use of the moons of Jupiter, finding it 9' 10" of time west of Paris in 1902, the value was found to be 9'20.974" of time = 2o 20.2435' of angle, but see below [D)barbat]. In 1713, he carried out the measurement along the meridian from Dunkerque to Perpignan. He started the map of France, continued by his son. He died at Thury, near Clermont. C)sar Fran'ois Cassini de Thury (17141784), son of the above, was born at the Observatory and succeeded his father, but due to administrative changes, he did not become Director until 1771. His principal work was a 1:870,000 map of France in 18 sheets and a 1:86,4000 map in 182 sheets. In 1784, he suggested linking the surveys of France and England. Died at Thury. Count Jacques (or Jean??) Dominique Cassini (17481845), son of the above, was born at the Observatory and succeeded his father as Director in 1784, but withdrew to Thury in 1794. He directed the French side of the survey linking France and England, using a circle designed by Borda and built by Lenoir. Cassini used two different models for the shape of the earth and obtained 9' 18.6" and 9' 20.6", but felt the first value was more correct. Roy, on the English side, obtained 9' 18.8". In 1987, the Ordnance Survey and the Paris Observatory commemorated the bicentenary of this measurement by redoing it using special GPS (Global Positioning System) equipment. The results were accurate to few centimetres, but my source doesn't state the value. [D)barbat.] LALANDE was Director from 1768 until his death in 1807. LAPLACE was also a director. ARAGO was Laplace's assistant from 1806 and then was co-worker with BIOT [Arago, pp. 1415 & 18] and later Director. In 1825, Arago, Mathieu and Kater determined the distance between Paris and Greenwich as 9' 21.62" of time. There is a monument to Arago on the Meridian just across Boulevard Arago at the southern end of the Observatory grounds. There are statues to LAPLACE and LEVERRIER (in front of the building) and a plaque to Roemer on the front of the building. FOUCAULT was physicist here (see also under the PANTH(ON, below, and under Foucault in Section 7A2). LUCAS was an assistant to LeVerrier in c18641870. Pierre FATOU worked here from about 1906. In 1902, Christie, Dyson and others, working with Loewy, the Director of the Paris Observatory and using telegraphic links, determined the distance between Greenwich and Paris as 9' 20.932" and 9' 20.994  .013 " with the variability due to the personal equations of the observers. The meridian of Paris passes through the building, being officially fixed on 21 Jun 1667 (the summer solstice of that year). There is a large South Bearing between the Boulevard Jourdan and the Avenue de la Tunisie in the Parc Montsouris, 14e, near the RER station Cit) Universitaire. A North Bearing of 1736 is on Montmartre near to the Moulin de la Galette [ MGG ]. France refused to adopt the 1884 treaty fixing the Prime Meridian at Greenwich until 1911. To commemorate the Millennium, a large number of medallions bearing the name ARAGO, with a N and S arrow, were installed along the meridian across France. They are not large, perhaps 10cm in diameter, set into the sidewalk (= pavement (UK)) and not very conspicuous. There is one behind the Luxembourg Palace, close to the sentry at the west side of the palace, clearly showing that the great vista through the gardens to the Observatory is not quite directly south. Another is in front of the palace, on the south side of Rue de Vaugirard, between Rue Garanci/re and Rue de Tournon. Another is at the entrance to the Louvre from the Place du Palais Royal. The Observatory has contained the International Time Bureau since its founding in 1919. This supervises Coordinated Universal Time (UTC). The Observatory started the first speaking clock service on 14 Feb 1933. There is a small museum which has occasional tours (first Saturday of each month at 2:30 you must write to the Director in advance at 61 Ave. de l'Observatoire, F-75014, Paris) [Baillie&Salmon, p.138] say "Visiting the Observatoire is a complicated procedure and all you'll see are old maps and instruments." [ MGG ] says there is "a small museum of old instruments, modern equipment in the park and dome of the upper terrace." The gardens are open, but not in the winter. Rue Cassini is just north of the building and there are a Avenue de l'Observatoire and a Fontaine de l'Observatoire nearby, while Boulevard Arago is to the south. An unusual political application of mathematics occurred in 1904 when the three mathematicians APPELL, DARBOUX and POINCAR( were appointed to study the authenticity of the memorandum (the 'Bordereau') which had led to DREYFUS' conviction as a traitor in 1894. The 'macromicrom/tre' of the Observatory, an instrument for measuring astronomical plates, was used to make a large number of measurements, which were carried out by various members of the staff of the Observatory. The mathematicians' report demonstrated that Bertillon's reassembly of the pieces of the memorandum was incorrect and his statistical deductions from it were unjustified. The memorandum was declared a forgery in 1906 and Dreyfus was rehabilitated. See [Suzanne D)barbat; An unusual use of an astronomical instrument: The Dreyfus affair and the Paris 'macromicrom/tre'; J.for the History of Astronomy 27 (1996) 45-52], though this is not very clear how the measurements were used. The PALAIS DE LA D(COUVERTE, Ave. Franklin Roosevelt, 8e, is located in part of the Grand Palais. It was established by Jean PERRIN in 1937 to present science to the public. It is one of the ancestors of the modern 'handson' science centres rather than a museum in the classical sense. There is a plaque, with basrelief, commemorating Perrin, on the west side of the little Square Jean Perrin which lies on the north side of the Palais but which is now used as the forecourt to the Porte Champs (lys)es of the Grand Palais. The Palais has fine demonstration of turning a sphere inside out by means of a sequence of models following Bernard MORIN's method. The PANTH(ON, Place du Panth)on, 5e, was originally intended as a new Church of Ste. Genevi/ve and has alternated several times between church and monument see [Cronin, pp. 104105; Okey, pp. 254255; Hare(2), pp. 359362]. The bones of VOLTAIRE and ROUSSEAU were brought here to initiate the Panth)on on 11 Jul 1791 and 11 Oct 1794, respectively. However, little of them may be here as the tombs were opened by fanatics in 1814. Voltaire's heart (cf Ferney, outside Geneva, Switzerland in Section 10), brain, one foot and two teeth were taken as relics at various times. [Ayer. Culbertson & Randall (3), pp. 9397.] [Dave Dutton; Horrors ; Futura, London, 1989, pp. 4041] says that in 1814 Voltaire's corpse was taken to a refuse dump and buried in quicklime. However, their presence has survived while many of the revolutionary heroes placed here were soon displaced Mirabeau lasted less that two years and Marat lasted about five months and some were replaced before they even got here! BERTHOLET, DE BOUGAINVILLE (the navigator/explorer, though [Hare(2), p.488] says the tomb of De Bougainville is in Montmartre Cemetery, but he was in the cemetery of St. Pierre, on the top of Montmartre, just west of Sacr) Coeur (only open on 1 Nov) and his heart remains there), L.N.M.CARNOT, M. F. S. CARNOT, CONDORCET, LAGRANGE, LANGEVIN, MONGE, PAINLEV(, PERRIN, Braille, Dumas (brought in 2002), Hugo, Malraux, Marat, Mirabeau, Zola are all here. DESCARTES (qv in Section 7A2) was brought to Ste. Genevi/ve in 1665, but was moved during the Revolution [Eves (4), p. 15; Scott, p. 6]. There is a statue of Voltaire by Houdon in front of his tomb in the crypt [Hare(2), p.361; DBS]. On the main floor of the Panth)on, there are some commemorative inscriptions on the pillars, including one to BERGSON. [Pierre Chevallier & Daniel Rabreau; Le Panth)on ; English translation by Kathleen Wilson Chevalier [sic]; Caisse nationale des Monuments et des Sites, 1977. DBS. MGG .] FOUCAULT (qv in Section 7A2) set up his pendulum here in Mar 1851 at the urging of President Louis Napoleon ([ MGG ] says 1849). (The choice of the Panth)on was undoubtedly primarily based on its height, but it was also the most conspicuous symbol of the struggle between the Church and reason/revolution/anticlericism in Paris. At the time it was a secular temple devoted to the great men of France, most of whom were distinctly anticlerical. Many of the contemporary reports referred to Galileo and attacked the church.) He used a 67 m wire and a 28 kg ball. He was assisted by the engineer Gustave Froment, who made the ball. The wire broke on the first trial, striking terror into Foucault and Froment! They designed a kind of parachute to prevent such accidents. The period was about 16 sec. A 6 m diameter circular table, marked in quarters of a degree, was set out on the floor, inside a larger railing. After one period, the ball could be seen to have moved about 2.5 mm on this scale. Foucault placed little ridges of sand on the table to record the path of the ball. [C. L. Stong; The Amateur Scientist ; Simon & Schuster, 1960, pp. 290301] says the lines moved 11o18' per hour, corresponding to 2.6 mm per period. He also gives an intuitive explanation that the movement is 15o per hour multiplied by the sine of the latitude. The latitude of Paris is 48o51', corresponding to 11.29o = 11o17.69' per hour. There are contemporary pictures in [Foiret et al., p. 16] and in [Deligeorges]. The demonstration first took place before a fashionable audience on 26 or 31 Mar 1851 some of the ladies fainted with excitement and other spectators said they could feel the earth move beneath them! By an ironic twist of fate, Napoleon made a coup d')tat in Dec 1851, forming the Second Empire, which restored the Panth)on to the church and Foucault's pendulum was promptly stopped and removed. Foucault then designed an improved support and drive mechanism for the Exposition Universelle of 1855. In 1902, after the laicisation of the Panth)on, Camille Flammarion and Alphonse Berget set up the demonstration again. They wanted to use the original ball, but the Mus)e would not permit it, so they used a 20kg ball that had been used in the Cathedral of Reims in 1851. They were able to use the original railing. Their wire was a length of piano wire, donated by the piano makers Pleyel, but they discovered it was 60 cm short and they had to raise their table. By Jul, they were able to test it and they had a grand opening on 22 Oct with over 2000 persons attending. The ball was held at the end of its swing by a silk cord which the Minister of Public Instruction burned with a candle to provide a smooth launch. In 1995, the demonstration was set up again in the Panth)on, by Jacques Foiret, engineer of the Conservatoire National des Arts et M)tiers, for a short exhibit to launch a national science festival on 5 Oct 1995, but it has been so popular that it was still present in Jan 1998. There is a pleasant video presentation showing the installation of the pendulum and some of the history, but one cannot get up to the railing. Foucault's original 28kg lead and brass ball of 1851 was used initially in 1995, but in 1996 it was replaced by a 47 kg ball similar to that used by Flammarion in 1902, though that weighed only 20 kg. The original railing was used again. Foiret devised a new safety mechanism. The period is 16.5 sec and the pendulum advances 272o per day or 3.11666...' per period, which corresponds to 2.7198... mm per period on the 6 m circular scale. [Deligeorges, p. 16] notes that some 10% of French people still think the sun goes around the earth! [Deligeorges. Foiret.] The south side of the PLACE DE LA CONCORDE, 8e, has a fountain with groups of statuary representing Marine Navigation and Inland Navigation. Place du Parvis see Notre Dame, above. House numbering was first used in 1463 on the PONT NOTREDAME, 4e. However [Okey, pp. 155156] indicates that this bridge was replaced after its collapse in 1499 and seems to imply that it was the new bridge that had numbering. [A. Brown, p. 35] gives 1463. The RUE DU CHERCHEMIDI, 6e, near St. Sulpice, commemorates a sundial which had two persons looking for noon when it was 2:00pm. No. 19 has a plaque representing this. [Hare(2), p. 432.] In the church of SAN SULPICE, 6e, there is a meridian line in the pavement of the south transept, engraved by LEMONNIER in 1743. Against the wall of the left transept is 'a curious Gnomon Astronomicus'. [Hare(2), pp.421422.] The French SENATE is comprised of distinguished citizens, appointed for life. De BOUGAINVILLE, LAGRANGE, LAPLACE, MONGE were Senators. CAUCHY's father was Secretary of the Senate, which was then housed in the Luxembourg Palace, 6e. The SORBONNE, 7 Rue des (coles (or Place de la Sorbonne), 5e, was founded as a theological college by Robert de Sorbonne (or Sorbon or Cerbon or Rathelois) (12011274), chaplain to St. Louis (= Louis IX), in 1253 the foundation is depicted in the murals on the first floor balcony over the lobby of the Grande Amphitheatre and Louis's Charter is on display in the National Archives (in the H=tel de Soubise, 60 Rue des FrancsBourgeois). However, the funding came from the queen's physician, Robert de Douai, who deserves to be remembered. At the time, there were already about a dozen colleges in Paris, but these seem to have vanished and the Sorbonne is considered the oldest part of the University. It originally had 16 students and was located in a house near the Roman baths, but it moved several times as it expanded. By the end of the 14C, the university had some 40 colleges; by the end of the 15C, there were about 50 and John Evelyn records 65 colleges in the late 17C. [Okey, pp. 9697.] In the late 17C, Richelieu rebuilt the college and church of the Sorbonne his tomb monument is in the church which is the only part surviving from his work [Okey, pp. 214 & 329]. In the church is a picture showing Robert Sorbonne presenting pupils to St. Louis [Hare(2), p. 370]. [Hare(2), p.369] says the quadrangle by the church is 'remarkable for its curious sundials'. After a brief closure by Napoleon, the University was reorganized in 1808 and the faculties of literature, science and theology were located here [Pengelley & Pengelley, p.115]. References to the University of Paris generally refer to the Sorbonne until the reorganization of the 1970s. The main building dates from 1889. The Rue des (coles site is now home to the Universities of Paris-III and ParisIV. The Grande Amphitheatre is where France and the world honoured PASTEUR at a great meeting on 27 Dec 1892 to celebrate his seventieth birthday. It contains murals representing science, medicine, etc. and statues of Sorbonne, Descartes, Lavoisier, Pascal, etc. [Pengelley & Pengelley, p.115.] In 1458, the Master of the Mint was sent to Mainz to learn about printing, but nothing came of it. In 1463, Fust and Sch?ffer brought some printed books to Paris for sale, but they were confiscated at the instigation of the scribes and booksellers the king paid a compensation of 2500 crowns in 1474. In 1479, two doctors of the Sorbonne, Guillaume Fichet and Jean de la Puin, invited Ulmer Gering and two other Swiss printers from Constance to establish a press in the Sorbonne. ([ MGG ] says this press was established by Louis XI in 1469.) By 1473, Peter Kayser, John Stohl and Ulmer Gering were printing in the Rue St. Jacques, at the sign of the Soleil d'Or, which sign was long a token of fine printing. Roman type was soon superseded by Gothic about 1480, but Roman type was reintroduced about 1500. At Gering's death, there were 40 presses in Paris, but these were reduced to 24 to insure sufficient profitability that printers would not be tempted to print prohibited or shoddy books. In 1556, an order, supposedly at the instigation of Diane de Poitiers, required a vellum copy of every book published to be deposited in the Royal Library this seems to be the first such order but cf Biblioth/que Nationale. [Okey, pp.148-150.] MERSENNE was a student. CAUCHY (17891857) was Assistant Professor of Mechanics in 1823-1830 and Professor of Mathematical Astronomy from 1848. BONNET taught here. LIBRI was professor of probability from 1831. CHASLES (17931880) was Professor of Higher Geometry from 1846. LIOUVILLE was Professor in 1857-1873. Charles HERMITE (1822-1901) was Professor, c1870-c1897. DARBOUX succeeded CHASLES as Professor of Higher Geometry. PAINLEV( was a Professor here. Marie Sklodovska (CURIE) entered in 1891 and came in first in physics in 1893 and second in mathematics in 1894. Pierre Curie became Professor of Physics at the Sorbonne, but was killed by a cart in 1906 and Marie was appointed to succeed him their first woman professor. She gave the world's first course on radioactivity here. [Wymer, chap. 6.] Paul APPELL (18551930) was dean of the Faculty of Sciences, c1904. GOURSAT taught here from 1885. Charles Emile PICARD (18561941) was professor from 1886. TANNERY was professor from 1903. (lie CARTAN (18691951) came to teach in 1909 and was named professor in 1912 until his retirement in 1940. Prince LouisVictor de BROGLIE was here when he received the Nobel Prize in Physics in 1929 for his discovery that matter had wave properties. FR(CHET (18781973) was professor in 19411949. Gaston (Maurice) JULIA (18931978) was a professor. Besides the murals on the first floor, there are other monuments, including statues of Archimedes and of Chemistry, etc. [Cronin, pp. 9091]. I have recently noted a frieze of busts on the side facing Rue St. Jacques, but did not have time to record the names. The TOUR DE L'HOROLOGE is the NE corner of the Conciergerie, on the Quai de l'Horologe, 1er, by the Pont au Change. It is asserted to contain the oldest public clock in the world, dating from 1370 [Cronin, p. 39; MGG ], though perhaps a dozen other clocks lay claim to 14C origins and I have not seen Paris mentioned in discussions of early clocks. [Don Lemon; Everybody's Scrap Book of Curious Facts ; Saxon, London, 1890, p.38] says the first clock resembling a modern clock was made by Henry Vick for Charles V of France in 1370, apparently referring to this clock. Legend says that Charles was unhappy with the IV for four and said it ought to be IIII and this has been followed ever since. [Hare (2), p. 266267] says the tower is restored and 'partially old' and that the clock "commemorates the oldest clock in Paris, constructed by the German Henri Vic, and erected by Charles V." This would have been 1370, but it seems that nothing of the original clock remains. The leaflet for the Conciergerie says the tower was built by John the Good in the 14C and that the clock was replaced by the present clock in 1585. [Okey, p. 312] says the clock was renewed in 1588 and that the bell was cast in 1371 and was used to signal the St. Bartholomew massacre at 2:00 on 24 Aug 1572. [Hare (2), pp. 103 & 266267] says the bell of S. Germain l'Auxerrois gave the first signal for the Right Bank and the Tour de l'Horologe gave the signal for the Left Bank a little later. Hare adds that the tower is modern. The UNIVERSITY of Paris began about 1109 when WILLIAM OF CHAMPEAUX began lecturing on logic [Ball (5), p. 222]. See also Ab)lard in Section 7A2, which dates it to 1208. [ MGG France ] dates it to 1215. [Pengelley & Pengelley, p.114] say it was established by Innocent III in the 13C. Ab)lard's teaching drew away so many of William's students that he retired in c1113, became a monk and founded the Abbey of St. Victor, in the area of Rue du Cardinal Lemoine, SW of Rue Monge [Hare(2), p. 347]. Johannes SACROBOSCO (= John of Holywood or Halifax) (c12131256) came here in 1221 and was professor of mathematics until his death. The Sorbonne, cf above, was established in 1253. At the time, there were already about a dozen colleges in Paris, but these seem to have vanished and the Sorbonne is considered the oldest part of the University. Any master could start his own college once he had permission from the Bishop's Chancellor. By the end of the 14C, there were some 40 colleges; by the end of the 15C, there were about 50 and John Evelyn records 65 colleges in the late 17C. [Okey, pp. 9697.] In 1349, there were 502 professors; in 1403, there were 909 [Okey, p. 105]. However, it is not clear when the multiplicity of colleges really came together as a university [Okey, p. 98] says the word already occurs in statutes of 1215. [Okey, pp. 9899] says the four main faculties were formed in the early 12C and the students and staff had formed themselves into four national groupings: French, Picards, Normans and English by this time. By 1245, these groups were meeting to elect a Rector, who superseded the Chancellor as head of the University and eventually became a kind of sovereign over the Left Bank which had 10,000 students. As at Oxford and Cambridge, the privileges of students led to many conflicts, often bloody and sometimes lethal. As part of the expulsion of the Jews from Spain, four camelloads of manuscripts were brought to Paris in the 13C, containing the works of and commentaries on ARISTOTLE, translated from Greek to Arabic to Latin. The study of Aristotle was initially prohibited but Aquinas (c12251274) managed to reconcile Aristotle and the Church. [Okey, p. 103.] In the 13C, Albertus Magnus, Thomas Aquinas, Duns Scotus and Roger Bacon taught at Paris [Okey, p. 104]. [Ball (5), p. 227] claims that the first student to fail out of a university was a Paul Nicolas who was refused his degree in Paris in 1426, despite his taking legal action. Petrus [Peter] RAMUS (15151572) was a student and presented a brilliant thesis that all of Aristotle was wrong! He later founded the chair of mathematics and wrote a popular book on arithmetic. His Dialectica was a logic text which was very antiAristotle and much simpler, rapidly displacing Aristotelian treatises in many universities, e.g. at Cambridge by 1580 and at Dublin, until the rise of Bacon and Descartes in the late 17C / early 18C [McDowell & Webb, p. 7]. John DEE lectured here on Euclid, in English, in 1550 [Ball (5), p. 19]. DE MOIVRE was a student of physics in the 1680s. The University resisted the Reformation and generally sank into scholasticism in the 1516C. In the 1718C, the number of colleges reduced. When the Jesuits were expelled in 1763, the University took over the Lyc)e Louis le Grand and made it the seat of the University and the main college, suppressing 26 small colleges and leaving only ten. [Okey, pp. 105106. Hare (2) p. 365.] (lie CARTAN (18691951) was professor in 19121941 (or 1940). Individuals were often associated with several of the higher educational institutions at the same time. The 1970s reorganization has split the University into 13 independent units cf Sorbonne above and five of these, along with five technical universities, are in the suburbs. The Universit) Paris V is named Ren) DESCARTES and is on Blvd. St. Germain by the Odeon Metro stop [ MGG ].  7-A-2. INDIVIDUALS.  See also: Arcueil, Fresnes, PortRoyaldesChamps, in Section 7B. ABEL lived at 41 Rue St. Marguerite, Faubourg St. Germain, in JulyDecember 1826 [Ore, pp. 136, 143 & 156]. (I can't find this on my map.) Peter (= Pierre) AB(LARD (or Abelard) (10791142) was a distinguished medieval logician and teacher. He came to Paris as a student at the school of Notre Dame and soon was engaged in a major controversy about whether abstractions could be understood without knowledge of any specific cases e.g. can one understand the concept of queenliness without ever knowing about queens? Despite its apparent silliness, the question has profound theological implications consider replacing 'queen' by 'god' in the previous example. Further, Ab)lard was attracting away the pupils of William of Champeaux. Consequently Ab)lard was dismissed. After teaching at nearby Melun for a while, he set up his own school at Mt. Ste. Genevi/ve, near the present Pantheon, on the Left Bank. A few schools had already been established in the area, but many more followed Ab)lard and it was the natural area for the University to be established in 1208. His illfated affair with H)lo5se produced a son who was named Astrolabe!! At that time, he lived in her family house at 10 Rue Chanoinesse, north of Notre Dame. They lived at nearby 9 Rue des Chantres. [Okey, p. 305.] [Hare(2), p. 314] says H)lo5se lived in a house at the corner of the Rue des Chantres and Quai aux Fleurs, where there was a commemorative plaque. In the Sorbonne, the first floor murals include Ab)lard teaching. The remains of Ab)lard and H)lo5se were transferred to P/re Lachaise cemetery in 1817, where the graves are a shrine for unhappy lovers. [Cronin, pp.8284 & 90. Okey, pp. 9093.] ALBERTUS MAGNUS (1193 (or 1206) 1280) taught at the Dominican convent on the site of 14 Rue Soufflot, near the Panth)on, in 12451248 [Cronin, p. 103; Okey, p. 104; Holmyard, pp. 111114]. Jean-le-Rond D'ALEMBERT (1717-1783) was abandoned by his parents on the steps of Saint Jean-le-Rond, which was the baptistery of NotreDame, qv in Section 7A1. Foster parents were found and he was christened with the name of the saint. [Eves, vol. II, pp. 32-33. Okey, p. 297.] When he became famous, his mother attempted to reclaim him, but he rejected her. Andr) Marie AMP.RE (17751836) was professor of mathematics at the (cole Polytechnique from 1809. In 1820 he heard of Oersted's observation that a magnetic needle is influenced by an electric current and developed an explanation which he presented the next week to the Acad)mie des Sciences. [Moore & Dahl, p. 7.] THOMAS AQUINAS (c12251274) taught at the University [Okey, p. 104]. Fran'ois ARAGO (17861853) was a student at the (cole Polytechnique from 1803. He became Laplace's assistant at the Observatory in 1806, rising to become Director. He and Biot extended the Delambre and M)chain meridian measurement from Barcelona to the island of Formentera (cf under Dunkirk in Section 7B and under Barcelona, Spain, in Section 10). Secretary of the Acad)mie des Sciences from 1830. Buried in P/re Lachaise. There is a bust in the Louvre. Cf Observatory in Section 7A1 for the commemorative medallions along the Paris meridian. Jean Robert ARGAND (17681822) was a Swiss working as a bookkeeper in Paris when he published his Essai sur une mani/re de r)presenter les quantities imaginaire dans le construction g)ometrique , introducing the Argand diagram for complexes. His book did not even have his name on the title page and was almost ignored, but he sent a copy to Legendre who mentioned it in a letter to Fran'ois Joseph Fran'ais, whose brother JacquesFr)d)ric Fran'ais found it after Fran'ois's death. The brother was a professor (see under Metz in Section 7B), recognised its interest and published an article in Gergonne's Annales des Math)matiques in 1813, leading to the discovery of Argand and widespread discussion and adoption of the idea. During 12341250, Roger BACON (1214?1294 (or 1292)) studied here under Petrus Peregrinus (one of the first writers on the magnet) and the taught here. He returned to Paris c1270 and was in prison for heresy in Paris during 12771291 when he composed his major works. Cf in Section 5B for details of his work. [Okey, p. 104. Holmyard, pp.115119.] Jean Sylvain BAILLY (17361793) was born in Paris. His father was in charge of the King's pictures, so they lived in the Louvre [Arago, pp. 94 & 101]. About 1760, he set up an observatory there, in one of the windows of the upper story of the south gallery [Arago, p. 101]. He was a noted astronomer, historian of astronomy and writer, being a member of all three Academies. In about 1773, he removed to Chaillot on the outskirts of Paris where Franklin visited him in 1777. He later was a major figure in the Revolution, first President of the National Assembly in 1789 (hence clearly depicted in one of David's paintings) and Mayor of Paris in 17891791. But the times passed him by and he was arrested while staying with the Laplaces in M)lun in 1793. He was sent to Paris, imprisoned in various places and summoned as a witness in the trial of Marie Antoinette. He was condemned, imprisoned in the Conciergerie and guillotined by the Jacobins in the moat on the south (river) side of the Champs de Mars in 1793. [Arago. Schmidt.] There is a bust of him in the Mus)e Municipale in the H=tel Carnavalet [Hare (2), pp. 175176] and a picture in the Conciergerie. The father of Antoine Henri BECQUEREL (18521908) was Professor of Physics at the Mus)e National d'Histoire Naturelle in the Jardin des Plantes and so our man was actually born in the grounds. He obtained an engineering degree in 1877 and held various posts in the civil service and academia, including the (cole Polytechnique and the Mus)e National d'Histoire Naturelle. His father had formed a collection of phosphorescent minerals and on 1 March 1896, he observed that uranium nitrate could expose a covered photographic plate in his laboratory at the Mus)e (plaque in rue Cuvier). He pointed the Curies in the direction of investigating the phenomenon. They shared the 1903 Nobel Prize in Physics. He died in Brittany. Henri BERGSON taught philosophy at the Coll/ge de France c1900. Nobel Prize in Literature, 1927. Pierre Eug/ne Marcellin BERTHOLET (18271907). PierreOssian BONNET (18191892), of the GaussBonnet theorem, taught at the (cole Polytechnique, (cole Normale and the Sorbonne. (mile BOREL (18711956) came to Paris as a student of the Coll/ge SainteBarbe and the Lyc)e LouisleGrand. In 1889, he was first on the admissions list of both the (cole Normale and the (cole Polytechnique, and entered the former because he had made friends with Darboux's son. He completed his doctorate in 1894 and spent 18931897 at Lille. He was called back to the (cole in 1897 and remained there for the rest of his life. He was also made Professor of the Theory of Functions of the University of Paris (Sorbonne) in 1909. He lived in Boulevard Arago. He was Deputy Director of the (cole in charge of science from 1910 to 1920 and lived in the (cole. In 1920, he resigned and was made Honorary Director and also translated his University chair to that of Theory of Probability and Mathematical Physics, once held by POINCAR(. About this time he was living in Rue du Bac. He was a member of PAINLEV('s party and a Deputy in 19241936. He was Minister of the Navy under Painlev) in 1925, initiating a submarine building program leading to ships named Pasteur, Pascal, Henri Poincar), Poncelet, Fresnel, Monge and Archim/de. During this period, he and Jean PERRIN promoted the creation of the Centre National de la Recherch) Scientifique (CNRS, at 15 Quai AnatoleFrance, 7e). Borel also led the foundation of the Institut Henri Poincar) in 1927 and served as Director or Joint Director until his death. [Collingwood]. Roger Joseph BOSCOVICH (17111787), the early atomist, lived and worked at 6 Rue de Seine, 6e, in 17751777 (plaque). BOURBAKI began at 12 noon on 10 Dec 1934 when H. Cartan, Chevalley, Delsarte, Dieudonn), Ren) de Possel and Weil met for lunch at the Caf) Capoulade. This group, with some variations, met regularly at the Caf). The group was not named and officially announced until the following summer, so the earlier group has been called ProtoBourbaki. See also: Nancy and Strasbourg in Section 7B. PierreLouisMarie BOURDON (17791854) was professor at St. Cyr, then at the Lyc)e Charlemagne and then the Coll/ge Henri IV. He was a prolific writer of texts. His (l)mens d'Arithm)tique went through 21 editions and his (l)mens d'Alg/bre of 1817 went through a number of editions and was translated both in England and in America, where it was popular for its clarity. Edward BRANLY (1844-1940), inventor of the Branly decoherer used in early radio, was a parishioner of St-Jacques-du-Haut-Pas, 252 Rue St. Jacques, 5e, where there is a commemorative plaque. He is buried in P/re Lachaise. Guillaume BUD(, first director of the Coll/ge Royale in 1530, is buried in St. Nicolas des Champs (252 bis Rue St. Martin, 3e) [Hare(2), pp 135136]. AdrienQuentin BU(E (17481826), one of those who developed complex numbers in the early 19C, fled the Revolution to England, but returned in 1813 and became an Honorary Canon of Notre Dame. George Louis Leclerc BUFFON (1707-1788), the needle-dropper, was very interested in mathematics before going into natural history he translated Newton's The Method of Fluxions and Infinite Series as La Methode des Fluxions, et des Suites Infinies in 1740. He became Superintendent of the Jardin des Plantes, 5e, in 1739 and laid it out from 1739. He transformed the gardens into one of the leading natural history research establishments in the world. He is commemorated by a statue, an Allee and a Rue in or near the Jardin. His house is preserved in the Jardin and has a plaque recording his death (here?). J. BURIDAN (13001361), the proposer of the idea of Buridan's Ass, lived in Paris about 1200. Legend says that Queen Jeanne de Burgogne had him tied in a sack and thrown from the Tour de Nesle into the Seine. Apparently this was a common whim of hers and Buridan's disciples had placed a barge of straw underneath to catch him. [Okey, p. 68.] He lived in the Rue St. Julien le Pauvre, 5e [Okey, pp. 313314]. Nicholas L)onard Sadi CARNOT (17961832) was the engineer and thermodynamicist, inventor of the Carnot cycle, etc. He is not to be confused with (his father?) Lazare Nicolas Marguerite Carnot (17531823), military engineer, a major figure in the Revolution and an important writer on mathematics, particularly 'the geometry of position', nor with the latter's grandson, (Marie Fran'ois) Sadi Carnot (18371894), engineer and President of France from 1887. There is a statue of Jacques CARTIER, the explorer, at the corner of Ave. Franklin D. Roosevelt and the Cours la Reine, 8e, just N of Pont des Invalides. Four CASSINIs were successively directors of the Paris Observatory (qv in Section 7A1) from its founding in 1672 till the Revolution. The first Cassini, Giovanni Domenico (= Jean Dominique) (1625-1712) came to Paris in 1669 and became a French citizen in 1673. In 1671-1673, he found the second and third moons of Saturn (Rhea and Japetus). (Huygens found the first of the moons in 1655.) In 1672, Cassini and Richer made the first reasonable measurement of the sun's distance cf under Observatory in Section 7A1. In 1675, Cassini discovered the 'division of Cassini' in the rings of Saturn. In 1684, he found two more moons of Saturn (Tethys and Dione). [Miniati et al., pp. 6970.] It was this Cassini who described the 'ovals of Cassini' and discovered the libration of the moon, the polar caps of Mars and the discrepancy in the eclipses of the moons of Jupiter later shown to be due to the finite speed of light. Cassini also worked at the Chteau of St-Germain-en-Laye, in the western suburbs of Paris. He is buried in the nearby St-Jacques-du-Haut-Pas, 252 Rue St. Jacques, 5e modern plaque in the floor by the altar. His assistant Olaus ROEMER (16441710) determined the speed of light from these results, getting within 30% of the correct result. In 1783, CASSINI DE THURY (17141784) was Director and proposed to George III the triangulation of southeast England so that connection with the completed French triangulation to Calais would resolve the disputed relative positions of the Greenwich and Paris Observatories. This led to the triangulations carried out by Roy (cf in Section3) and Count Jacques (or Jean??) Dominique CASSINI (1748-1845, son of the above) and the founding of the Ordnance Survey. Rue Cassini is just north of the Observatory. AugustinLouis CAUCHY (17891857) was born in Paris. His father was Secretary of the Senate, so the family lived in the Luxembourg Palace during Cauchy's teens. He attended the (cole Polytechnique in 18051807 and the (cole des Ponts et Chauss)es in 18071809. He then worked on the Canal Saint Martin in La Villette in the NE of Paris, then on the harbour at Cherbourg. Professor at the (cole Polytechnique in 18151830, Assistant Professor of Mechanics at the Sorbonne in 1823-1830 and a Professor at the Coll/ge de France to 1830. Feeling bound by his allegiance to the Bourbons, he followed them into exile in 1830, not returning until 1838. Professor of Mathematical Astronomy at the Sorbonne from 1848. FA  DI BRUNO was one of Cauchy's last pupils in 18491851. Cauchy died at his country house in the suburb of Sceaux. [Smithies. Giacardi & Roero, pp.132134.] Michel CHASLES (17931880) taught geodesy, astronomy and applied mathematics at the (cole Polytechnique in 18411851. He was appointed to a specially created chair in Higher Geometry at the Facult) de Sciences of the Sorbonne in 1847. He founded the Soci)t) Math)matique de France in 1872. He is buried in P/re Lachaise Cemetery. The du CHTELETs lived at the H=tel Lambert, 27-31 Quai d'Anjou, 2le St. Louis, 4e, [Crosland, vol. 3, p.72]. [Eastman, p. 107, with photo] says it is 13 Quai d'Anjou, 2le StLouis and that the Marquis du Chtelet bought it for his wife Gabrielle (Emilie le Tonnelier de Breteuil, Marquise du Chtelet) and VOLTAIRE to live in and that they lived there intermittently from 1733 to 1748. [Cronin, p.191] says it is 2 Rue St. Louis en l'2le. Ernst Florens Friedrich CHLADNI (17561827) was Professor of Physics in Breslau (qv in Section 8) when he developed Chladni figures c1800. He came to Paris in 1808 to present his work at the Institut and Laplace had him give a two hour demonstration to Napoleon, who gave him 6000 francs. Alexis Claude CLAIRAUT (17131765), was born, lived and died in Paris. He was a prodigy, being elected to the Acad)mie des Sciences at the age of 18. He computed the return date of Halley's comet. Zerah COLBURN, the American calculating boy, was admitted to the Lyc)e Henri IV, but could not afford the expenses. Jean Antoine Nicolas de Caritat, Marquis de CONDORCET (17431794) hid from the Convention at 15 Rue Servandoni, 6e, near St. Sulpice, but was eventually discovered and executed [Cronin, p. 179180]. However, in the Panth)on, it says he was found dead in the prison of BourgEgalit) (= BourglaReine), a bit south of Paris. Gaspard Gustave de CORIOLIS was a professor at the (cole Polytechnique. In 1835, he analysed the effect named for him. Marie Sklodovska (CURIE) (18671934) entered the Sorbonne in 1891 and came in first in physics in 1893 and second in mathematics in 1894. She first lived with her sister and brotherinlaw at 92 Avenue JeanJaur/s, La Villette, 19e. Married Pierre Curie (18591906), a teacher at the (cole de Physique et Chimie, 42 Rue Lhomond, on 26 Jul 1895. Pierre and his brother had discovered piezoelectricity c1880. In 18951900, they lived at 24 Rue de la Glaci/re, 13e, just south of the university area, then further south at 108 Boulevard Kellermann, 13e, (plaque) until 1906. Discovered the intense radioactivity in pitchblende in 1898 and they soon discovered the presence of two new elements: polonium and radium. She suggested the term 'radioactivity'. They then processed several tons of material in a vanished shed in the (cole Sup)rieure de Physique et de Chimie Industrielles de la Ville de Paris [photo in Wymer, p.6:22]. [ MGG France ] says the outline of the shed is shown in the paving pattern of the courtyard of the School at 10 Rue Vauquelin, 5e. From 1900 to 1914, they worked at the Curie Laboratory, 12 Rue Cuvier, 5e, probably now covered by part of the Universities Paris VI & VII. She received her doctorate and they received the Nobel Prize in Physics, shared with Becquerel, in 1903. Pierre became Professor of Physics at the Sorbonne, but was killed by a cart in the Rue Dauphine near the Pont Neuf in 1906 and Marie was appointed to succeed him their first woman professor. She gave the world's first course on radioactivity. Nobel Prize in Chemistry, 1911. Shortly after Pierre's death, she moved to a house at 6 Rue du Chemin, in the southern suburb of Sceaux, Pierre's native village, and stayed there until 1912. In 1912, she moved to 36 Quai de B)thune, 2le StLouis, 4e, and lived there until her death. Both Curies were buried at Sceaux, but in 1995 they were translated to the Panth)on she being the first woman to be so honoured. [Wymer, chap. 6. DBS.] The Institut Curie was built for her in 1914 at 26 Rue d'Ulm, 5e, (apparently now entered from 11 Rue PierreetMarieCurie), near the (cole Normale Sup)rieure. (My 1986 MGG shows the Institut de Radium also on the Rue d'Ulm, but my 1991 map shows the site as part of the (cole Nationale Sup)rieure de Chimie.) The Curies had two daughters. The elder, Ir/ne (18971956), assisted her mother and married Fr)d)ric Joliot (19001958), another of her mother's assistants, in 1926, and they adopted the name JoliotCurie. Ir/ne succeeded her mother at the Sorbonne. They created the first artificial isotope in 1934 and received the Nobel Prize in chemistry for 1935. After the fall of France, they managed to smuggle heavy water out of the country. Both Marie and Ir/ne died of leukaemia, probably caused by overexposure to radiation. (Jean)Gaston DARBOUX (18421917) was at the (cole Normale and the Sorbonne. He was perpetual Secretary of the Acad)mie des Sciences in the early 20C. See under the Observatory in Section 7A1 for his connection with the Dreyfus case. Abraham DE MOIVRE was a student of physics at the University, Coll/ge d'Harcourt, in the 1680s. After the Revocation of the Edict of Nantes, he went into seclusion in the priory of St. Martin (possibly that which became the Conservatoire National des Arts et M)tiers ??) and then emigrated to England, having no contact with France until he was elected a Foreign Associate of the Academy of Sciences just before his death. Ren) DESCARTES (1596 (or 1598) 1650) lived at 14 Rue Rollin, 5e, (demolished) in 1613-1617 [Alexanderson; Crosland, vol. 3, p. 74] and in 1644 and 16471648 [Eastman, p. 86]. [Hare(2), p. 495] says he lived in Rue Pourtales, formerly Rue Neuve S. Etienne, to the south of Boulevard Bonne Nouvelle, 2e, but I cannot locate either rue on my map. After his death in Stockholm, his body was returned to Paris, arriving on 25 Jun 1665 [Hare(2), p. 359], though the coffin had been looted by his followers for relics in Stockholm. Supposedly, the coffin was shipped overland from Copenhagen to avoid piracy by English admirers! The remains were in Ste. Genevi/ve, then in Lenoir's Museum of French Monuments, then finally moved to St-GermaindesPr)s in 1819. His previous presence in Ste. Genevi/ve, which became the Panth)on (Section 7-A1), led me to believe he was there. [Culbertson & Randall (3), pp. 161162. Scott, p. 6.] His headstone (or gravestone) is in St-Germain-des-Pr)s, in the second chapel on the right of the apse. [D. E. Smith (2)] gives the inscription. There is a portrait of him by Franz Hals in the Louvre [Alexanderson]. Stephen Jay Gould [S. J. Gould] says the (purported) skull of Descartes is in the Mus)e de l'Homme, apparently on display [Culbertson & Randall (3), p.162; Eastman, p. 86]. The Universit) Paris V is named Ren) Descartes and is on Blvd. St. Germain by the Odeon Metro stop [ MGG ]. Denis DIDEROT (1713-1784) lived at 3 Rue de l'Estrapade, 5e. He died at 39 Rue Richelieu, 1er, and is buried in St. Roch, 296 Rue St. Honor), 1er. [Crosland, vol. 3, pp. 76 & 97. MGG .] Bust by Houdon in the Louvre. There is no monument in St. Roch and they do not know where he lies. Johannes DUNS SCOTUS (c12651308) taught at the Franciscan school of theology in Paris [Okey, pp.77-78 & 104]. [Hare(2), pp. 388390] identifies this as the Convent of the Cordeliers, on the south side of Rue de l'(cole de M)dicine, 6e, where Universit) Paris VI (Cordeliers) is now. Hare says that remains of the Convent contain the surgical Mus)e Dupuytren, but this is now longer listed in Paris guide books. The statue of the Virgin on the central pier of the west porch of the lower chapel at the SainteChapelle is said to have bowed to Scotus in 1304 in recognition of his promotion of the doctrine of the Immaculate Conception! [Okey, p. 306]. However, he is best remembered as the eponym of 'dunce' in recognition of the sterile scholasticism of his followers. Gustav EIFFEL included a flat for himself at the top of the Eiffel Tower, 7e, and retired there at age 62 to conduct aerodynamic experiments [Cronin, p. 267]. ERASMUS studied at the College de Pouillerye in the 15C. He was offered the directorship of the Royal College of France in 1517, but declined. [Okey, pp. 98 & 163.] Portrait by Holbein in the Louvre. Francesco FA  DI BRUNO (18251888) came to Paris in 18491851 and became one of Cauchy's last pupils. In 1855157, he returned to pursue his doctorate. [Giacardi & Roero, pp. 144146.] Jean FERNEL (1497-1558) was a distinguished physician who wrote three books on mathematics, including one which gives his measurement of the earth's meridian. He recreated and developed the Greek hodometer (described by Heron) into the waywiser. He was buried in Saint Jacques de la Boucherie, of which the Tour Saint Jacques, 4e, is all that remains. [Sarton, pp. 191-194. Gunther (4), p. 57.] Oronce FINE (= Orontius Finaeus) (14941555) became professor at the Coll/ge Royal in 1532 and died in Paris. Bernard Le Bovier de FONTENELLE (16571757) died in Paris. Jean Bernard L)on FOUCAULT (18191868) was born in Paris, but his family moved to Nantes when he was young. After his father's death in 1829, the family returned to Paris and he attended the Coll/ge Stanislas. He started to study medicine, but found he could not stand blood and went into physics. Worked on photography, arc lamps, interference of light (determining the relative speeds of light in air and water and showing the speed varied inversely as the refractive index), telescope mirrors and lenses. In 1843. he collaborated with a doctor to produce an atlas of microscopic anatomy published in 1845 as a supplement to the doctor's Cours de Microscopie [Darius, pp. 12 & 2223]. In 1845, at the request of Arago, Foucault and Fizeau made the first known photograph of the sun showing sunspots [Darius, p. 16] (another source dates this as 1855). POINSOT suggested and Foucault created the gyroscope, which also demonstrates the rotation of the earth an 1851 version is in the Conservatoire National des Arts et M)tiers [Foiret et al., pp. 811 & 27]. Physicist at the Paris Observatory from 1855. He conceived his famous pendulum experiment about 1849. In early Jan 1851, he first set up the experiment in his cellar in Rue d'Assas with a 2m wire and a 5 kg weight and recorded its first success on 8 Jan at 2 in the morning. This was the first 'internal' demonstration that the earth rotated. ARAGO then invited him to set it up at the Observatory where he could get an 11 m wire and this was opened on 3 Feb. Later, Prince Louis Napol)on Bonaparte, President of the Republic (later Napol)on III), invited him to set it up in the Panth)on, qv in Section 7A1, where he used a 67 m wire and a 28 kg ball [contemporary pictures in Foiret et al., p.16, and in Deligeorges]. He was assisted by the engineer Gustave Froment who made the ball. A report states that this demonstration took place before a fashionable audience on 26 Mar 1851 some of the ladies fainted with excitement and other spectators said they could feel the earth move beneath them! He presented his results in three papers read to the Acad)mie des Sciences on 3 Aug and 27 Sep 1851 and published as: 'Demonstration physique du mouvement de rotation de la terre au moyen du pendule', Comptes rendus 32 (1851) 135138; 'Sur une nouvelle d)monstration experimentale du mouvement de la terre', Comptes rendus 35 (1852) 421424; 'Sur les ph)nom/nes d'orientation des corps tournants entrain)s par un axe fixe ! la surface du terre. Nouveaux signes sensibles du mouvement diurne, Comptes rendus 35 (1952) 424427. Foucault then designed an improved support and drive mechanism for the Exposition Universelle of 1855. He is buried in Montmartre Cemetery. In Oct 1995, the demonstration was set up again in the Panth)on for a short exhibit, but has been so popular that it was still present in Jan 1998. [Deligeorges. Foiret.] In 1850, Foucault confirmed Fizeau's 1849 result that light travels faster in air than in glass which was a confirmation of the wave theory of light. Foucault also discovered the eddy currents generated in a conductor when moved through a magnetic field. Jean Baptiste Joseph FOURIER (1766?1830) was a student at the (cole Normale, c1794. He was sentenced to the guillotine by Robespierre in 1794, but Robespierre was overthrown the day before his execution was due [Ben Selinger; Why the Watermelon Won't Ripen in your Armpit and other science conundrums ; Allen & Unwin, Australia, 2000, p. 194]. He was unanimously elected the first Secretary of the Institute of Egypt in 1798. [Archibald (4). Arago, p. 394.] He was Governor of Lower Egypt in 1798-1801 [Eves (6), p. 58] or Commissioner at the Divan of Cairo [Arago, p. 395]. He led one of the expeditions of exploration which examined ancient monuments and he suggested the publication of the great report on Egypt. He was was a professor at the (cole Polytechnique up to 1806. Napol)on made him a baron and during Napol)on's return from Elba in 1815, he made Fourier a count and Prefect of the Rhone, based at Lyons, from 10 Mar to 1 May. In 1815, he was penniless in Paris and giving lessons for his living. The Prefect of Paris found out and made him director of the Bureau de la Statistique of the Pr)fecture of the Seine. He was elected to the Acad)mie in 1816, but this was vetoed by the government, so he was elected again in 1817 and this was permitted. [Arago, pp. 436437.] He was Prefect of the Department of Is/re, whose capital is Grenoble, from 1802 to 1817 (1815??) [Eves(6), p. 58; Math. Intell. 10:2 (1988) 51]. He was Permanent Secretary of the Acad)mie des Sciences in 18221830. In 1827, he suggested that man's activities might have an effect on the climate, but no one took him seriously. Buried in P/re Lachaise. JacquesFr)d)ric FRAN&AIS (17751833) was at the (cole Polytechnique in 17971800. He rose to become General of the Engineers and Professor of the Military Art in Metz. Benjamin FRANKLIN (17061790) was US ambassador to France in 17761785. He lived at the H=tel de Valentinois, which was at 62 Rue Raynouard, 16e, at the corner of Rue Singer. Here he erected the first lightning rod in France(??). He may have had an office at 26 Rue de Penthi/vre, 8e. [Eastman, p. 87. Hare (2), p. 463.] He invented bifocal glasses in 1784. It was his experience of the late nights of Parisian society that led him to propose daylight saving time in 1784. He even estimated the number of candles that would be saved. VOLTA came to visit him and they dined many times. A source says he had a house in Passy. Bust by Houdon in the Louvre. (variste GALOIS (18111832) was born at 54 Avenue G)n)ralLeclerc, 14e, (plaque) [Alexanderson]. But [Solovyov], [Picard] and [Bell, p. 362] say he was born in BourglaReine, some 10 km south of the centre of Paris, making it still 5 km beyond the P)riph)rique and outside Paris. He was a student at the Coll/ge Royal de LouisleGrand (now the Lyc)e LouisleGrand) in 18231830. Failing to enter the (cole Polytechnique, qv in Section 7-A1, in 1830 he entered the Preparatory School or (cole Normale which continued the Coll/ge. He was expelled in Dec 1830 and became a political activist. He spent Aug 1831 to Apr 1832 in Sainte P)lagie prison. The infamous duel with Pescheux d'Herbinville took place near the Glassier pond in the southern suburb of Gentilly. He died in the Cochin Hospital this is now at 27 Rue du Faubourg St. Jacques, 14e, but I don't know how long it has been there. He was buried in a common grave at Montparnasse Cemetery, but no trace of the grave remains. [Solovyov. Picard.] The duel was over Galois's involvement with St)phanieF)licie Poterine du Motel, who was d'Herbinville's fianc)e, but it has been claimed that the affair was a political frameup by government agents in order to eliminate Galois. The [ MGG France ] is unusual among guidebooks in that it refers to many mathematicians and scientists, particularly under Paris. However, it is wise not to depend on such works for technical information it says: "Evariste Galois put forward the theory of sets; his concepts were developed by Cauchy." Pierre GASSENDI (1592-1655) was professor of mathematics (more properly astronomy) at the Coll/ge Royale from 1645. He lived in the H=tel de Montmor, 79 Rue du Temple, 3e. Montmor was treasurer to Louis XIII and Montmor's son invited the scientists of the day to meet here. These meetings led to the founding of the Acad)mie des Sciences, qv in Section 7A1. [ MGG .] Gassendi was professor at Aix from 1617. On 7 Nov 1631, he made the first observation of a planetary transit of the sun when he saw a transit of Mercury. [Scott, p. 202.] It seems likely he was at Aix at this time, but one source says he was in Paris [Owen Gingerich; review of: Eli Maor; June 8, 2004 Venus in Transit ; Princeton Univ. Press, 2000; Times Literary Supplement (11 Aug 2000) 29]. Gassendi was a priest, but he was a firm believer in Copernicus. He revived the atomistic ideas of Lucretius and spent much time proclaiming that Epicurean philosophy was compatible with Catholicism. [Berry, p. 28.] He is buried in St. Nicolas des Champs, 252 bis Rue St. Martin, 3e, [Hare(2), pp 135136]. Joseph Louis GAYLUSSAC (17781850) was a student at the (cole Polytechnique from 1797. On 6 Sep 1804, GayLussac ascended in a balloon at Paris to 23,400 ft and later made several longer ascents, taking samples of the air which proved to have the same composition at all heights. In 1808, he published his "Memoir on the combination of gaseous substances with each other". He also showed that chlorine was an element in 1809 and discovered boron. He taught at the (cole Polytechnique. He is buried in Division 26 of P/re Lachaise [Culbertson & Randall (3), p. 34]. [ MGG-Dordogne Perigord Limousin Quercy .] Sophie GERMAIN died at 13 Rue de Savoie, 6e, in 1831 (plaque) [Alexanderson]. Charles HERMITE (18221901) was a student at the (cole Polytechnique for one year in c1840 but was sent away because his lame leg made him unfit for military service. He was later a lecturer from c1862. He was Professor at the (cole Normale in c1867 and at the Sorbonne, c1870-c1897. He died in Paris. Philippe de la HIRE (16401718), who edited the early proceedings of the Acad)mie des Sciences and reported a method of constructing magic squares which he learned as ambassador to Siam, is buried in St-Jacques-du-Haut-Pas, 252 Rue St. Jacques, 5e modern plaque in the floor by the altar. Guillaume Fran'ois Antoine de L'HOSPITAL, Marquis de SainteMesme (16611704) was born and died in Paris. (The family name is often modernized to L'H=pital, but the older form seems to be the form he used.) His Analyse des Infiniment Petites of 1697 (or 1696?) was the first textbook on calculus, including the rule named for him, but it is now known to have been ghost written by John I Bernoulli. Christiaan HUYGENS (16291695) spent 16641681 in Paris as Director of the Acad)mie Royale des Sciences, with a substantial pension from Colbert and living in the building. He wrote his Horologium Oscillatorium (1673) here and dedicated it to Louis XIV. He developed the spiral balance spring and a watch using it, obtaining a French patent in 1675 (though Hooke had described the idea in 1658 and apparently made some watches using it). Huygens later used this in his 1682 planetarium, now in the Museum Boerhaave, Leiden. Denis Papin, inventor of the pressure cooker, was a student/assistant of his and in 1673 they built a gunpowder engine which was a primitive internal combustion engine. He designed, had built and played a harpsichord with 31 notes to the octave. In 1678, he proposed a wave theory of light though he had started work on this in 1672, he didn't publish until his Trait) de la lumi/re in 1690. Relations between France and The Netherlands deteriorated after 1672 and in 1681 he felt it prudent to return to The Hague (or he went back for his health). Colbert died in 1683 and Huygens had his belongings removed from Paris in 1685. [Museum Boerhaave, pp. 67 & 4547. Van Helden & van Gent, p. 5.] MarieEnnemondCamille JORDAN (18381922) was a student of engineering at the (cole Polytechnique, but studied mathematics on the side. He was professor at the (cole in 18731912 and at the Coll/ge de France. His Cours d'Analyse and Trait) des Substitutions et des (quations Alg)briques were standard works for a generation. He died in Paris. [Biggs, Lloyd & Wilson, pp.217218.] William THOMSON (later Lord KELVIN) see under Thomson, below. LAGRANGE (1736-1813) was briefly housed in an apartment in the Louvre when he came to Paris in 1787. Vagliente writes that he was in the Hotel de la Briffe, Quai des Th)atins, which seems to be a part of the Louvre. Lagrange brought the completed manuscript of the M)canique Analytique and it was published in 1788. In 1788, he was living at 4 Rue Fromanteau (or Froidmanteau), Section du Mus)um. Vagliente states that Lagrange lived at 128 Rue du Faubourg St. Honor/, 8e, quartier du Roule, at the time of his death, but that building was torn down c1955. Perhaps his greatest monument is the metric system. [ MGG France ] says it was adopted in 1795. Joseph Jerome LALANDE (17321807) studied astronomy at the Coll/ge de France and then became Professor of Astronomy there in 1762. Director of the Observatory from 1768 until his death. He also edited Montucla's History of Mathematics . [Schmidt.] Paul LANGEVIN (18721946) was Professor at the Coll/ge de France from 1902. He succeeded Pierre Curie at the (cole de Physique et Chimie in 1904 and was Director of the Coll/ge from 1925. He developed sonar during WW1. LAPLACE (17491827) came to Paris by 1769 and was soon a professor at the (cole Militaire from 1769 to 1776, where he discovered his expansion for a determinant [Whittaker]. Elected to the Acad)mie des Sciences in 1773. He was a major promoter of the metric system. Exposition du Syst/me du Monde appeared in 1796. The first two volumes of his Trait) de M)canique C)leste appeared in 1799. Napoleon made him Minister of the Interior in 1799, but he was suitable for such a post and was replaced after six weeks. Made a Senator. In 1803, he became Chancellor of the Senate, a post of little power but good salary. The following volumes of Trait) de M)canique C)leste appeared in 1802, 1805, 1825. There is a statue of him at the Observatory [Alexanderson]. He was originally buried in P/re Lachaise, but his remains were removed to the family estate near Beaumont in the late 19C. Adrien Marie LEGENDRE (1752-1833) was born in Paris and was professor at the (cole Normale Sup)rieure and the (cole Militaire [Archibald (3), pp. 45-46]. There are 16C tombs of a Roberte Legendre and her husband in the Louvre [Okey, p. 343], but I don't know if there is any connection with the mathematician. Urbain J. J. LEVERRIER (18111877) was at the Paris Observatory when he deduced Neptune in 1845-46. He also noted that the perihelion of Mercury was advancing more rapidly than Newtonian physics could account for, but he proposed in 1845 that this was due to a planet between Mercury and the sun which he called Vulcan. (Win some, lose some!) He later succeeded Arago as Director from 1854 to 1870 and 18731877. There is a statue of him at the Observatory. Guglielmo LIBRI (18031869) came to Paris in 1831 and became professor of probability at the Sorbonne and a member of the Acad)mie. In 1840, he was made secretary of a commission to catalogue manuscripts in French libraries. His Histoire des Sciences Math)matiques en Italie appeared in four volumes in 18381841. His political attitude made enemies and in 1848, he was accused of appropriating manuscripts. He protested innocence, but fled to London. He was tried in absentia and sentenced to ten years imprisonment, but it was never clear whether he was guilty or not. [Giacardi & Roero, p. 139.] On the other hand, [Luca Antoccia et al; Leonardo Art and Science ; Giunti Gruppo Editoriale, Florence, 2000, pp. 94, 102, 104] specifically says Libri stole various sheets, including the entire Codex on the Flight of Birds , from the Leonardo da Vinci codices that Napoleon had brought from Milan and which were in the Institut de France. He took them to England and assembled some of them into codices which he sold to Lord Ashburnham (the socalled Ashburnham codices 2037 and 2038) which the French government bought back in 1891. Libri disbound the Codex on the Flight of Birds and sold five folios in England and the other 13 to an Italian Count whose heirs sold it to a Russian prince who bought one of the missing folios and donated them to the Savoia family in 1883. This was deposited at the Biblioteca Reale and the four other pages were acquired in 19031920. At least one booklet that Libri took has never been relocated. Fran'ois(douardAnatole LUCAS (18421891) was a student at the (cole Normale in 18611864, then an assistant to LeVerrier at the Paris Observatory until c1870. He served in the artillery during the FrancoPrussian War, then taught at schools, including Lyc)e Charlemagne (18761879 & 18901891) and Lyc)e Saint Louis (18791890). It was at the latter that he devised the Tower of Hanoi, by "Professeur N. Claus (de Siam), Mandarin du Coll/ge LiSouStian". [Harkin] states that he lived at 56 Rue Monge, 5e, which [Lucas] identifies as the site where PASCAL died see Pascal, below, but I don't read [Lucas] as stating that he, Lucas, lived there he says about the legend of the Tower of Hanoi: "mais nous pouvons affirmer que le tout a )t) imagin), il y a une dizaine d'ann)es, au no 56 de la Rue Monge, ! Paris, dans la maison habit)e alors par M. Viette, ministre de l'Agriculture, et btie sur l'emplacement de celle oI mourut Pascal, le 19 aoEt 1662." [Harkin] could be read as saying that Lucas gives his address in the Preface to his Th)orie des Nombres , but it is not there in the 1958 reprint. MASCHERONI lived at 20 Rue Monsieur, 7e, (plaque in Italian) [Alexanderson]. There is a 'monstrosity in the form of a tomb to MAUPERTUIS' (1698-1759) in Saint-Roch, 296 Rue St. Honor), 1er, [D. E. Smith (2)], in the second chapel on the right [Hare (2), p. 107]. Pierre Louis Moreau de Maupertuis (16981759) supervised the first accurate measurements of a degree (but cf Paris Observatory in Section 7A1 for an earlier measurement). He first surveyed from Dunkirk to Perpignan to provide the data for the meter (This can't be right, see Dunkirk in Section 7B these measurements were to determine the flattening of the earth.) This line was later extended to Barcelona. He then led an expedition (including Clairaut) to Lapland (see Finland in Section 10), while Pierre Bouguer and CharlesMarie de La Condamine (17011774) went to Peru in 1736, to determine the shape of the earth. Maupertuis's data was enough to confirm Newton's prediction that it was flattened at the poles even before the Peru expedition had returned. Maupertuis also formulated the principle of least action. He was President of the Berlin Academy of Sciences for some time. Nicolaus MERCATOR (c1620-1687), a discoverer of ( dx/(1+x), designed and constructed the fountains at Versailles, outside Paris [Eves, vol. II, p. 4]. Father Marin MERSENNE (1588-1648) studied at the Sorbonne and later lived from 1619 (or 1620) to his death at the Convent of St. Francis of Paula near the Place Royale in Paris [H. de Coste; Life of Marin Mersenne ; given in David, pp. 196-228 see pp. 200-204]. (Other sources call it the Minim Convent de l'Annonciade.) Another source says it was on what is still called Rue des Minimes, near the Palais Royale, and was destroyed in the French Revolution. Gaspard MONGE (1746-1818) was buried in the cemetery of P/re Lachaise. As an active Jacobin, he was acting head of the government on the day Louis XVI was executed [Tattersall]. He was also Minister of the Navy. He was in official disfavour when he died and had been expelled from the Academy in 1816, but his students erected a monument with a bust. In 1989, he was translated to the Panth)on. The square in front of the (cole Polytechnique building was named for him, but has been recently renamed after Langevin and the (cole has removed to the suburbs. There is a Place Monge and a Hotel Monge a bit further down the Rue Monge. [Alexanderson. Brooke.] Claude Louis Marie Henri NAVIER (17851836) was a student and then a teacher at the (cole des Ponts et Chauss)es. Alfred NOBEL (18331896) lived at 5359 Ave. Malakoff, 16e, c1870c1890. It was during this period that he and his brothers developed the Baku oil fields and developed the first oil tankers. [Wilhelm, pp. 1316, with photo on p. 14]. He also lived at SevranLivry, 15km NE of Paris, where his house is in a park with an explosives museum; tel: (33) 1 49 36 51 75 [Glenys Crocker; The Gunpowder Industry ; Shire Album 160, (1986); 2nd ed., 1999, p. 32]. Nicole ORESME (1323?1382) was Bursar of the College of Navarre in the University of Paris in 1348-1356, and then became Master of the College in 13561361. He was the first to write scientific works in French. He is best known for his translations of Aristotle and his writings on economy and money, but he wrote several works on the sphere and seems to be the first to see the need for a Date Line. He was one of the first to draw the graph of an equation. Paul PAINLEV( (1863-1933), the aerodynamicist and politician, is buried in the Panth)on [Archibald]. Studied at the (cole Normale Sup)rieure. Doctorate in 1887. Professor at the Sorbonne. The Dreyfus Case aroused his interest in politics and he served as a Deputy for Paris from 1906. He was one of the first airplane passengers, flying with one of the Wright brothers. He was Minister of Education, then of War, twice Prime Minister (Borel served under him as Minister of the Navy) and Minister of War and then, appropriately, Air Minister in 19301931 and 19321933. There are a square and a place named for him just north of the Sorbonne. Blaise PASCAL (16231662) stayed with the Duc de Roannez at 18 Rue du Cloiture-Saint-Merri, 4e, about 1647. His unsuccessful attempt to persuade the Duc's sister to enter a convent led to a (fortunately) unsuccessful assassination attempt on Pascal. It was on the Pont de Neuilly, to the west of Paris, that he had a narrow escape from being drowned by runaway horses which led to his renunciation of the world [Hare(2), pp. 468469]. He lived at 54 Rue MonsieurlePrince, 6e, in 16541662 (plaque) [Alexanderson has a photo; I have a photo.], then moved to his sister's house at 67 Rue du CardinalLemoine, 5e, where he died. However, [Lucas, p. 183] identifies the site of his death as 56 Rue Monge, 5e. In 1992, I visited both sites they are not different doors of the same building and both are much later than Pascal, probably late 19C. 56 Rue Monge is a hotel (across from a Hotel Monge) and they had never heard that Pascal lived on the site. More recently, I find that [Hare(2), p. 495] says Pascal died in Rue Pourtales, formerly Rue Neuve S. Etienne, to the south of Boulevard Bonne Nouvelle, 2e, but I cannot locate either rue on my map. [Don Lemon; Everybody's Scrap Book of Curious Facts ; Saxon, London, 1890, p. 3334] asserts Pascal invented the omnibus and obtained a privilege to run public carriages in Paris which held eight passengers, but that the idea did not long survive him. However, Lemon dates this and Pascal's death as 1667, which might be a misprint. Pascal's remains are in St-(tienne-du-Mont, Place Ste. Genevi/ve, 5e; they were previously in the nearby Ste. Genevi/ve, demolished in 1807. Pascal's epitaph in St-(tienne-du-Mont is quoted by Smith [D. E. Smith (2); I have a photo; there is a photo in: Bernard Mahieu; L'Eglise Saint(tienne du Mont de Paris ; S. I. D. E. S./(ditions de la Tourelle, Paris, 1985, fig. 17]. It is on the first pillar on the right (south) side after passing through the screen into the chancel. The tomb itself, with a bronze bust, is generally said to be near the Lady Chapel [Alexanderson. Crosland, vol. 3, p. 78.] [Hare(2), pp.354-355] says the inscription is in the third chapel on the right while the tombstone is against the wall of the south aisle of the choir. Hare says this tombstone, with a Latin inscription by Boileau, was at PortRoyaldesChamps and then moved to the village church of MagnylesHameaux before coming here. Hare adds that the coffin of Pascal was brought here from PortRoyal after its ruin, presumably in 1709. [Cronin, p. 103] says Pascal is buried in the Lady Chapel. [Mahieu, op. cit., fig. 26] shows 'Tombeau de Pascal' as being on the pillar to the right of the Lady Chapel. When I visited in 1992 and 2000, I only saw a tablet on the right hand entrance pillar of the Lady Chapel which said he was 'near this pillar' I have a photo. A modern guidebook says the epitaph and this tablet are all that remains and that the epitaph is a replacement of the original. There is a statue in the Tour SaintJacques, 4e, where Pascal repeated the PuydeD=me experiments on atmospheric pressure in 1648 [Hare(2), pp. 232232; MGG ; I have a photo]. (Pascal was a follower of the religious thought developed at PortRoyaldesChamps (qv in Section 7B) which was started by Jean Duvergier de Havranne, Abb) de. St. Cyran ( 1672), who is buried in S. Jacques du Haut Pas, 252 Rue St. Jacques, 5e modern plaque in the floor by the altar. One of the earliest references to a pigeonhole problem has one of the other PortRoyal thinkers explaining it to the Duchesse de Longueville (-1679), a friend of the movement. She initiated the reconstruction of this church, laid the first stone and paid for most of the work. There is a memorial plaque in a side chapel (ask the custodian to let you in) which says her entrails were buried in the chapel. ([Hare] says she is buried in this church, but without a monument.) [Hare(2), pp. 337338. DBS.]) Louis PASTEUR (18221895) was a student of chemistry at the (cole Normale in 18431848 and began the studies of crystals that led to his discovery of stereoisomerism. He received a doctorate in crystallography in 1847. He returned as Director of Scientific Studies in 18571867. [Wymer, p. 2:7, 10, 15.] The (cole has been at 45 Rue d'Ulm, 5e, south of the Panth)on, from 1847. On the right of the courtyard is the building where Pasteur worked and which is now the school's infirmary. The room where he carried out the experiments that disproved spontaneous generation is now a cupboard for children's toys, with a plaque outside it. [Pengelley & Pengelley, pp.119120.] A grateful France built a Institut Pasteur at 25 rue du Docteur Roux (off Boulevard Pasteur), 15e, and Pasteur and his wife lived in it. The living quarters is now the Mus)e Pasteur, displaying much apparatus used, and often made, by him, as well as his own paintings (he could have been a professional artist). He and his wife are buried in a crypt in the basement, with a plaque recording his main achievements, which starts with "1846 Molecular dissymmetry". The Grande Amphitheatre of the Sorbonne is where France and the world honoured Pasteur at a great meeting on 27 Dec 1892 to celebrate his seventieth birthday. Jean PERRIN (18701942) was Professor at the University in 19101926. Nobel Prize in Physics, 1926, for confirming Einstein's theory of the Brownian motion. Main founder of the Palais de la D)couverte in 1937. Cofounder, with Borel, of the Centre National de la Recherch) Scientifique (CNRS, at 15 Quai AnatoleFrance, 7e). Commemorative plaque, with basrelief, on the west side of the little Square Jean Perrin which lies on the north side of the Palais de la D)couverte but which is now used as the forecourt to the Porte Champs (lys)es of the Grand Palais. Fran'oisAndr) Danican PHILIDOR (17261795), the first of the modern chess masters, was also an accomplished musician, a member of the choir at the Chapel Royal in VERSAILLES. At the age of 11, he composed a motet performed there. [Golombek. Murray, p. 60]. Two other Philidors are also listed in the Gramophone Classical Catalogue . (Charles) Emile PICARD (18561941) was born and died in Paris. He taught at the (cole Normale. Henri POINCAR( (18541912) lived at 63 Rue ClaudeBernard, 5e [Alexanderson]. He received his doctorate from the University of Paris in 1879. He taught briefly at Caen but soon returned to Paris where he remained. He was Professor of the Theory of Probability and Mathematical Physics in the University of Paris in 18861889, then Professor of Mathematical Astronomy and Celestial Mechanics from 1889. His 1890 memoir on the threebody problem includes the first attempt to mathematically describe chaos. His three volume Les M)thodes Nouvelles de la M)canique C)leste appeared in 1892, 1893, 1899. His three volume Le'ons de M)canique C)leste of 19051910 provided a simplified approach to the same material. Gold Medal of the Royal Astronomical Society in 1900. Louis POINSOT (17771859) was born in Paris and was in the first class of the (cole Polytechnique in 17941797. He became a civil engineer and was professor at the Lyc)e Bonaparte from 1819, but another source says he taught there until 1816. He was Professor of Analysis and Mechanics in 1809-1816, but another source says he was the first such professor in 18161825. About 1850, he suggested and Foucault created the gyroscope, which demonstrates the rotation of the earth an 1851 version is in the Conservatoire National des Arts et M)tiers, qv in Section 7A1. Later he was primarily an examiner and administrator. Died in Paris and is buried in P/re Lachaise. Sim)onDenis POISSON (17811840) was a student at the (cole Polytechnique, then assistant professor in 1802 and succeeded Fourier in 1806, when he was 25. He died at Sceaux. J. V. PONCELET (1788-1867) was Commandant of the (cole Polytechnique in 1848-1850. Gaspard Fran'ois Riche de PRONY (17551839) organised the calculation of new tables under the Republic, using division of labour which much influenced Babbage. He was first Professor of Analysis at the (cole Polytechnique from 1794 to 1815 and Director of the (cole des Ponts et Chauss)es from 1799 to 1839. [Hyman, p. 43.] Director of the Cadastre (Land Survey) from 1791. Petrus (= Pierre = Peter) RAMUS (1515-1572) was a student and presented a brilliant thesis that all of Aristotle was wrong! He later was the first Professor of Mathematics at the University (qv in Section 7A1). He was the author of a popular arithmetic in 1555. He lived (or at least worked) in Rue St. Jean de Beauvais where he was killed in his study in the St. Bartholomew Massacre in Paris on 24 Aug 1572. [Ball (5), p. 14. Hare (2), p.348.] Jean Eugene Robert, later ROBERTHOUDIN (18051871), was the most famous conjurer and mechanic of 19C Europe. He built a number of automata such as a singing bird, a commercially successful alarm clock which produced a lighted taper, a famous Writer which could write answers to questions or sketch portraits. The Writer was exhibited at the Palace of Industry of the Paris Exhibition in 1844 and won a silver medal. One of his most intriguing items was the famous Mysterious Clock, whose hands were enclosed in a glass case with no connections to the outside, but kept time. He had a theatre at 164 Galerie de Valois in the Palais Royal from 3 Jul 1845. This included the famous Light and Heavy Chest, effected by an electromagnet, which was used in Algeria in 1856 to impress the Algerians with the supernatural powers commanded by the French, especially when a high voltage was applied to the handles. He later developed a number of electrical devices, including an electrical master and slave clock system which he developed and exhibited at the Universal Exhibition of 1855, receiving a Gold Medal. In 1971, France issued a postage stamp commemorating him and showing the Mysterious Clock and his suspension illusion. [Dawes, pp. 121127.] See also Blois in Section 7B. ROBERVAL died in Paris. Abraham ROBINSON was a student at the Sorbonne in 1939, but then fled to England. Olaus ROEMER (16441710) was Cassini's assistant at the Observatory and first determined the speed of light. JeanJacques ROUSSEAU (17121778) was born on the 2nd floor of 2 Rue de JeanJacques Rousseau, 1er, [Hare (2), p. 109]. His remains were translated from Ermenonville to the Panth)on on 11 Oct 1794. Count RUMFORD (17531814) came to Paris and married Lavoisier's widow in 1802, and withdrew from scientific life. The marriage ended after four years and he bought a house in Auteuil, where he lived until his death. In 1894, Bertrand RUSSELL was an Honorary Attach) to and lived at the British Embassy, 3539 Rue du FaubourgStHonor), 8e, [Eastman, p. 104]. Johannes SACROBOSCO (= John of Holywood or Halifax) (c1213-1256) came here in 1221 and was professor of mathematics at the University until his death. He was buried in the Cloister Sodalium Mathurinalium (= Mathurine Convent), where his astrolabe was placed on his tomb. [D.E.Smith, p. 221.] Ch. F. STURM (18031855) was professor at the (cole Polytechnique and the Sorbonne. Thomas Aquinas see under Aquinas, above. William THOMSON (later Lord KELVIN) came to Paris in 1845, just after his tutor gave him three copies of Green's 1828 Essay , which Thomson had been unable to find. He was thrilled by it. In a letter to Larmor in 1907, Kelvin recalls that he visited Liouville and showed him the Essay and then went to Sturm's but found him not in. He returned to his lodgings at 31 Rue MonsieurlePrince, 6e, and that evening, Sturm came in a state of great excitement to see the Essay . It was republished in J. reine angew. Math. in 1850-1854. Thus the ideas of potential, Green's theorem and Green's functions were brought to light. [A. R. Hall(2), p. 22.] The geometrician VERNIQUET made the first trigonometrical plan of Paris in the mid 18C. He worked at the Franciscan monastery at 15 rue de l'(cole de Medicine, 6e. The site is now part of the University of Paris VI. The H=tel Verniquet, 21 Rue MichelleComte, 3, is named for him. [ MGG .] Fran'ois VI.TE (= VIETA) (1540-1603) died in Paris. Fran'oisMarie Arouet, known as VOLTAIRE, (1694-1778), was born in Boulevard du Palais, 2le de la Cit), 4e?, though [Eastman, p. 106] just says somewhere below the Pont StMichel, quoting a 1969 biographer. He lived at this unknown house until 1701, when the family moved to the Palace Arouet, Boulevard du Palais, 2le de la Cit), 1er, now covered by part of the Palace of Justice. He entered the Lyc)e Louis le Grand in 1704. He was in the Bastille for eleven months in 17171718 and two weeks in 1726, after which he went to England for three years. He was a guest at the Chteau of Maisons, in the NW suburb of MAISONSLAFITTE, Yvelines, for a period c1724 when he was exiled from Paris [Eastman, p. 74]. During 17331748, he lived intermittently with his mistress and collaborator, the Marquise Gabrielle du Chtelet, qv above, at the H=tel Lambert, 13 Quai d'Anjou, 2le StLouis, 4e, bought for them by her husband. However, after the publication of his Lettres Philosophiques , he had to flee Paris and they moved to CireysurBlaise, qv, which was in Lorraine. He published El)ments de la Philosophic de Newton in 1737. FRS and FRSE in 1743. Elected to the Acad)mie Fran'aise in 1746. Again exiled from Paris in 1747. In 17501752, he stayed with Frederick II at Potsdam. He then wandered for several years until settling near Geneva, qv. In 1778, he returned to Paris in triumph, but died shortly thereafter. He stayed briefly at a number of other locations, including 21 Rue Moli/re, 1er, in 1730 and H=tel de la Fontaine Martel, 20 Rue de Valois, 1er, in 1753. [Hare(2), p. 517] says they lived at 25 Rue Fontaine Moli/re, which clearly is the present Rue Moli/re, at the time of the Marquise's death in 1749 and that he then shared the house with a friend. [Hare (2), p. 223] says he lived for some time in a demolished house in front of St. Gervais and Protais, 4e, which does not correspond to any of the sites previously mentioned. He died at 27 Quai Voltaire, 7e, the house of his friend the Marquis de Villette, where there is a plaque (I have a photo), and he had lived there briefly in 1723. The Paris church had denied a request for a Christian burial, so his corpse was dressed as if alive and driven to the Abbey of Seilli/res, near RomillysurSeine, 35 km NW of Troyes, where his nephew, Abb) Migot, gave him a Christian burial [Culbertson & Randall (3), pp. 9697]. His brain was taken by the doctor who did the postmortem and his heart was taken by his close friend, De Villette, and is now in Ferney (outside Geneva, Switzerland, qv in Section 10). The armchair in which he died is in the Mus)e Municipale in the H=tel Carnavalet [Hare (2), pp. 175176]. There are statues of him in the small Square Honore Champion (at the end of Rue de Seine, behind the Institut de France) and the marble original of the famous Houdon bust is in the foyer of the Salle Richelieu of the Com)die Fran'aise [ MGG ]. The plaster version of the bust is in the Biblioth/que Nationale while the terracotta version is in Voltaire's house, 'Les D)lices', now the Institut et Mus)e Voltaire, Geneva, Switzerland. Other versions of the bust are in the Louvre, Sans Souci (Potsdam) The Palace of the Legion of Honor (San Francisco, California) [Okey, p. 322] says Houdon made many replicas of his works to avoid starvation during the Revolution. [Hare(2), p. 346] says the (or a) Houdon statue was erected in the square at the start of Rue Monge in 1872. The Institut de France has a famous statue of him in the nude by Jean Baptiste Pigalle (eponym of Place Pigalle) [Cronin, p. 246], but I recently saw this (or a copy) in the Louvre, qv in Section 7A1, which has another Houdon statue of him (if I read my notes correctly). Some of his remains were brought to inaugurate the Panth)on (see Section 7-A-1). [Crosland, vol. 3, pp. 71, 83, 87, 97, 98, 105. Eastman, pp.106-107. DBS.]  7-B. ELSEWHERE IN FRANCE.  I have given D)partement names, but my map is old and I think some names have changed. In particular C=tesduNord seems to now be C=tesd'Armor. Henry MOSELEY (18011872) attended a school in ABBEVILLE, Somme, briefly in his teens, probably to learn French. Henri Eug/ne PAD( (18631953) was born in Abbeville. The University of AIX(ENPROVENCE), BouchesduRh=ne, was founded in 1409. With the growth of Marseilles in the 19C, the University declined and now has only Law and Letters. [ MGG .] Pierre GASSENDI (15921655) was professor at Aix from 1617. On 7 Nov 1631, he made the first observation of a planetary transit of the sun when he saw a transit of Mercury. [Scott, p. 202.] It seems likely he was at Aix at this time, but one source says he was in Paris. There is a bust of him in the Mus)e d'Histoire Naturelle. Fabri de PEIRESC lived in Aix and drew the first map of the moon in 1636. [ MGG .] I recall seeing a statue or bust to him somewhere. Victor VASARELY (19061997) established a foundation to display and popularize his geometrical opart at Aix in 1971. A report said it was being dissolved in early 1997, but I found it open in 2002. The building is a set of hexagonal rooms, about 10m (30 ft) on an edge. The seven display rooms have just one picture on each wall, but these pictures are about 10m square! Nicole ORESME (1323?1382) was born at ALLEMAGNE, near Caen, Calvados. LEONARDO DA VINCI (14521519) lived from 1516 and died at Le Clos Luc), Rue Victor Hugo, adjacent to the Chteau of AMBOISE, IndreetLoire there once was a tunnel connecting them. Legend asserts that he died in the arms of Fran'ois I, but the king was near Paris on the day [Ackermann, p. 358]. The house is now a museum with models of his designs. He was buried in the church of St. Florentin, Amboise, but the bones were transferred in 1869 to the Chapelle St-Hubert in the Chteau. [Crosland, vol. 3, p. 12. Eastman, pp. 51 & 398.] Another source says the tomb was violated and the remains were dispersed during the religious wars of the 16C. Most French church mazes seem to be obstructed by chairs, but the reconstructed maze at AMIENS, Somme, (originally built 1288, destroyed 1708 (or 18251828), rebuilt 1894) was unobstructed during my visit in 1987 [Fisher, pp. 39 & 41, with colour photo on p. 39 and diagram on p. 65]. Fran'ois(douardAnatole LUCAS (18421891) was born in Amiens and used an anagram of 'Lucas d'Amiens' as the inventor of the Tower of Hanoi: 'N. Claus (de Siam)'. (douard BRANLY (18441940), inventor of the decoherer which could receive wireless signals was born here (or at least lived here for some time) [ MGG ]. The chteau of ANCYLEFRANC, Yonne, was designed by Sebastiano SERLIO (14751554), a noted Italian architect brought to France by Fran'ois I in 1541. Cf under Sheldonian Theatre in Section 5A. Charles Augustin de COULOMB (17361806) was born in ANGOUL*ME, Charente [ MGG ]. Louis PASTEUR (18221895) lived at ARBOIS, Jura, from the age of four (or five) and attended the local school until he was 17. Beside the N83, outside the town, is Pasteur's vine, where he carried his studies on fermentation. His father's tannery, which Pasteur converted into his vacation home, is in the town. The Maison Familiale, 83 rue de Courcelles, is now a Mus)e Louis Pasteur and is essentially unchanged since Pasteur's day. There is a statue of him in the main square of the town. [Pengelley & Pengelley, pp.103107.] ARCUEIL, ValdeMarne, just to the south of Paris, is where CAUCHY spent his childhood. LAPLACE also had a house here, which was looted in 1871 [Whittaker]. Laplace's house was adjacent to that of his friend BERTHOLET, the chemist, and they headed the informal 'Soci)t) d'Arcueil', which even published M)moires de la Soci)t) d'Arcueil. AUBAGNE, BouchesduRh=ne, has a 17C triangular belfry in Place de l'Observance. When Benjamin FRANKLIN came to France in 1776, bad weather forced him to land at AURAY, Morbihan, where he stayed at No. 8, Quai Benjamin Franklin (plaque) [ MGG Brittany , p. 55]. Jean Baptiste Joseph FOURIER (1766?1830) was born and grew up in AUXERRE, Yonne [Eves (6), p.57]. From the age of about eight, He attended a military school run by the Benedictines of the Convent of St. Mark. Lack of money prevented his entering the army, so he went to the Abbey of StBeno3tsurLoire, intending to become a priest, but the outbreak of the Revolution lead to abandoning his religious plans and he was appointed Professor of Mathematics at his old school in Auxerre, where he also lectured on rhetoric, history and philosophy when those chairs were vacant. [Arago, pp. 377380]. WILLIAM OF OCKHAM (or OCCAM) (12851347) was imprisoned on charges of heresy at AVIGNON, Vaucluse, but escaped and settled in Munich, c1330, qv in Section 8. At some point, he was excommunicated. John Stuart MILL (1806-1873) brought his wife to Avignon, for her health, but she died in 1858 at the extant H=tel de Europe, 12 Place Crillon. He spent most of his remaining years in a cottage, the Hermitage de Monloisier, near the cemetery of St.Veran on the road to Pont-des-Deux-Eaux, about 5 km SE of Avignon. He (they?) are buried in St.Veran. [Crosland, vol. 3, p. 16. Eastman, p. 58.] In the Mus)e du PetitPalais is a fine painting of Theseus and Ariadne in the Labyrinth. (tienne BEZOUT (17391783) died at BASSESLOGES, near Fontainebleu, SeineetMarne, but I can't find this on my map. There is a large maze in the Cathedral of BAYEUX, Calvados [Fisher, pp. 35, 39, 41; Pennick, pp. 116119]. The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet. BEAUMONT DE LOMAGNE see Toulouse, below. LAPLACE (1749-1827) was born in BEAUMONT-EN-AUGE, Calvados, a few miles south of Deauville. He spent his youth here and was a student at the Benedictine Priory in 1756-1765. The town square, the Place Verdun, has a fine statue of him holding a compass and leaning on a globe with books of Galileo and Newton at his feet and with medallions of Galileo and Newton on the base of the statue. At the corner of the square is a house (with two memorial inscription) believed to be on the site on his grandmother's house where he was born. However, other traditions assert he was born at the family farm or estate of (ferme du) M)risier, a bit southwest of the town (on the N175 about 1 km west of the D58), though Hinz argues that the house in the town is more likely. The townhall has a small museum with a bust, a portrait and some books. There is a Laplace grave with a grand monument in the cemetery of Beaumont. a bit south of the town hall, but this grave is empty it had been Laplace's grave in P/re Lachaise Cemetery, Paris (Section 7A1). Further south, between Lisieux and Orbec, near St. JuliendeMailloc, the home of Laplace's great-great-grandson (the Count of ColbertLaplace), the Chteau de Mailloc, burned down on 11 December 1925, destroying most of the papers and relics of Laplace. (Some had been previously lost at Arcueil (qv above) and others were lost at Caen in World War II.) In 1888 (or 1878), Laplace's body was transferred from P/re Lachaise to the Colbert-Laplace mausoleum near the Chteau. It is 200 (or 100) meters from the Lisieux-Orbec road, D519, about halfway between the two towns, starting at the bus stop by the Chapelle des quatre Mailloc (or Chapelle de Mailloc). [Archibald (2), p. 94. Whittaker, with photo of the tombstone. A.G.Howson. Hinz (with photos).] Gaspard MONGE (1746-1818) was born in BEAUNE, C=ted'Or. There is an 1849 statue of him in the Place Monge. [Brooke.] Gilles Personne de ROBERVAL (16021675) was born in BEAUVAIS, Oise. There is a fine astronomical clock in the Cathedral. [ MGG .] (However, see Roberval below.) The abbey of Le BECHELLOUIN, Eure, SW of Rouen, was an intellectual centre in the 11C. St. ANSELM (10331109) was abbot and wrote his major work here before becoming Archbishop of Canterbury in 1093. BESAN&ON, Doubs, is the clockmaking capital of France and the local Fine Arts Museum contains many examples of fine and pioneering timepieces, from hourglasses to the present time e.g. the 'most complicated watch in the world' (18971904). The Cathedral of St. John has an astronomical clock. [ MGG. ] Sylvestre Francois LACROIX (17651843) was professor here. Emile L)onard MATHIEU (1835=1890) was Professor of Pure Mathematics to 1873. Louis PASTEUR (18221895) studied art at the Royal College here in 18391842. His art was good enough that he could have been a professional artist. [Pengelley & Pengelley, p.104.] The Chteau of BLOIS, LoiretCher, has a famous spiral staircase, sometimes attributed to Da VINCI. Denis PAPIN (1647c1712), assistant to Huygens and then Boyle, the first to consider the use of steam power and inventor of the pressure cooker, Curator of the Royal Society in 16841687, was born in Blois. In 1780, Charles Augustin de COULOMB (17361806) retired to an estate here and devoted himself to research. Jean Eugene Robert, later ROBERTHOUDIN (18051871), the most famous conjurer and mechanic of 19C Europe, was born at Blois and later lived at The Priory, in nearby Saint Gervais, where he died. He built a number of automata such as a singing bird, a commercially successful alarm clock which produced a lighted taper, a famous Writer which could write answers to questions or sketch portraits. The Writer was exhibited at the Palace of Industry of the Paris Exhibition in 1844 and won a silver medal. One of his most intriguing items was the famous Mysterious Clock, whose hands were enclosed in a glass case with no connections to the outside, but kept time. The Priory was filled with electrical and other devices, including an electrical master and slave clock system which he developed and exhibited at the Universal Exhibition of 1855, receiving a Gold Medal. In 1971, France issued a postage stamp commemorating him and showing the Mysterious Clock and his suspension illusion. [Dawes, pp. 121127.] See also in Section 7A2. In mid 1998, a museum, the Maison de la Magie, was opened in a restored 19C mansion near the Chteau. This includes his famous mechanical miniature orange tree which produced real fruit and his miniature bake shop. [Paul Webster; He enchanted Queen Victoria; now Blois pays tribute to a famous son; The Guardian (17 Aug 1998) 13.] Jean Alexandre Eug/ne DIEUDONN( (19061992) was professor at the University of BORDEAUX, Gironde, to 1933. Jacques OZANAM (16401717) was born in BOULIGNEAUX (or Bouligneux), NW of VillarslesDombes, Ain, between BourgenBresse and Lyon. BOURG-EN-BRESSE, Ain, about 55 miles NNE of Lyon, is the native town of Claude-Gaspar BACHET de Meziriac (1581-1638), author of what has been called the first book on recreational mathematics: Problemes plaisans et delectables qui se font par les nombres , 1612 (2nd ed., 1624). He also produced the first printed Greek and Latin version of Diophantos' Arithmetica in 1620. (It was in Fermat's copy of this work that Fermat wrote the famous marginal note now called his Last Theorem; Fermat's son published an edition with his father's annotations in 1670, but the original copy was lost in a fire.) Bachet's other literary interests were sufficient for him to be elected one of the first forty members of the Acad)mie Fran'aise in 1635 and his contemporaries thought he was the most learned of the forty. Bachet was buried in the parish church of Notre-Dame de Bourg and his epitaph was once at the right of the main altar. [Collet & Itard, p. 31.] See also: Brou, below. The University of BOURGES, Cher, was founded by Louis XI in 1463. It was a major university for about a century, but it was a casualty of the Wars of Religion. LouisAntoine, Comte DE BOUGAINVILLE (17291811) led the first French scientific voyage, also the first French circumnavigation of the world, starting from BREST, Finist/re, on 5 Sep 1766 and returning three years later. Napoleon made him a Senator and he now rests in the Panth)on, though his heart remains at his original place of burial, the cemetery of St. Pierre, on the top of Montmartre, just west of Sacr) Coeur, Paris. One of the Solomon Islands is named for him. Oronce FINE (= Orontius Finaeus) (14941555) was born in BRIAN&ON, HautesAlpes. BROGLIE, Eure, is the seat of the De BROGLIE family. The previous owner, Prince LouisVictor de Broglie (1892??), received the Nobel Prize in Physics in 1929 for his discovery that matter had wave properties. Surprisingly, he started out as a medieval historian and was attracted to physics and his discovery "purely on the grounds of intellectual beauty". [Ward, p. 141.] BROU, Ain, near BourgenBresse, is where Joseph LALANDE (17321807) was born. At the church, he constructed a famous analemmic sundial, some 12 m across. [Peter Ransom; Sundial corner no. 4: Le Peyrou, Montpellier; BSHM Newsletter 2526 (SpringSummer 1994) 2123.] The Institut des Hautes Etudes Scientifiques was founded in 1938 at BURESSURYVETTE, Essonne, a bit SW of Paris, beyond Orsay. DIEUDONN( was here in 19591964. LAPLACE was a student at the University of CAEN, Calvados, from 1765. Henri (Paul) CARTAN (1904-) taught at the Lyc)e in 19281929. The University of CAHORS, Lot, was founded in 1331 or 1332 by Pope John XXII. Ripley's Believe It or Not Annual 1976 , p. 59, says there are many houses claiming to be the birthplace of COLUMBUS and shows a plaque on one in CALVI, Corsica (HauteCorse), but it is generally considered that he was born in Genoa (see in Section 9B). Castres see under Toulouse, below, though it is some 60 km east of Toulouse. AB(LARD (10791142) died at the Priory of S. Marcel de Chlons [Hare (2), p. 246], presumably at CHLONSSURMARNE, Marne. GERGONNE was a student at the (cole d'Artillerie in Chlons. Presumably this is the same ChlonssurMarne. Luigi Federico MENABREA (18091896) was born at CHAMB(RY, Savoie, and died in the adjacent village of St. Cassin [Giacardi & Roero, pp. 140141]. Leonardo Da VINCI (14521519) may have had some hand in the design of the Chteau of CHAMBORD, LoiretCher, which has a notable doublehelical staircase [ MGG ]. In 1847, while on a visit to Switzerland, William Thomson (later Lord KELVIN) narrates: "I was walking down from Chamounix [now spelled CHAMONIX, HauteSavoie] to commence the tour of Mont Blanc, and whom should I meet walking up but JOULE, with a long thermometer in his hand, ...." Joule was in fact on his honeymoon but was about to measure the temperature at the top and bottom of a waterfall to see if there was detectable increase at the bottom, and he detected this! [Lenihan (2), p. 17. On p. 62, Lenihan indicates he had this from one of Crowther's books, but cites the wrong one it is in: J. G. Crowther; British Scientists of the 19th Century ; Kegan, Paul, Trench Trubner & Co., 1935; Routledge & Kegan Paul, 1962, p. 188. Chamonix is in France, while the summit of Mont Blanc is in Switzerland, so it seems the events were probably in France.] Lewis Fry RICHARDSON was an ambulance driver in 19161919 and worked out an example of his numerical weather prediction, using the draft copy of his book. At the battle of CHAMPAGNE, the MS was lost, but was rediscovered some months later! The book was eventually published in 1922. His wartime experiences led him to his studies on The Mathematical Psychology of War , 1919. These are essentially based on 'predatorprey' equations and the understanding depends on graphical techniques which had not yet been recognised. (Champagne is a rather vague region mostly in the Dept. of the Marne. Jacques INAUDI (18671950) was a mental calculating prodigy. He could multiply 5digit numbers in his head at age seven and went on to become a professional calculator. Though he did not learn to read and write until he was 20 and is described as having no abilities outside mental arithmetic, his obituaries cite two books by him: Curiosit)s Math)matiques and Mes Probl/mes . Has anyone ever seen these? He lived for many years, up to his death, at CHAMPIGNY, Yonne. [Barlow, pp. 4651.] Connoisseurs of mazes will know that they occur on the floors of Gothic cathedrals. CHARTRES Cathedral (of N=tre Dame), EureetLoir, has the only original floor maze in any French cathedral, 12 metres in diameter, with a path length of 294 metres, dating from 1235 (or 12401260) [Fisher, pp. 35 & 41, with photo on p. 63 and diagrams on p. 64]. It is usually encumbered by chairs. See also: Amiens; Bayeux; Orleans; SaintQuentin; SaintOmer, above and below. At Chartres, there are figures of Aristotle and Pythagoras at the top right corner of the north door of the cathedral. [Mackinnon (2) has a photo of Pythagoras and Peter Ransom has sent a postcard of him.] In 1690, a storm caused the iron cross on a new steeple to become strongly magnetised, which occasioned an early book on magnetism by the Abb) de Vallemont in 1692. Michel CHASLES (17931880) began teaching as a private tutor in Chartres. Ren) DESCARTES (15981650 or 15961650) spent his childhood at 126 Rue de Bourbon, CHTELLERAULT, Vienne, a house which had belonged to his grandparents. It is now a Descartes Museum. La Haye, qv below, claims to be his birthsite, but some sources claim he was born somewhat unexpectedly, in a ditch along the N10 between Dang) and Chtellerault! [Crosland, vol. 3, pp. 29 & 37. Eastman, pp. 4142. MGG .] As a young engineer, CAUCHY helped build CHERBOURG harbour, Manche, in 1809-1812. This may be the largest monument of a mathematician Carath)odory working on the Aswan Dam is the only comparison I can think of. While at Cherbourg, he obtained his results on polyhedra, proved Fermat's conjecture on sums of polygonal numbers and began his work on groups [Smithies]. The Chteau of CIREY-SUR-BLAISE, Haute-Marne, was owned by the Marquis and Marquise du CHTELET. She was the translator of Newton and mistress and collaborator of VOLTAIRE during 1733 to 1748, so he often stayed there. He found it especially useful as it was in the independent Duchy of Lorraine so he could avoid French arrest warrants, particularly when he had to flee Paris after the publication of his Lettres Philosophiques in 1734. He published El)ments de la Philosophie de Newton in 1737, so much of it was probably written here. The Chteau is 6 km from DoulevantleChteau on the D2. [Crosland, vol. 3, p. 31. Eastman, p. 74.] I can't locate either of these sites on my map, but there is a Blaise on the D2 at the D40 a bit north of Chaumont. CLERMONT, Oise see Thury, below. Blaise PASCAL (1623-1662) was born in the Rue de Gras, CLERMONT-FERRAND, PuydeD=me, but the house was demolished in 1958 (shame!). It was SW of the cathedral and a slab marks the site [ MGG ]. There is a statue in the square and a Lyc)e Pascal (where Bergson taught in the 1880s). [Crosland, vol. 3, p. 31.] There is an example of his adding machine in the Mus)e de Ranquet and there is a Rue Pascal [ MGG ]. Szolem MANDELBROJT (18991983) was professor at the University of ClermontFerrand in 19301938. It was in COUTANCES, Manche, that POINCAR( was getting onto a bus and realised the connection between Fuchsian functions and nonEuclidean geometry. Jean van HEIJENOORT (19121986) was born at CREIL, Oise, about 50 km north of Paris [Philip J. Davis; Passion and structure; review of Anita Burdman Feferman: Politics, Logic, and Love: The Life of Jean van Heijenoort ; SIAM News 26:3 (May 1993) 8]. Petrus RAMUS (15151574) was born at CUTH, Picardy [Ball (5), p. 14]. I can't locate this. In DAX, Landes, is a statue of JeanCharles de BORDA. He was a mathematical seaman who worked on the survey of the meridian from Dunkirk to Barcelona and was on the commission which devised the metric system (cf under Bureau des Longitudes in Section 7A1. [Email from Peter Ransom, 29 Aug 2001.] DESCARTES see under La Haye, below. The Florentine explorer Giovanni da VERRAZANO set out from DIEPPE, SeineMaritime, on 17 Jan 1524, on the voyage that discovered New York Harbour and Manhattan Island. (He managed to miss both Chesapeake and Delaware Bays!) Samuel de CHAMPLAIN was from Dieppe. [ MGG .] ALEKHINE, the chess champion, lived in a house outside Dieppe (plaque). Charles HERMITE (18221901) was born in DIEUZE, Moselle. In the Place de la Lib)ration, DIGNE, AlpesdeHauteProvence, there is a statue of Pierre GASSENDI (1592-1655) who was Provost of the Cathedral there in 1634-1645 before becoming Professor of Mathematics at the Coll/ge Royal in Paris [Letter from Malcolm Smithers]. On 7 November 1631, he was the first person to predict and observe the transit of a planet (Mercury) across the sun. (He was probably at Aix, qv above ??) Boulevard Gassendi passes through Place de la Lib)ration. [ MGG ] and [Poole, p. 50] say he was born at nearby Champtercier. At DIJON, C=ted'Or, is a clock brought as a war spoil in 1382. It may represent the oldest extant clock but it is not running and little of the original is left [HowgraveGraham, p. 23]. According to [ MGGBelgium/Luxembourg , p. 222], Philip the Bold, Duke of Burgundy, stole the striking jacks from the belfry at Kortrijk (Courtrai), WestVlaanderen, Belgium and presented them to the (glise NotreDame in Dijon in 1382. In 1961, they were returned to Kortrijk and again top the 14C belfry (belfort) there. This information puts a different light on the previous assertion. Cf Section 10: Belgium: Kortrijk. The family of George Louis Leclerc BUFFON (1707-1788), the needle dropper and translator of Newton's Fluxions , moved to Dijon when he was ten and he attended the Jesuit school here, showing ability in mathematics. PASTEUR was Professor of Physics here before going to Strasbourg in 1849. Ren) Louis BAIRE was professor. DINAN, C=tesduNord, has a Tour de l'Horologe with a clock of 1498, though the works were actually made in Nantes [Ward, p. 179]. Louis PASTEUR (18221895) was born at D<LE (or Dole), Jura, but moved to nearby Arbois when he was five. The Maison Natale de Pasteur, 43 rue Louis Pasteur, is now a museum. There is a statue in a nearby park. [Pengelley & Pengelley, pp.103-107 & 108109.] (lie Joseph CARTAN (18691951) was born and went to school in DOLOMIEU, near TourduPin, Is/re (not on my maps). In the 1790s, DELAMBRE and M)chain measured the meridian from DUNKERQUE (Dunkirk), Nord, to Barcelona to determine the length of the kilometre which was to be 1/40,000 of the polar circumference of the earth. They finished in 1799. See also Barcelona, Spain, in Section 10. JeanJacques ROUSSEAU (17121778) spent his last weeks at ERMENONVILLE, Oise, about 10 km SSE of Senlis. He was buried on the 2le des Peupliers in the lake there. On 11 Oct 1794, his remains were translated to the Panth)on. [Pierre Chevallier & Daniel Rabreau; Le Panth)on ; English translation by Kathleen Wilson Chevalier [sic]; Caisse nationale des Monuments et des Sites, 1977, p. 15. EB .] ESTAGEL, Pyr)n)esOrientales, about 20km west of Perpignan, is where ARAGO was born and lived until he was about seven [Arago, pp. 1 & 3]. Many of the cities and towns in the area have features named for him. FERNEYVOLTAIRE, Ain, is on the Swiss border and is a suburb of Geneva so is mentioned under Switzerland in Section 10. JeanFran'ois CHAMPOLLION (17901832) was born at FIGEAC, Lot. Sebastiano SERLIO (14741554) died at FONTAINEBLEU, SeineetMarne. Cf AncyleFranc, above, and under Sheldonian Theatre in Section 5A. After the outbreak of the Franco-Prussian War in 1870, Sophus LIE tried to return from Paris to Germany by walking to Italy. He was arrested as a German spy in Fontainebleu and imprisoned for a month. [Beckert & Schumann, p. 112.] See also BassesLoges, above. Fran'ois VI.TE (= VIETA) (1540-1603) was born at FONTENAY-LE-COMTE, Vend)e [Archibald (3), p. 81]. (Older sources describe this as being in Poitou.) BOREL, then aged 70, and three other Academicians were imprisoned at FRESNES in 1941 for some years on suspicion of Resistance activities [Collingwood]. Presumably this is the town about 11 km south of Paris, in the ValdeMarne. Jacques de VAUCANSON (17091782) was born in GRENOBLE, Is/re. Jean Baptiste Joseph FOURIER (1766?1830) was Prefect of the Department of Is/re, whose capital is Grenoble, from 1802 to 1817 (1815??) [Eves (6), p. 58; Math. Intell. 10:2 (1988) 51], where he organized the drainage of the marshes of Bourgoin [Arago, pp. 405406]. While there, he managed to get a young professor of history, named CHAMPOLLION, deferred from army service [Arago, p. 407]. Despite his administrative duties, Fourier produced his Th)orie Math)matique de la Chaleur ! Apparently he had been made a baron by Napol)on and during Napol)on's return from Elba in 1815, he made Fourier a count and Prefect of the Rhone, based at Lyons, from 10 Mar to 1 May. Marie Henri Beyle [= Henri STENDHAL] (17831842) was born in Grenoble and studied mathematics at the Central School there. He wrote of his difficulties with the rule of signs in his semiautobiographical Vie de Henry Brulard . (lie CARTAN attended the Lyc)e JeansondeSailly in Grenoble until 1888 when he went to the (cole Normale Sup)rieure. HONFLEUR, Calvados, across from Le Havre, was a major port for exploration. CHAMPLAIN set out to found Quebec in 1608 and La SALLE set out in 1681, travelling the length of the Mississippi and naming the region Louisiana [ MGG ]. [Ward, p. 305] indicates that DESCARTES (15981650 or 15961650) grew up at the manor house of KERLEAU, between Vannes and Elven, Morbihan. LA FL.CHE, Sarthe, had a noted Jesuit College Henri IV or Coll/ge Royal where DESCARTES (in 16071615 [Scott, p. 1, says 16041612 this probably depends on which date of birth is used]) and Marin MERSENNE were students. When the Jesuits were expelled in 1803, it became a military preparatory school, reorganized as a military school by Napol)on in 1803. It is today the Prytan) Militaire and may be visited. [Eastman, pp. 4142.] LA HAYE, IndreetLoire, about 45 km south of Tours, is thought to be the birthplace of Ren) DESCARTES (15981650 or 15961650 [Scott, p. 1]) and the town now calls itself La Haye-Descartes or even just Descartes. The probable birth house, which was his great-grand-mother's, is a monument, with a plaque and statue, though [Alexanderson] says the statue is in front of the Town Hall. Other sources say he was born near Chtellerault, qv above. He was baptised in St. George's. He visited his family here in 1644 and 1648. [Crosland, vol. 3, p.37. Scott, pp. 1 & 56.] Denis DIDEROT (1713-1784) was born in his father's house in LANGRES, HauteMarne, now 6 Place Diderot. There are some mementoes in the H=tel du Breuil Saint-Germain. [Crosland, vol. 3, pp. 38-39.] PASTEUR was Professor at the University of LILLE, Nord, in 18541857 and began his studies on fermentation [Pengelley & Pengelley, pp.104-105]. BOREL taught at the University in 18931897 [Collingwood]. Henri CARTAN taught here in 19291931. MANDELBROT taught here. (Marie Fran'ois) Sadi CARNOT (18371894), of the distinguished family of scientists and politicians, was born in LIMOGES, HauteVienne [ MGG ]. Nicole ORESME (1323?1382) was Bishop of LISIEUX, Calvados, about 30 km south of Le Havre, from 1377 until his death there in 1382. He was the first to write scientific works in French and apparently the first to suggest an International Date Line. Gabrielle (Emilie le Tonnelier de Breteuil, Marquise du Chtelet) du CHTELET died in childbirth at LUNEVILLE, MeurtheetMoselle, where she is buried under an unmarked black marble slab in the church of Saint-Jacques. [Crosland, vol. 3, p. 40.] On the right side of the southern west doorway of St. John's Cathedral (Primatiale StJean) in LYON (Lyons), Rh=ne, there is a quatrefoil panel with four rabbits having four ears, from about 1315 [HamannMacLean, pp. 400403; DBS my photo is rather better than HamannMacLean's, possibly because his was taken before the facade was cleaned in 1982]. See in Section 11 for other sites. There is a fine striking ASTRONOMICAL CLOCK in the north transept of the Cathedral, first recorded in 1393 and restored, repaired and/or extended from 1572, in 1660-1662, in 1779, 1894, 1954 and 1993. [N. Reveyron; Primatial Church of SaintJohntheBaptist, Cathedral of Lyon ; Translated by Val)rie Thollon & Diana Sarran. Association Lyon Cath)drale, Lyon, nd [c2000], pp. 5862] gives an extended description and photos. There is also a handsome external clock face, but it's not stated whether the two are connected. In the Place de la CroixRusse, visible from the CroixRousse Metro exit, there is an 1840 monument to Joseph Marie JACQUARD (1752-1834): Inventeur du metier pour la fabrication des etoffes de luxe. [ Chambers Encyclopedia , 1885], says this is in 'the main square' of Lyon, on the spot where silk weavers broke up his punched-card controlled loom. I had some trouble locating it, but eventually someone in one of the tourist information offices knew where it was. The base of the statue has an inscription saying the statue was first erected in the Place St. Anthony but was moved to its present location in 1901. However, there is currently no Place St. Anthony (or St. Anthoine) in Lyon, but local leaflets say the CroixRousse area was a centre of the silkweaving business. The base also says Jacquard was born in Lyon and died in Oullons, presumably the southern suburb of Lyon. At the back of Jacquard is a plaque showing a loom in use. Didier-Petit & Co., Quai de Retz no. 34, were the weavers who made the silk portrait of Jacquard. Babbage stopped here to buy one en route to Turin in 1840. [Hyman, p. 182.] In the Mus)e des Tissus, there is a model of JACQUARD's original 1801 mechanism [Anna P. Benson; Textile Machines ; Shire, Aylesbury, 1983, p. 23]. There is a Museum of Printing and Banking (Mus)e de l'Imprimerie et de la Banque) [ MGG ]. Jacques OZANAM (16401717) was initially a teacher in Lyon. During Napol)on's return from Elba in 1815, he made FOURIER a count and Prefect of the Rhone, based at Lyon, from 10 Mar to 1 May. Andr) Marie AMP.RE (17751836) was born in Pol)mieux, near Lyon [ MGG ], but I cannot find this in my French maps. Jean Fr)d)ric FRENET (18161900) was professor at the University of Lyon and Director of the Observatory. MarieEnnemondCamille JORDAN (18381922) was born in Lyon [Biggs, Lloyd & Wilson, pp. 217218]. (lie CARTAN was lecturer at the University in 18961903. MARSEILLES, BouchesduRh=ne, was a Greek colony and had a Greek university around 1C, 'the last refuge of Greek teaching in the West' [ MGG ]. Lucas was attending a meeting of the Association Fran'aise pour l'Avancement des Sciences in Marseilles, a stack of plates fell, a piece hit his cheek, the wound became infected and he died about a week later. Andr) WEIL taught at the University in 19321933. M(LUN, SeineetMarne, on the Seine, about 40km south of Paris, is where LAPLACE was staying in 1793 when BAILLY came to visit and was arrested [Arago, pp. 222224]. JacquesFr)d)ric FRAN&AIS (17751833) was Professor of the Military Art at the (cole d'Application du G)nie et de l'Artillerie in METZ, Moselle, in 18111833. In 1813 he published a memoir on complex numbers, based on results in a letter to his late brother, Fran'ois Joseph Fran'ais (17681810), from Legendre, who had got the ideas from an anonymous booklet. This turned out to be Argand's Essai and this publication made the ideas widely known. Am)d)e MANNHEIM (18311906) was Lieutenant of Artillery at Metz when he devised the Mannheim slide rule in 1850. By the 1860s, it was popular throughout Europe and by the end of the century, it was common throughout the world [Thompson, pp. 1314]. Gaspard MONGE (1746-1818) attended the military school at M(ZI.RES where his development of descriptive geometry led to a professorship in 1768 and to the subject being declared a military secret [Brooke]. I presume this is the M)zi/res in HauteVienne. BOREL went to the Lyc)e in MONTAUBAN from age 12 [Collingwood]. I presume this is the Montauban in TarnetGaronne. (Le Comte) George Louis Leclerc de BUFFON (1707-1788), the needle dropper and translator of Newton's Fluxions , was born in MONTBARD, C=ted'Or. At age 10, the family moved to Dijon. He later lived intermittently at his country estate in Montbard. There are several sites associated with him, including the Chapelle de Buffon where he is buried. [Crosland, vol. 3, p. 46.] There is a small village named Buffon nearby. He carried out experiments in ironsmelting and set up an ironworks on his estate in the 1770s. A medical school was founded at MONTPELLIER, H)rault, in 1137 which is sometimes claimed to be Europe's first, but Salerno seems to be earlier, in 1096. Montpellier is certainly the oldest extant medical school in Europe. Montpellier became a university in 1287. But [Pengelley & Pengelley, pp. 110112] say the Faculty of Medicine, and hence the University, was founded by Cardinal Conrad, the Papal Legate, on 17 Aug 1221. But Pengelley & Pengelley add that medicine had been studied at Montpellier in rabbinic schools going back to the 11C. JosephDiez GERGONNE (17711859) was Professor of Astronomy at the University (or Acad)mie) of Montpellier, H)rault, from 1816, then Rector from 1830 (1831?) until he retired in 1844. PierreOssian BONNET (18191892) was born in Montpellier. The Faculty of Medicine has a bust of CARDAN [Letter from Peter Ransom, 28 Jul 1993]. In the park near the Roman aqueduct is a 1926 analemmic sundial where the observer acts as the gnomon [Peter Ransom; Sundial corner no. 4: Le Peyrou, Montpellier; BSHM Newsletter 2526 (SpringSummer 1994) 2123.] (lie CARTAN was lecturer at the University in 18941896. Jacques CARTIER met King Fran'ois I at MONTSTMICHEL, Manche, in 1532 and was commissioned to explore northern America. There is a commemorative plaque near the main staircase. [Ward, p. 130.] Cf SaintMalo, below. LUCAS taught in a lyc)e in MOULINS, Allier, in 18721876. JosephDiez GERGONNE (17711859) was born in NANCY, MeurtheetMoselle. In Nancy, there is said to be a statue of General Charles Denis Sauter BOURBAKI (Pau, 1816 Bayonne, 1897), believed to be the eponym of the mathematician [Eves (2), pp. 134-135]. However, on a visit to Nancy, no one in the mathematics department nor the tourist office knew of such a statue. See under Paris (Section 7A2) and Strasbourg, below, for more about the history of Bourbaki. One correspondent notes that it is typical of Bourbakis not to be where they are expected. The University was transferred from Pont!Mousson to Nancy by order of Duke Stanislas in 1769. The old Universit) de Nancy buildings include an Instituts de Math)matiques et Physiques at the corner of Rue de Fr/res Henry and Rue de la Craffe this has the name carved on the facade, with the main branches of physics and mathematics carved along the sides of the building. Under Math)matiques are: G/om/trie, Analyse, M/canique, Astronomie. Emile L)onard MATHIEU (18351890) was professor from 1873. There is a Place CARNOT, but it is named for and contains a statue of (Marie Fran'ois) Sadi Carnot (1837-1894), engineer and President of France from 1887, a later member of that illustrious family. Henri POINCAR( (18541912) was born at 2 Rue de Guise in the old city. At some point he taught at the University and it is now named for him. There is also a Lyc)e Henri Poincar). There are two Rue Poincar)s one named Henri Poincar), adjacent to the Lyc)e, and one named for his cousin Raymond, onetime President of France. Henri LEBESGUE (1875-1941) taught at the Lyc)e Central in Nancy during 1899-1902 while creating his theory of integration. The present Institute of Mathematics was created in 1953 and was named for (lie Joseph CARTAN (1869-1951) who was professor in 19031909. Henri CARTAN was born here in 1904. Nancy was one of the spiritual homes of Nicolas BOURBAKI, whose books say he is professor at Nancago. When I was a student in the 1960s, it was claimed that several libraries had actually spent many weeks trying to locate Nancago! Jean DELSARTE, one of the moving spirits of Bourbaki, taught at Nancy from 1928 until his death in 1968, becoming Dean of the Facult) des Sciences. GROTHENDIECK was a student of his. DIEUDONN(, DUBREIL, GODEMONT, LERAY, LIONS, L. SCHWARTZ, came to teach here under Delsarte's influence. DIEUDONN( was professor in 19371955. JeanPierre SERRE (1926 ) was Chairman of the Science Faculty in 1954=1956. The Museum of Lorraine History (Mus)e Historique Lorrain), Grande Rue, is in the heart of the old city. It contains two fine brass globes (terrestrial and celestial) and a set of diagrams for designing sundials engraved on a large piece of slate, from the early 17C. There is a room devoted to the scientific interests of the 18C Duke Stanislas, who founded an Academy in Nancy it contains telescopes, microscopes, clocks, watches, dials, quadrants, a dividing engine, related books, etc. In late autumn 1903, the University of Nancy was the origin of one of the greatest scientific delusions of all time comparable to the more recent cases of polywater and cold fusion. The Professor of Physics, R. Blondlot, announced the discovery of a new type of 'rays', but their only manifestation was that they caused faint light sources to become slightly brighter. Blondlot named them 'N rays' to commemorate Nancy. By the next summer, some 50 papers had appeared from Blondlot and several other investigators and the French Academy awarded him the Lalande Prize of 20,000 francs and its gold medal. However, many other investigators could not obtain any results and the American physicist R. W. Wood, visiting Cambridge for a BAAS meeting in September, was encouraged to go to Nancy to investigate. Wood soon realised that Blondlot's observations were delusions and confirmed this by making substitutions of materials in the darkened laboratories. He then removed the aluminium prism which was the key component of Blondlot's spectroscope and found that Blondlot's observations were not affected! Blondlot's assistant began to suspect Wood and asked to check the observations. Wood pretended to remove the prism, but left it in place, but the assistant announced that no Nrays could now be detected. Wood promptly informed Nature of his findings and N rays disappeared. Sadly Blondlot soon went mad and died. [Weber, pp. 7779 excerpts Wood's description of his visit.] Peter (= Pierre) AB(LARD (10791142) was born at Le Pallet, near NANTES, LoireAtlantique [ MGG Brittany , p. 31]. (tienne BEZOUT (17391783) was born at NEMOURS, SeineetMarne. Henry CAVENDISH (17311810) was born in NICE, AlpesMaritimes, because his mother had gone there for her health [Ball (5), p. 114; Low, p. 41]. GERGONNE was Professor of Transcendental Mathematics at the (cole Central, N2MES, Gard, c1810, when he founded the Annales de math)matiques pures et appliqu)es, the first mathematical journal. It appeared monthly until 1832. (Jean)Gaston DARBOUX (18421917) was born in N2MES. AB(LARD retired to a hermitage, called the Paraclete, at NOGENTSURSEINE, Aube, in c11241126, but students continued to flock to him [Okey, p. 92]. He was buried here and H)lo5se was buried beside him, but the tomb was removed to safety during the Revolution and then to P/re Lachaise in Paris in 1817. Lazare Nicolas Marguerite CARNOT (17531823) was born at NOLAY, C=ted'Or, near Beaune. Marin MERSENNE (15881648) was born near (or in) OIZ(, Maine, on 8 Sep 1588. (I can't locate this. Maine is an old province, roughly comprising modern Mayenne and Sarthe.) The church of St. Euverte, ORLEANS, Loiret, has a large 13C floor labyrinth [Fisher, p. 41]. ORNANS, Doubs, was the native town of Pierre VERNIER (15801637). He was commandant of the castle when he published the Vernier scale method in 1631. [Espy, p. 103.] By 1870, verniers allowed measurement of ' of arc. North of PAIMPOL, C=tesd'Armor, the area towards Arcouest Point has long been a popular summer resort for artists, academics and writers. Fr)d)ric and Ir/ne JOLIOTCURIE were frequent visitors and are commemorated by a monument of two identical blocks of pink granite below the smaller car park. [ MGG Brittany , p. 172.] [Philip S. Watson; The Giant's Causeway ; HMSO, Belfast, 1992, p. 1] says there is a columnar basalt formation similar to Giant's Causeway (cf Section 6D) at PAV( DES G(ANTS in France, but I haven't yet located this. Fran'ois ARAGO (17861853) was born at Estagel, near PERPIGNAN, Pyr)n)esOrientales [ MGG ]. His family moved to Perpignan about 1793, where the father was treasurer of the mint [Arago, p.3]. There is a Place Fran'ois Arago and also a Bd. Henri POINCAR(. The mountain of PIC DU MIDI DE BIGORRE, HautesPyr)n)es, in the central Pyrenees, has a major observatory. The first observations of the solar corona during an eclipse were made here in 1706. [ MGG . Sim)onDenis POISSON (17811840) was born in PITHIVIERS, Loiret, about 70km S of Paris. There is a plaque on his birth house. (Peter Ransom has sent photos.) In PLEUMEURBODOU, C=tesd'Armor, is the Rad=me et Mus)e des Telecommunications. This was the European end of the first transatlantic satellite communication via Telstar on 11 Jul 1962. An extensive museum has been made on the site, using the original radar dome. [ MGG Brittany , p. 179. Ward, p. 208.] Fran'ois VI.TE was a student at the University of POITIERS, Vienne. DESCARTES spent about a year as a student in 16151616 [Scott, p. 1]. Poitiers has the modern Futuroscope The European Park of the Moving Image. Pol)mieux see under Lyon. PONT MOUSSON, MeurtheetMoselle, about 30 km north of Nancy, was the seat of a Jesuit university from 1572 until it was translated to become the University of Nancy in 1769. One of the most famous and popular of recreational mathematics books, Recreation Mathematicque , appeared here in 1624 and went through at least 56 editions over the next century. The book bears the name Hendrik VAN ETTEN, but has long been attributed to his teacher Jean Leurechon, though the reasons for this are not very compelling. See my The Bibliography of some Recreational Mathematics Books for details. The old university buildings by the river are now the Lyc)e Jacques Marquette, commemorating Father Marquette, the discoverer of the Mississippi, who taught here. The famous Jansenist abbey of PORT-ROYAL-DES-CHAMPS, Yvelines, where PASCAL spent many years, was about 12 km SW of Versailles on the D91. It was the centre of religious controversy in the mid 17C and was suppressed in 1660, then closed in 1709, when troops moved out the nuns with only 15 minutes notice and then pulled down all the buildings and ploughed over the site [Okey, p. 232; Scott, p. 200]. Only the ruins remain. The famous episode of Pascal's toothache being relieved by study of the cycloid took place here in 1658. PUYDED<ME is a mountain a bit west of ClermontFerrand and gives its name to the D)partement of PuydeD=me. It is 1465 m (= 4806 (or 4888) ft) high. On 19 Sep 1648, PASCAL arranged for his brotherinlaw Florin (or Fran'ois) P)rier to measure the height of a column of mercury in a tube at the top. He found it was 8.4 cm shorter than at ClermontFerrand, conclusively proving Torricelli's assertion that the column was supported by the weight of the atmosphere. [ MGG ]. Pascal had obtained the glass tube from the glassmakers of Rouen where my source claims Pascal was living at the time. VOLTAIRE was a guest at the Chteau of La Rivi/reBourdet, QUEVILLON, SeineMaritime, for a period c1723 when he was exiled from Paris [Eastman, p. 74]. I cannot locate this, but there are two suburbs of Rouen with the name Quevilly. The world's largest maze (in 1997) was at REIGNAC SUR INDRE, IndreetLoire. A local architect named Bernard Ramus read about the maize mazes in the US (see under Shippensburg in Section 10: USA). His partner, Isabelle de Beaufort, built a small version in 1996 and was amazed when 80,000 visitors came, with 3000 in one day. So she developed the idea to having the field deliberately planted as a maze the American versions were cut through ordinary plantings. The 1997 version covered 37 acres and had six different mazes, of different styles. [Paul Webster; Lost days in world's largest maze; The Guardian (18 Jul 1997) 16.] The Cathedral at REIMS (or Rheims), Marne, had a great floor maze, constructed in 1240. It was destroyed by Canon Jacquemart in 1779 because he couldn't stand the noise of children tracing the maze during mass. DESCARTES' father was a member of the parliament of Brittany which sat at RENNES, IlleetVilaine, and [Scott, p. 1] says the family frequently stayed there when Descartes was young. He spent the winter of 1622-1623 there and visited his family there in 1625 [Scott, pp. 23]. DIEUDONN( (19061992) was professor at the University of Rennes in 19331937. Gilles Personne de ROBERVAL (1602-1675) was a native of the town of ROBERVAL, about 13 km NE of Senlis, Oise [Archibald (3), p. 81]. But the MGG says he was born at Beauvais, cf above. In the Chapelle Miraculeuse at ROCAMADOUR, HauteVienne, is a "miraculous clock, one of the oldest known and dating back perhaps to the 4th century. It is made of iron and rings out of its own accord to foretell miracles." [ Dordogne Perigord Limousin Quercy (Michelin Green Guide); 1st ed., Dickens Press, London, 1965; pp. 151152]. A 4C clock would be quite remarkable even it wasn't miraculous. I wonder if this is a misprint for 14C ?? Sylvestre Francois LACROIX (17651843) was professor at ROCHEFORT, CharenteMaritime, early in his career. DESARGUES worked on the fortifications of La ROCHELLE, CharenteMaritime, where Descartes visited him [Pedoe]. It is claimed that DESCARTES took part in the siege in 1628, but the evidence is only one 17C mention of it [Scott, p. 3] this may be what Pedoe is referring to ??. La Rochelle was also a port for explorers de la Salle set out from here and explored the Mississippi [ MGG ]. Ren) Antoine Ferchault de R(AMUR (16831757), of the temperature scale, was born in La Rochelle. John Theophilius DESAGULIERS (1683-1744), the scientific expositor, was born in La Rochelle, but went to Oxford to study and generally remained in England. The Chteau of ROCHERSS(VIGN(, IlleetVilaine, has a 'whispering wall' (my term) in the garden which was laid out by Le N=tre. [ MGG Brittany , p.212] states it is semicircular and gives a 'double echo'. It also says that the talkers should stand at two points marked by stones, so I think it is probably a semielliptical wall. Mme. de S)vign) (16261696), the 17C writer, lived here and refers to it as "that little wall that repeats words right into your ear". On the portal of the Library of the Cathedral of ROUEN, SeineMaritime, is a sculpted example of the 'two heads, four men' pattern, neatly enclosed in a quatrefoil frame, dated to 12901300. This is the oldest physical version of the idea which is the predecessor of the 19C Dead Dogs puzzle and Sam Loyd's Trick Ponies. (An English psalter of the end of the 13C has a 'two heads, four horses' pattern, but it may derive from Islamic sources.) The pattern also occurs on a misericord in the Cathedral and on the Palace of Justice in Rouen. The city clock (Gros Horologe) in Rue du GrosHorologe is probably the oldest extant clock, built in 1379. It has only one hand. It was moved to its present site in 1529 it had been on the adjacent belfry was too difficult to see. It was converted to pendulum control and ran until 1929 when the works were replaced by electric motors [HowgraveGraham, p. 23; Ward, pp. 7980]. Earliest known clock to have chiming at quarter hours [F.A.B. Ward, p. 21]. Bernard Le Bovier de FONTENELLE (16571757) was born in Rouen. (mile BOREL (18711956) was born in SAINTAFFRIQUE, Aveyron, and attended a school run by his father until age 12. He remained associated with the town all his life. By 1924, he was Maire of SaintAffrique and Conseiller G)n)ral for Aveyron. He was elected Deputy for SaintAffrique in 1924 and served in the following two parliaments until 1936. He is buried there. [Collingwood.] After the affair with H)lo5se and his retirement to the Paraclete, Peter (= Pierre) AB(LARD (10791142) became abbot of SAINTGILDASDERHUYS, Morbihan, in 1126. He found the country and the monks both savage and the monks were sufficiently antagonistic to him that they tried to poison him and he only escaped through a secret passage in 1132. [ MGG Brittany , pp.31 & 219. Ward, p. 308.] Joseph Louis GAYLUSSAC (17781850) was born at SAINTL(ONARDDENOBLAT, HauteVienne and there is a Rue GayLussac there [ MGGDordogne Perigord Limousin Quercy. ]. On 20 Apr 1534, Jacques CARTIER set out from SAINTMALO, IlleetVilaine, and discovered the mouth of the St. Lawrence River and Canada. He applied the Huron word Canada, meaning village, to the whole area. On 19 May 1535, he set out on his second voyage and explored the area further, reaching modern Montreal where the rapids were impassable, and wintering over. His third voyage, in 1541, found little new. StMalo commemorates him in the name of one of its main docks and his head is preserved in a reliquary in the Cathedral of St. Vincent. There is material on him in the Mus)e d'Histoire de la Ville et d'Ethnographie du Pays Malouin. He retired to a farm called Limo-lou in the nearby village of Roth)neuf and his manor house in Rue David Macdonald Stewart is a museum. [ MGG Brittany , pp.221, 224 & 226.] Pierre Louis Moreau de MAUPERTUIS (1698-1759), the first French advocate of Newton's work and the first to accurately measure the earth (see Section 7A2), was born in StMalo and lived in the Rue de la Harpe [Crosland, vol. 3, p. 56]. There is also material on him in the Mus)e d'Histoire de la Ville et d'Ethnographie du Pays Malouin. [ MGG Brittany , p.224.] He was President of the Berlin Academy of Sciences for some time. Julien Offray de la MATTRIE (17091751) was born in StMalo. His L'Homme Machine of 1748 first clearly asserts that man is a thinking machine. [Richard L. Gregory; Mind in Science ; Weidenfeld and Nicolson, London, 1981, p. 381.] [ MGG Brittany , pp.222 & 224] says LAMMENNAIS (17821854) taught mathematics in the College here before entering the local seminary. He later lost his faith and was a controversial writer, serving a year's imprisonment in 1840, but being elected to the National Assembly in 1848. There is also material on him in the Mus)e d'Histoire de la Ville et d'Ethnographie du Pays Malouin. Albert GIRARD (15951632) is believed to have been born at ST. MIHIEL, Meuse. There is a large maze in the Abbey of St. Bertin at SAINTOMER, PasdeCalais, (1109) [Fisher, pp. 41 & 67 with diagram on p. 66, states this was destroyed in the 18C and another book says it was destroyed; Pennick, pp. 116119, 121 gives a diagram; MGG indicates it still exists]. There is a large maze in the church of SAINTQUENTIN, Aisne, (1495) [Fisher, p. 39 with diagram on p.38; Pennick, pp. 116119]. SCEAUX, Hts. de Seine, is treated as part of Paris, though it is a distant suburb see under Curie in Section 7A2. The Paris church had denied a request for a Christian burial for VOLTAIRE, so his corpse was dressed as if alive and driven to the Abbey of SEILLI.RES (or Scelli/res), near Romilly(surSeine), Aube, about 35 km NW of Troyes, where his nephew, Abb) Migot, was the abbot and gave him a Christian burial [Culbertson & Randall (3), pp. 9697]. [Dave Dutton; Horrors ; Futura, London, 1989, pp. 4041] states that when the Abbey was sold, the body was exhumed and there was a scramble for relics until the government decreed his body belonged to the state. Nonetheless, the left foot and two teeth disappeared before he was reinterred in the Panth)on in 1791, qv in Section 7A1. [Pierre Chevallier & Daniel Rabreau; Le Panth)on ; English translation by Kathleen Wilson Chevalier [sic]; Caisse nationale des Monuments et des Sites, 1977, pp. 1415.] The Church of St. Stephen in SENS, Yonne, was the site of a debate between AB(LARD and St. Bernard in c1132. However, St. Bernard simply denounced a number of statements in Ab)lard's writings and refused to debate. Ab)lard withdrew in disgust and was condemned to perpetual silence! [Okey, pp. 9293.] S.VRES, Hts. de Seine, is also treated as part of Paris though it is a distant suburb. Johannes GUTENBERG (c13981468) lived in STRASBOURG, BasRhin, from 1433 to 1445. In 1434-1444, he was at the Inn of the Crossed Swords, believed to have been somewhere near the present Place Gutenberg. By 1440 he had developed all the necessary techniques and equipment to carry out printing, but no example is known. In 1445 (or 1444), he left Strasbourg and nothing is known of him until he reappears in his native city of Mainz (qv in Section8) in 1448 and starts printing there. There is a statue of him in the Place Gutenberg, holding a sheet with "Et la lumi/re fut" ("And there was light"). [Eastman, p. 47. DBS.] Strasbourg Cathedral has perhaps the most elaborate of all astronomical clocks. The earliest version was built in 13521354, including an automaton cock, now in the Museum of Decorative Arts in Palais Rohan, said to be the oldest automaton extant [Hillier, pp. 1920 with photo on p. 20]. In the early 16C, the original clock died and a new one was built in 15711574 on the east side of the south transept, under the direction of the mathematician and astronomer Conrad DASYPODIUS (15311601). The cock continued to be part of the new clock. Although Copernicus' book had appeared forty years earlier, the clock was based on the Ptolemaic system, possibly because some work had started in 15471548. It was soon confused by the change to the Gregorian calendar in 1582, though this wasn't adopted in Strasbourg for another century. In 1788, the clock stopped completely. JeanBaptiste SCHWILGU( (17761856), a selftaught mechanic, renovated and extended it in 18381842, when many of the 16C parts were transferred to the Museum of Decorative Arts including the cock, but a copy of it was installed in the new clock. The basic structure is that of the 16C clock it stands 18 m high and the base is 7.3 m wide. At the top of the left tower is a painting of Urania, the muse of Astronomy, with wings labelled Geometria and Arithmetica and adorned with appropriate symbols. Just below is a portrait of COPERNICUS, labelled "Nicolai Copernici vera efigies ex ipsius autographo depicta". This is a 16C copy from the selfportrait of Copernicus which had been borrowed from Danzig it is the only extant version of the selfportrait [Armitage, p. 121]. Below Copernicus is a portrait of Schwilgu). The most elaborate operation of the clock takes place at 12:30, which is local noon. Tickets go on sale at 11:50 in summer and 12:00 in winter. [Roger Lehni; Strasbourg Cathedral's Astronomical Clock ; (ditions la Go)lette, Paris, 1992.] Lehni's guide to the Cathedral says that the clock drives the handsome outside clock over the nearby south door of the Cathedral. The Collegium Wilhelmitanum (Thomasstift) has a contemporary oil painting of KEPLER, the only picture from his later years (perhaps the only authentic portrait), which Kepler sent to Matthias Bernegger in 1619 [Gerlach & List, p. 14, with colour plate on p. 15; Seck, pp. 5657; Boll, p. 18]. PASTEUR was Professor of Chemistry here for five years, 18491854, and did most of his studies on crystals and stereoisomers here [Wymer, p. 2:1012]. He married Marie Laurent, daughter of the Rector of the University [Pengelley & Pengelley, p.104]. Elwin Bruno CHRISTOFFEL was professor from 1872. Wilhelm Conrad R>NTGEN (18451923) worked here for some time in the 1870s. Heinrich WEBER (18421913) was Professor here from 1895 and died here. Maurice Ren) FR(CHET (18781973) was professor in 19191928. Henri CARTAN taught here from 1929, with a two year break at Lille in 19291931. Andr) WEIL (1906?1998) was professor in 19331940. Weil recalls that Cartan constantly pestered him with questions about how to present material and that on a winter day in late 1934, he suggested that they and their friends ought to get together and organize the material in the best way and so BOURBAKI was born. The founding members were H. Cartan, Chevalley, Delsarte, Dieudonn), Mandelbrojt, Weil and some others who dropped out. Weil is credited with being the moving force of the group [Cartan]. The name Bourbaki was derived from a Napol)onic general Charles Denis Sauter Bourbaki (Pau, 1816 Bayonne, 1897) whose name had been used in a student prank lecture at the (cole Normale in 1923. In 1948, it was discovered that the Nicola5desBourbaki family is a distinguished Cretan family, one of whom had assisted Napol)on's expedition to Egypt and whose son was consequently allowed to attend a French military school and whose descendent (grandson?) was the eponymous general. [Andr) Weil; The Apprenticeship of a Mathematician ; Birkhuser, 1991. Excerpted in Birkhuser's Mathematics Quarterly, Winter 91/92, pp. 36.] See also: Paris (Section 7A2) and Nancy, above. VOLTAIRE was a guest at the Chteau of Sully, SULLYSURLOIRE, Loiret, for a period of six months in 1716 when he was exiled from Paris [Eastman, p. 74]. THURY, near Clermont, Oise, was where the CASSINI family had their country estate see under Observatory in Section 7A1 and Cassini in Section 7A2. Pierre (de) FERMAT (1601-1665) was born in Beaumont de Lomagne, near TOULOUSE, HautGaronne [Eves (6), p. 5]. Peter Ransom has sent a photo showing a plaque on the house and an adjacent plaque saying that the tower of the house is 15C. Ransom also sent a photo showing the street name sign Rue Pierre Fermat near the birthplace. The 'de' was added when he became a Conseiller to the Toulouse Parliament. He died in Castres, some 60 km to the east. According to Eves [Eves (4). p. 12; Eves (6), p. 6], he was buried in the Church of the Augustines in TOULOUSE. The tombstone was later moved to the local museum. ([Alexanderson] does not mention this.) Fermat was originally buried in St. Dominique in Castres, and was moved to the Augustinian Church in 1675. There is a portrait of him in the local Acad)mie des Sciences and a Rue Fermat near the Pr)fecture [Alexanderson]. Robin Whitty tells me that the leading school in Toulouse is the Lyc)e Pierre Fermat. Thomas Jan STIELTJES (18561894) was professor at the University in 1886-1894 [Archibald (3), p. 76] and died there. Edouard JeanBaptiste GOURSAT (18581936) was Professor of Analysis in 18811885. ALCUIN of York retired to be abbot at TOURS, IndreetLoire, c800, and died here. There is a statue of DESCARTES, labelled "Cogito, Ergo Sum", in Tours, facing the Loire by Pont Wilson. AdrienQuentin BU(E (17481826), one of those who developed complex numbers in the early 19C, was organist at St. Martin in Tours. Henri BERGSON (18591941) stayed at La Gaudini/re. (lie CARTAN was a student at a coll/ge in VIENNE, Is/re. Abraham DE MOIVRE (16671754) was born and went to school in VITRY, Champagne, but there is no known monument. Presumably this is VitryleFran'ois, Marne.  8. MONUMENTS IN GERMANY.  I have given Land names when I can determine them. I did not originally separate West (DBR) and East (DDR), which was fortunate as they have reunited. Many details come from [Beckert & Schumann] and [Polya]. Gauss is commemorated on the current 10DM note and there was a commemorative stamp to him in the 1970s?? About 1985, a group of mathematicians in East Germany began collecting information on 'material evidence' (Sachzeugen), which includes everything covered in the present collection. It was planned to publish a book with Teubner, but with the unification, it has been decided to extend it to all Germany and so the publication has been deferred. Peter Schreiber (Fachbereich der Mathematik, ErnstMoritzArndtUniversitt Greifswald, F.L.Jahn Strasse 15a, D2200 Greifswald, Germany) is director of the project. [Schreiber.] GAUSS made an attempt to determine if the angles of a triangle added up to 180o. He measured between three mountain tops: Brocken in Harz (1142 m); (Grosser) Inselberg in the Thuringian forest (ThGringer Wald) (916 m); Hohenhagen (or Hoher Hagen) at Dransfeld near G?ttingen (508 m). [Hans Reichenbach; Von Kopernikus bis Einstein ; Ullstein, Berlin, 1927; translated by Ralph B. Winn as: From Copernicus to Einstein ; Philosophical Library, NY, 1942; corrected ed., Dover, 1980, p. 115.] Mt. Hohenhagen is near Dransfeld, qv below. On it is the Gaussturm, which contains a bust of Gauss. Theodore von KRMN (18811963) was director of the Institute for Aerodynamics at the RheinischWestflische Technische Hochschule (RWTH) in AACHEN, NordrheinWestfalen, in 19131934. The main lecture theatre complex is named the Krmn Auditorium and there is a photo and a bust of him in the foyer. The Aachen ComputerMuseum is at Sommerfeldstrasse 32, tel: 024180 76 07. It is based on the personal collection of Prof. Ameling and is the oldest in Germany. Limited opening telephone beforehand. Helmut HASSE (18981979) died in AHRENSBURG, SchleswigHolstein, near Hamburg. The University of ALTDORF, Bayern, about 22 km ESE of NGrnberg, was developed from a gymnasium founded by Melanchthon in NGrnberg in 1526 which migrated here to escape the commercial atmosphere of the city in the late 16C. It became a university in 1622. As the University of Erlangen developed, that in Altdorf declined and was abolished in 1809. [Headlam (2), pp. 78 & 9192.] Daniel SCHWENTER (15851635), author of a notable book on mathematical recreations, was professor at the University [Ahrens (2), vol. II, p. 325]. LEIBNIZ (16461716) received his Doctorate in Law from the University in 1667, after being rejected by Leipzig for being too young. He remained there until 1672. See also: NGrnberg, below. ALTENBURG, ThGringen?, south of Leipzig, is considered to be the home of skat, the popular German card game [Baister & Patrick, p. 151]. The Castle contains the Museum of Playing Cards, and also contains the Staatliche LindenauMuseum, named for Bernard von LINDENAU (17791854), who was director of the observatory at Gotha in 18081817 before going into state service and becoming a Cabinet Minister. The Museum contains busts of Lindenau, J. S. BAILLY and LALANDE. [Schmidt.] WEYL studied at the Gymnasium of ALTONA, an outer suburb of Hamburg. ANNABERG-BUCHHOLZ, Sachsen, was the home of Adam RIESE (or RIES) (1492-1559) and his house is a museum in the section of town called Rieseberg and there is an Adam-Riese-Strasse [Berlet, pp. VII-VIII; Lehmann, p. 8, shows the house]. Tycho BRAHE was in AUGSBURG, Bayern, in 1568 when he built his first large astronomical instrument a quadrant with a radius of 21 ft. This was calibrated to 10" and was in use until 1574 when it was destroyed by a storm. [McPeak]. In the State Gallery (Staatsgalerie in der Kunsthalle) is a surrealist painting called 'The Mathematics Room' by Zimmermann [ MGG , p. 46]. The DEDEKIND family generally vacationed in BADHARZBURG, Niedersachsen, and they bought a house there, now numbered HerzogJuliusStrasse 30 and still known as the Dedekind House. The city bought the house in 1907 and it now houses a day centre for senior citizens. [Gerke & Harborth, pp. 663 & 689, the latter being a photo]. Moritz PASCH (18431930) died in BAD HOMBURG, Hessen, on the northern outskirts of Frankfurt. Gottlob FREGE (18481925) died in BAD KLEINEN. The only one I can find is in MechlenburgVorpommern. About 10 km ESE of BAD MFNSTEREIFEL, NordrheinWestfalen, on the road to Altenahr, a large radiotelescope, 100 m in diameter, is visible from the road. Wolfgang KRULL (18991971) was born in BADENBADEN, BadenWGrttemberg. BAMBERG, Bayern, was an early centre of printing, being the third city to have a printing press, in 1461, after Mainz and Strasbourg. Probably the first German arithmetic book, an untitled text known as "Das Bamberger Rechenbuch", by Ulrich Wagner, was printed here by Heinrich Petzensteiner on 1483. Johannes SCH>NER wrote several mathematics books and ran his own printing shop here until 1526 when he moved to Nuremberg. In BERLIN , there are many streets named for mathematicians, but I was surprised to find myself at the corner of Kantstrasse and Leibnizstrasse beside the Kant Billiard Cafe and the Leibniz Spiel Halle! Friedrich I established the Berlin Akademie (originally Societt) der Wissenschaft in 1700, though it was his wife, Queen SophieCharlotte, and LEIBNIZ (16461716) who were the actual founders. Leibniz was the first President. Upon the accession of Frederick's grandson, Frederick the Great, in 1740, the Academy was reorganized and flourished over the next 25 years, with Euler, Maupertuis, Lambert, Voltaire and Lagrange as members. Maupertuis was President of the Akademie for some time, c1750. The Societt produced a Miscellanea Berolinensia from 1710, but I don't know how long it lasted. The present Akademie der Wissenschaften stands of the E side of Platz der Akademie [Baister & Patrick, p. 55]. EULER came to Berlin on 25 Jul 1741 as Director of the mathematical section of the Academy. In 1742-1743, he stayed at the 'auf der Neustadt bey der Potsdamschen BrGcke in dem Barbonessischen Hause'. (Neustadt was Dorotheenstadt in 1907, but the name doesn't appear on current maps. The area was somewhere near the intersection of Friedrichstrasse and Unter den Linden, not far from the University.) He then lived from 1743 to 1766 in Brenstrasse, identified as 21 Behrenstrasse in 1907. Behrenstrasse is immediately south of Unter der Linden and a plaque was to be erected in 1908. His property included the present No. 20 and extended to Franz?sischen Strasse. He later bought an estate in Charlottenburg. In 1766, he returned to St. Petersburg. [Valentin.] LAGRANGE succeeded Euler in 1766 and was here until Frederick's death in 1786 when he went to Paris in 1787. He wrote the M)canique Analytique here. In 1799, the Bauakademie was founded the first engineering school in Germany. ABEL lived at Franz?sische Strasse 39 in January-April 1827 [Ore, pp. 157 & 162]. The University of Berlin was founded in 1810 by Wilhelm von Humboldt and now bears his name. It was a major mathematical centre until the early 20C. JACOBI was a student and a Docent from c1824 to 1827. Gustav Peter Lejeune DIRICHLET (1805-1859) taught here from 1829 to 1855 [Rowe]. A new Chair of Geometry was created for STEINER in 1834. Rudolf LIPSCHITZ (18321903) was a student under Dirichlet. RIEMANN spent two years here as a student, listening to Dirichlet and Jacobi. Ferdinand Gotthold Max EISENSTEIN (18231852) was born in Berlin and was at the University, studying under M. Ohm and Dirichlet, later a Dozent from 1847 to his death [Fraenkel]. KUMMER was Dirichlet's successor from 1855 to 1883. Martin OHM was professor c1856 and died in Berlin. WEIERSTRASS was extraordinary professor at the University and ordinary professor at the Industrial Institute (later the Technische Hochschule) from 1856, ordinary professor at the University from 1864. He had many notable students, including Sonya KOVALEVSKAYA, who was his private student in 18701874, and the following students or associates, etc.: BOLZA, CANTOR, DEDEKIND, FROBENIUS, HANKEL, HEINE, H>LDER, HURWITZ, KILLING, KLEIN, LIE, LINDEMANN, MITTAGLEFFLER, PINCHERLE, SCHOTTKY, H. A. SCHWARZ. Weierstrass died in Berlin. Hermann Amandus SCHWARZ (18431921) succeeded Weierstrass as professor in 18921917 and died here. KILLING was here in 18671878. Hermann von HELMHOLTZ (1821-1894) was a student of medicine and later Professor of Physics in 1871-1885, working on electromagnetism HERTZ and PUPIN were his students. In 1884, Pupin came to learn about Maxwell's ideas, having found no one at Cambridge who understood them. Helmholtz taught Pupin and Pupin then took the ideas back to Columbia and lectured on them. In 1885, Helmholtz was appointed head of the PhysicoTechnical Institute probably the forerunner of the KaiserWilhelmInstitut. [Guthrie, p. 275.] He died in BerlinCharlottenburg. Eduard HEINE (18211881) was born in Berlin. Gustav Robert KIRCHHOFF (18241887) was a Privatdozent for three years from c1845 and returned as Professor of Theoretical Physics from 1875 [Biggs, Lloyd & Wilson, p.218]. KUMMER lived at 14 K?thener Strasse when he came to Berlin, then moved to 10 Sch?neberger Strasse, where he lived until his death [Hensel]. Leopold KRONECKER (18231891) was a student in 18411845, studying under Dirichlet and Steiner. But he then had to run his family estates for 10 years. He returned to Berlin in 1855 and did some lecturing. From 1861, he was a member of the Berlin Academy of Science and lectured at the University. He then succeeded Kummer as professor from 1883 until his death. It was at a Berlin Congress in 1886 that he stated: "God made the integers; all the rest is the work of man." [Perfect. Fraenkel.] Eugen NETTO (18461919) was one of his students here. He died here. (Ferdinand) Georg FROBENIUS (18491917) was born in Berlin, succeeded Kronecker as Professor in 1893, until his death in 1917 at BerlinCharlottenburg. Constantin CARATH(ODORY (18731950) was born in Berlin where his father was a diplomat for the Ottoman Empire. His father became ambassador to Belgium in 1875 and the family moved there. At Easter, 1900, when he had decided to study mathematics, Carath)odory enrolled at Berlin and attended lectures of H.A.Schwarz and Frobenius, but translated to G?ttingen in 1902. He succeeded Frobenius as Professor in Berlin in 19171919, but then went to Greece to establish a new university at Smyrna cf under Greece and Turkey. Jacobi returned to Berlin as a member of the Prussian Academy of Sciences and remained until his death in 1850. HENSEL was a professor. CANTOR (PhD in 1867), LIE (1869-1870), HANKEL (1861-1862) and HAUSDORFF (1888-1889) were students. Immanuel Lazarus FUCHS (18331902) was professor in 18661869 and then from 1884. SCHOTTKY was here. BIEBERBACH succeeded Carath)odory as Professor in 19211945. SCHUR was a professor from 1919 until dismissed in 1933. He managed to get to Israel. Edmund LANDAU (1877-1938) was born in Berlin. He studied at the University, receiving his doctorate in 1899 and worked here until 1909. He retired back to Berlin in 1933 when he was forced out of his post at G?ttingen and died here. Max Karl Ernst Ludwig PLANCK (18581947) was here, receiving the Nobel Prize in Physics for 1918 for his 1900 paper postulating that energy is discretised. VON LAUE was here. Erwin SCHR>DINGER (18871961) was here, receiving the Nobel Prize in Physics in 1933. WEISSKOPF was his assistant for a time, developing his renormalization method, but fled in 1937. KNOPP was here to 1920. VON MISES became first Professor of Applied Mathematics in 1920. BOCHNER, E. HOPF, H. HOPF, R. BRAUER, A. BRAUER, FENCHEL, FREUDENTHAL, B. NEUMANN, R. RADO received doctorates here in 19201933. SZEG> (professor to 1926), E. HOPF, H. HOPF, A. BRAUER were here. VON NEUMANN was a student of chemistry in 19211923 and Privatdozent in 19261929. Oswald TEICHMFLLER (19131943) was Dozent from 1938. HASSE was at the Akademie der Wissenschaft in 19451949, then at the University in 19491950. Johann Elert BODE (17421826) was director of the BERLIN OBSERVATORY. This was where Johann Gottfried GALLE and Heinrich D'Arrest on 23Sep1846 pointed a Fraunhofer 9 inch telescope at the location specified by LEVERRIER and verified the existence of Neptune on their first night of viewing [P. Moore (4), p.44]. Airy said: "Nothing in the whole history of astronomy can be compared to this." WEIERSTRASS (18151897) came to Berlin in 1856 as Professor at the Industrial Institute (later the Technische Hochschule) as well as extraordinary professor at the University. Franz REULEAUX (18291905) was Professor of Mechanical Engineering and Kinematics and Director at the Polytechnic of BerlinCharlottenburg in 18641896. This was later the Technische Hochschule, now(??) the Technical University(??). Heinrich WEBER was professor at the Polytechnische Hochschule in 18831884. Du BOISREYMOND (1831-1889) was professor from 1884. Ernst STEINITZ taught at the Technische Hochschule in 18911910. Georg HAMEL (18771954) was professor at the Technische Hochschule from 1919. Konrad ZUSE was a student at the Technische Hochschule, graduating in 1935. He built his first computer, the Z1, here in his parents' living room, in 19361938. Ernst HAECKEL (18341919) obtained his degree in medicine here in 1857, but soon went into comparative anatomy at Jena, qv, below. CHRISTOFFEL was professor at the Gewerbeakademie in 18691872. WITTGENSTEIN studied aerodynamics at the Technische Hochschule from c1908. It was about 1909 that he became seized by philosophy. [Wittgenstein.] WIGNER taught at the Technische Hochschule in 1929 [IHHS, p. 64]. Hans GEIGER (18821945) was professor of physics at the Technische Hochschule from 1936. ([Moore&Dahl, p. 27] says Chadwick studied with Geiger in Berlin, c1922.) EINSTEIN was at the Royal Prussian Academy of Sciences, the Kaiser-Wilhelm-Institut (now the Max-Planck-Institut in Dahlem) and the University from 1913. He was Director of the Institut from 1914. He lived at Wittelsbacherstrasse 13 in 19141917. In 19171932, he lived in a fifth floor flat at Haberlandstrasse 5 (now N?rdlingerstrasse 8). Nobel Prize in Physics, 1921. Cornelius LANCZOS (Korn)l Lnczos) was his assistant in 19281929. Leopold INFELD (18981968) came to do graduate work but was refused entrance until Einstein arranged for him to be admitted as a special student. Von NEUMANN and Eugene (Jen) WIGNER (doing his doctorate in chemical engineering) were students of Einstein. In 1929, Einstein bought land and built a cottage at Waldstrasse 7, in the eastern suburb of Caputh. This was confiscated and raided in 1933. Though now a national memorial, the house is not open to the public. [Eastman, p. 116.] Otto HAHN was Director of the KaiserWilhelmInstitut for chemistry from 1928 Nobel Prize in Chemistry in 1944 for recognising nuclear fission in 1938, with Strassman they found that bombarding uranium with neutrons produced atoms with mass about half that of uranium. The Royal Military School was also important. Martin OHM (1787-1854), brother of George Simon OHM of Ohm's Law, taught here to 1828. He seems to be the first to really develop the ideas of how the number systems are constructed algebraically, particularly how the negatives and then the rationals are constructed. He gave some ideas of this in 1818 and then gave most of the ideas in 18281833, providing a fairly clear and mature version in 1842. DIRICHLET succeeded Ohm in 1828 and continued teaching here after starting at the University. [Shields (2). Rowe.] The Staatsbibliothek ((East German) State Library) is in Unter den Linden and has about 6 million books [Baister & Patrick, p. 45]. See also Potsdam, below, which is only about 10 km to the W. Emanuel LASKER (18681941) was born in BERLINCHEN, Brandenburg, and was sent to school in Berlin in 1879 [Schonberg, p. 97]. (There were two Berlinchens in Brandenburg, one about 100 km NNW of Berlin, the other about 135 km ENE of Berlin and now Berlinek, Poland.) BernkastelKues see Kues, below. Christoph GUDERMANN was Professor at the University of BONN (Rheinische FriedrichWilhelmsUniversitt Bonn), NordrheinWestfalen, in the 1830s. WEIERSTRASS (18151897) was a student of economics, law, etc. from 1834 to 1839, but was not interested and didn't even bother to take his exams. He attended some classes of Gudermann, but in 1839, they were both at MGnster. MARX was a student in 1835-1836, residing at Josephstrasse 764 [Eastman, p. 149]. Eduard HEINE (18211881) studied and taught here. HELMHOLTZ was Professor of Anatomy and Physiology in 1855-1858, but found teaching of anatomy irksome. Rudolf LIPSCHITZ (18321903) was a Professor from 1864 till his death here. Heinrich HERTZ (18571894) succeeded CLAUSIUS as Professor of Physics from 1889 until his death. His pupil LENARD succeeded him and observed but did not recognize Xrays. Julius PLFCKER (18011868) was professor. KLEIN was a student in 1865-1868 and assistant to PlGcker in 1866-1888. CLAUSIUS was Professor of Physics in the 1870s. Hermann MINKOWSKI (18641909) was professor in 18921895. Eduard STUDY (18621930) succeeded Lipschitz in 1904. A plaque at the University commemorates Felix HAUSDORFF (1868-1942), who was Professor there from 1921 until his dismissal in 1935. He, his wife and her sister committed suicide rather than live under the Nazis. [Monna.] Constantin CARATH(ODORY (18731950) was Professor in 19081909 [Behnke]. Wolfgang KRULL (18991971) moved to Bonn in 1939 and was in the naval meteorological service during the War. Afterwards, he resumed teaching at the University. He died in Bonn. [J. J. Gray (2).] Johan H. W. GEISSLER (18151879) was mechanic to the University when he developed a greatly improved vacuum pump in 1855. This produced the first vacuua low enough to permit electrical discharge through them, with remarkable colours. Geissler tubes were the forerunners of neon lighting, Xray tubes, electronic valves (= vacuum tubes), etc. In 1982, the Max Planck Institute for Mathematics was founded in Bonn with Friedrich Hirzebruch as Director. It has been the principal mathematical centre in Germany since that time. It is about to move into the Furstenberg Palais facing MGnsterplatz and the statue of Beethoven. The Forschungsinstitut fGr Diskrete Mathematik, Nassestr. 2, has a good collection of old calculating instruments [Annegret Maussner; Meilensteine auf dem Weg zum Computer Historische Rechenmaschinen und Rechenhilfsmittel ; Forschungsinstitut fGr Diskrete Mathematik, Rheinische FriedrichWilhelmsUniversitt Bonn, nd [c1990?]. With English translation of the text.] WEIERSTRASS was taught at the gymnasium at BRAUNSBERG (now Braniewo, Poland) in 18481855. In 1848 he published his first great paper in the school Prospectus. He later sent it to Crelle's Journal fGr die reine und angewandte Mathematik and it appeared in 1854. He was awarded an honorary doctorate by K?nigsberg in 1854, a year's leave to do research in 1855 and in 1856, he was Professor in Berlin! [A. C. Baker.] Wilhelm KILLING was professor at the Lyceum Hosianum, Braunsberg. GAUSS (17771855) was born at 30 Wilhelmstrasse, BRAUNSCHWEIG (= Brunswick), Niedersachsen, which was a museum. According to Eves [Eves (3), pp. 115-116], this was destroyed in the second war, as stated in [Alexanderson], but its contents had been stored and are now in the municipal library. There is a modern building on the site, with two plaques stating that Gauss was born on the site [I have a photo]. He was baptised Johann Friedrich Carl Gauss, but always signed himself Carl Friedrich or C. F. [Gardiner]. Gauss attended the KatharinenVolksschule from age 7 and/or the ancient MartinoKatharineum Gymnasium in Breite Strasse (mostly destroyed in the War) and studied at the Collegium Carolinum (the forerunner of the Technische Hochschule, now the Technical University) from age 15 to 18 [Gerke & Harborth, p. 659; Ahrens, pp. 911]. According to Ahrens, it was at the KatharinenVolksschule that the nineyear old Gauss, a new student in the arithmetic class which went up to 14year olds, instantly added up the arithmetic progression set by BGttner. (Every version of the story seems to give a different progression, so I suppose the actual progression is now irretrievable.) BGttner was so impressed that he obtained an arithmetic book from Hamburg for the boy. At age 15, he had already started his investigations of the arithmeticgeometric mean. During 17951798, he was a student at G?ttingen. Gauss was visiting Braunschweig and still lying in bed on 29 Mar 1796 when he realised the connection of the cyclotomic polynomial to the construction of the ngon and how to construct the 17-gon. Ahrens [p. 11] says Gauss sent the slate on which he had done the calculation to Wolfgang Bolyai, who preserved it. (Where is it now??) He came back to Braunschweig in 1798 and produced his Disquisitiones Arithmeticae (1799) and his thesis proving the Fundamental Theorem of Algebra at the nearby University of Helmstdt (now Helmstedt). He may have been here when he rediscovered the lost asteroid Ceres in 1801. He became professor at G?ttingen in 1807. There is a statue of Gauss on the Gaussberg, which Dedekind promoted. On the base, at Gauss's right, the sculptor has carved a star 17gon, which is much clearer than an ordinary 17gon. [Alexanderson. I have a photo.] Julius Wilhelm Richard DEDEKIND (18311916) spent most of his life at Braunschweig. His father was a lawyer and Director of the commercial section of the Collegium Carolinum, so Richard was probably born in the official residence at 41 Bohlweg, but the College moved away and the site has long been rebuilt. He was baptised at St. Katharinen in the Hagenmarkt. He also attended the MartinoKatharineum Gymnasium. He studied at the Collegium Carolinum in 18481850. This College has evolved into the present Technical University. When it became a Polytechnic in 1862, it invited Dedekind to be Professor and he came and stayed for the rest of his life. He lived at a number of sites: Hagenmarkt 9 (18621870); Wendenstrasse 32 (18701872); Petrithorpromenade 24 (now Inselwall 12) (18721891); Bismarckstrasse 13 (now 11) (18911894); a firstfloor flat in KaiserWilhelm Strasse 45 (now Jasperallee 87) (18941916), where he died. Of these, only the last survives to any extent, and it was burnt in the war and restored. A few years ago, Prof. Harborth had a plaque erected on this building. [Gerke & Harborth, p. 689, has a photo before the plaque was erected. I have later photos.] A plaque has also been erected on the Old Building of the University, facing Pockelsstrasse [I have photos.] There are portraits of Gauss and Dedekind in the Forum Building of the University, adjacent to the Senate meeting room [Gerke & Harborth, p. 694 gives photos. I have photos]. Dedekind is buried in a family grave in section 29 of the Hauptfriedhof in Helmstedter Strasse beyond the Hauptbahnhof there is a convenient guide and map to the Friedhof at the entrance [Gerke & Harborth, pp. 663 & 692693 692 is a photo of the grave and 693 is a diagram showing who is where; I have a photo]. [Gerke & Harborth, p. 665] say there is a writing table of Dedekind's in the Landesmuseum, but when I asked about it, the attendants did not know of it, so it may not be on exhibit. Dedekind's successor was K. O. FRIEDRICHS, who left for the USA in 1930. Braunschweig was the home of the noted publishing firm of Vieweg until recently. The Vieweg building is now the Landesmuseum. The famous Brunsviga calculators were made in Braunschweig by Firma Grimme, Natalis & Co, later Brunsviga, now assimilated into Olympia AG. The Landesmuseum has an exhibition of these and other calculating machines including replicas of the Schickard, Pascal and Leibniz machines and models of some of Leibniz's ideas, including a decimalbinary converter. See also WolfenbGttel, below. Henry OLDENBURG (16191677), joint first Secretary of the Royal Society, was born in BREMEN. DIRICHLET was professor at the University of BRESLAU (now WROCLAW, Poland) in 1827-1829. EISENSTEIN was a student, receiving a doctorate honoris causa in his junior year [Fraenkel]. KUMMER was a professor in 18421855 and developed his theory of ideals here. KRONECKER studied with him. KIRCHHOFF was professor of physics from 1850 to 1854. LIPSCHITZ was Professor in 18621864. Ernst Florens Friedrich CHLADNI (17561827) was Professor of Physics when he developed Chladni figures c1800 cf in 7A2. He created experimental acoustics and is considered the Father of Acoustics. Moritz PASCH (18431930) was born in Breslau. Adolf ANDERSSEN (18181879) was born in Breslau and became Professor of Mathematics at the Friedrichs Gymnasium where he stayed the rest of his life. He was 'World Chess Champion' c18621866. [Schonberg, pp. 4951.] STURM was professor from 1892. Constantin CARATH(ODORY (18731950) was professor at the new Technische Hochschule in 19101913 [Behnke]. Max BORN (18821970) was born in Breslau, Nobel Prize in Physics, 1954. Ernst STEINITZ (18711928) taught at the Technische Hochschule in 19101920. The painted hall of the University includes a portrait of EUCLID. The BROCKEN in SachsenAnhalt is the highest peak (1142 m) in the Harz Mountains and is famous for the 'Brocken Spectre', an optical effect of a low sun casting one's shadow into a cloud. It was one of the mountains of GAUSS's geodetic triangle, cf beginning of this Section. [Baister & Patrick, pp. 171172] report that this was a military area and hence inaccessible, but that in 1990 it was reopened. At BURGHAUSEN, Bayern, is a clock tower with two clocks and two sundials, because the builders could not agree which was more accurate [[Ripley's Believe It or Not! , 8th series; Pocket Books, 1962, p. 22]. Cassel is an older spelling of Kassel, qv below. Cologne (or C?ln) see K?ln, below. Friedrich Otto Rudolf STURM (18411919) was Professor 'fGr darstellende und neuere Geometrie' at the Technische Hochschule, DARMSTADT, Hessen, in 18721878. Ruth MOUFANG (1905-1977) was born in Darmstadt. Paul WOLFSKEHL (18561908?) was born in Darmstadt. He left 100,000 DM (perhaps 1,000,000) as a prize for a resolution of Fermat's Last Theorem. Supposedly he was on the verge of suicide, having been rejected by his heart's desire, and became so wrapped up in the Fermat problem that he forgot the moment he had planned to shoot himself and his will to live returned. See: [Simon Singh; Fermat's Last Theorem and the Wolfskehl Prize; M500 159 (Dec 1997) 78] for a report on this and two other theories for the the prize first: pure gratitude for the career in mathematics which he had taken up when he discovered he had multiple sclerosis and second: that he wanted to spite his wife. The economic disasters of 20C Germany eroded the value, but it had recovered to about 30,000 when the prize was awarded to Andrew Wiles on 27 Jun 1997. WEIERSTRASS (18151897) taught at the Catholic Gymnasium in DEUTSCH KRONE (now Wacz, Poland) [A. C. Baker]. Near DRANSFELD, Niedersachsen, about 16 km SW of G?ttingen, is Mt. Hohenhagen (or Hoher Hagen) (508 m), one of the points used by GAUSS in his geodetic work see the beginning of this Section. On it is the Gaussturm, which contains a bust of Gauss. DRESDEN is the capital of Sachsen (Saxony), which was a wealthy independent state. Part of the monumental centre is a series of pavilions called Der Zwinger (The Keep). One pavilion is the Mathematisch-Physikalisches Salon which contains a substantial display of globes, telescopes, clocks, calculators, automata, etc. There is a globe by Mercator, a globe clock by Jost BGrgi, an original Pascal adding machine, Arithmometers of Thomas (de Colmar) (c1820) and BGrkhardt (1878) and a number of early clockwork automata including 'The Drumming Bear'. The nearby BrGhl Terrace has a celebrated view. DIRICHLET relates that walking along it inspired his proofs, simplifications and extensions of Gauss's results on biquadratic reciprocity. [Rowe, pp. 18-20.] Otto Xavier SCHL>MILCH (18231901) worked here, founding and editing the Zeitschrift fGr Mathematik und Physik. Gerardus MERCATOR (= Gerhard Kremer) (15121594) migrated to the court at DUISBURG, NordrheinWestfalen, in 1552 and remained there for the rest of his life. He produced the map based on his projection in 1569. Though he was not the originator of the projection, nor the first to use it, he was the first to apply it to a practical nautical chart. His great Atlas appeared in three parts, in 1585, 1589 and 1595. In the Goethe Museum, DFSSELDORF, NordrheinWestfalen, is what is believed to be the oldest extant box of magic tricks, a Christmas present from Goethe to his grandson in 1830 [Detlef Hoffmann & Margot Dietrich; Karten zum Zaubern ; Heimeran Verlag, Munich, 1979, pp. 2021]. Florence NIGHTINGALE studied at the Diakoniewerk KAISERWERTH (Institute of Protestant Deaconesses), Alte Landstrasse, 121, in Kaiserwerth, a northern suburb of DGsseldorf, a bit N of the airport, for two weeks in 1850 and three months in 1851. The actual hospital where the Deaconesses worked still stands; it is the Altenheim Stammhaus, 32 Kaiserwerther Markt. at the corner of An St. Swidbert. The library has some memorabilia of Nightingale. In 1975, a 410 bed hospital was added to the complex and named the Florence Nightingale Hospital there is a bust of her in the lobby. [Pengelley & Pengelley, pp.147148.] (Christian) Felix KLEIN (18491925) was born in DGsseldorf. Hermann WEYL (18851985) was born in ELMSHORN, Prussia. The only one I can find is in Niedersachsen. The University of ERFURT, ThGringen, was founded in 1392, but closed in 1816. Its site was the present 39 Michaelis Strasse. [Baister & Patrick, pp. 127, 129]. Ephraim Salomon UNGER (17891870) was a Dozent at the University, but he and his brother set up their own school of mathematics in 1820, which became a state school in 1834. Unger is best known for a number of textbooks. George Simon OHM (1780 (or 1789 or 1787) 1854, the physicist, of Ohm's law) and his brother Martin OHM (17921872, a mathematician) were born in ERLANGEN, Bayern, about 20 km N of NGrnberg. G. S. Ohm studied at the University of Erlangen. The University of Erlangen started about 1800 and soon supplanted that in Altdorf, qv above. Von STAUDT was Professor at the University until 1867. He died and was buried here, but the grave was later moved to his native city of Rothenburg. HANKEL was Professor in 1867-1869. KLEIN was Professor from 1872, when he presented his 'Erlanger Programm': "A Comparative Review of Recent Researches in Geometry", until 1875. LINDEMANN was Klein's student, receiving his doctorate in 1873 [Gupta]. Emanuel LASKER received his doctorate here in 1902, whilst being the World Chess Champion in 18941921 [Schonberg, p. 11]. Max NOETHER was Professor here in 18751921 and Emmy NOETHER (18821935) was born and grew up here. She entered the University in 1900. She completed her doctorate in 1907 under Paul GORDAN. [Perl, pp. 173174.] TIETZE was professor in 19191925. KRULL was at Erlangen in 19281939, developing the Krull dimension and Krull valuations. Idealtheorie appeared in 1935. [J.J.Gray(2).] See also: Altdorf, NGrnberg, both in this Section. Michael STIFEL (c14871567) was born at ESSLINGEN, BadenWGrttemberg, just E of Stuttgart, and was a monk at the Augustinian Monastery there in 1511, but later converted to Lutheranism. Johannes GUTENBERG (13981468) left Mainz and lived in FRANKFURT (am Main), Hessen, in 1454-1457. He printed some letters of indulgence, a calendar and a papal bull there. He returned to Mainz. In Frankfurt, there is a monument to Gutenberg, Fust and Sch?ffer in the Rossmarkt. Johann Benedict LISTING (18081882) was born at Frankfurt [Biggs, Lloyd & Wilson, p.219]. Otto HAHN (18791968) was born in Frankfurt, but seems to have left as a student. Nobel Prize in Chemistry, 1944, for recognizing nuclear fission. Honorary Citizen in 1959. The Otto Hahn foundation was established in 1969. Arthur Moritz SCHOENFLIES (18531928) helped found the University of Frankfurt in 1914 and taught until 1922. He got BIEBERBACH appointed to a chair in 1915. Bieberbach published his conjecture in 1916, then went to Berlin in 1921. Carl Ludwig SIEGEL (18961981) was professor in 19221937. Max von LAUE (1879-1960) was at the University, receiving the Nobel Prize in Physics in 1914. Cornelius LANCZOS (Korn)l Lnczos) taught here in the early 1930s [IHHS, p. 65]. MOUFANG was a student at the University of Frankfurt in 1925-1930, then a Privatdozent from 1946 and a Professor from 1957. On the main street of the suburb of FrankfurtH?chst is a chronogram over a doorway: LoCVs Iste DoMVs oratIonIs VoCabItVr. See also: Bad Homburg, Goddelau, both in this Section. LINDEMANN was at the University of FREIBURG (im Breisgau), BadenWGrttemberg, from 1877 to 1883, becoming Professor in 1879 [Gupta]. It was here that he showed that ! is transcendental. There is a bust. Paul David Gustav du BOISREYMOND (18311889) was professor in 18701874. Wolfgang KRULL (18991971) was a student at Freiburg and did his Habilitation Thesis in 1922. In 1925, he proved the KrullSchmidt theorem. He went to Erlangen in 1928. [J. J. Gray (2).] There are statues of Arithmetic and Geometry on the Cathedral. GEISA, ThGringen, was the birthplace of Athanasius KIRCHER (16021680) and there is a monument to him, a memorial at his birthsite and a street named for him [BGchel & Schreiber]. He is best known for inventing the Magic Lantern, described in his Ars Magna Lucis et Umbrae of 1645 [Dawes, p. 84]. Moritz PASCH (18431930) was Professor at the University of GIESSEN, Hessen, in 18741911. R>NTGEN was Professor of Physics at the University in 18791888. Ludwig BIEBERBACH (18861982) was born at GODDELAU, Hessen, south of Frankfurt [Mehrtens, p.197]. The DSB says that GAUSS communicated his results on the relocation of Ceres to F. X. von ZACH at the GOTHA Observatory, ThGringen,in Dec 1801, and von Zach found Ceres where it had been predicted. The University of G>TTINGEN , Niedersachsen, was founded in 1733, with first lectures in 1734 and official opening in 1737, by George II of England, who was also Elector of Hannover and BraunschweigLGneberg. The town has a Municipal Museum (Stdtisches Museum) which includes historical exhibits on the history of the town and university. See [Neuenschwander & Burmann] for many details. JnosAndrs [= Johann Andreas von] SEGNER (17041777) was the first Professor of mathematics in 17351755. Segner built an observatory, which he shared with Mayer for a time. [Neuenschwander & Burmann.] Tobias MAYER (17231762) was here, working in a tower on the city wall from 1751. He refined the method of lunar distances for determining longitude, determining more accurate positions of the moon and devising the reflecting circle for more accurate measurements [G. L'E. Turner, p. 35]. He was professor from 1749. [Neuenschwander & Burmann.] Abraham Gotthelf KSTNER (17191800) succeeded Segner as professor in 1755 and succeeded Mayer as director of the Observatory in 1762. Georg Simon KLFGEL (17391812) was a student under KSTNER at the University in the 1750s. Benjamin FRANKLIN visited G?ttingen in July 1766 and stayed at Prinzenstr. 21 (plaque). Thomas YOUNG was a student, c1800. Carl Friedrich GAUSS (1777-1855) came as a student in 17951798. He was professor from 1807 and an observatory was promised, but not built until 1816. He then became Director of the Sternwart (Observatory) on Geismar Landstrasse and lived in it from then until his death [Rowe, p. 17]. Gauss had Wilhelm Eduard WEBER (1804-1891) appointed Professor of Physics in 1833. They erected an iron-free magnetic observatory and, in 1834 (or 1833), a telegraph to connect it with the astronomical observatory three miles away. [Dibner.] [Alexanderson; Lietzmann, plate VI, opp. p. 70 (= plate IV, opp. p. 96 in later editions); Rowe, p. 15] have a photo of the Gauss & Weber statue in G?ttingen, where they seem to be discussing the telegraph rather than mathematics [Alexanderson]. They did not have time to develop the idea and passed it on to a Prof. Steinheil of Munich. In 1838, Steinheil discovered that one only needed a single wire the earth could complete the circuit. The G?ttingen telegraph was later destroyed by lightning. The Sternwarte is no longer used as an observatory and is now the GaussMuseum. There is a Gaussstrasse. Weber was expelled for protesting against the King's suspension of the Constitution in 1837, but returned in 1849. According to Eves [Eves (4), p. 25], the brains of GAUSS and DIRICHLET are preserved in the physiology department at G>TTINGEN. Gauss is buried in St. Alban's Cemetery (Albanifriedhof) and there is a medallion of him on the tomb. [Eves (4), p. 26. Muir. Photo in Rowe, p.22.] [Alexanderson] relates that Gauss is reputed to have asked for a 17gon on his tombstone cf Braunschweig, above. Dirichlet is buried nearby [photo in Rowe, p. 24]. There is a bust of Gauss in the University Library. See also Dransfeld, above. I have a picture book of G?ttingen showing the GaussWeber statue, the Sternwarte and the Tower at Dransfeld. Johann Benedict LISTING (18081882) was a student of Gauss from 1829 and graduated in 1834. In 1839 he returned as Professor of Mathematical Physics and Optics. His Vorstudien zur Topologie of 1847 was one of the first systematic treatises on the subject and introduced its name. The idea of the M?bius band occurs in Listing's notebooks for 1858, a few months before it appears in M?bius's notes, but neither published the idea for some years. His work on optics led to an honorary MD from TGbingen in 1877. He died in G?ttingen. [Biggs, Lloyd & Wilson, p.219.] Peter Gustav LejeuneDIRICHLET (18051859) succeeded GAUSS as Professor in 18551859. Moritz Abraham STERN (18071894) was a professor. Bernhard RIEMANN (18261866) was a student under Gauss here and Dirichlet in Berlin, doing his thesis with Gauss here in 1851 and giving his famous Habilitationsvortrag on 'The hypotheses which lie at the foundations of geometry' in 1853. He succeeded Dirichlet in 1859, but came down with tuberculosis a few years late and spent much of the rest of his life in Italy, vainly hoping for a cure. Alfred CLEBSCH (1833-1872) succeeded Riemann as Professor from 1868. Lazarus FUCHS (18331902) was professor in 18741875. G?ttingen awarded the first doctorate in mathematics to a woman, Sonya KOVALEVSKAYA, in 1874 at Weierstrass's urging, and the first doctorate to a woman student, Grace CHISHOLM, see below [Perl, p. 155]. Richard DEDEKIND was here in 18501858. He was Gauss's last doctoral student, receiving this degree in 1852. He attended the lectures of Riemann and Dirichlet. He submitted his Habilitationsschrift in summer 1854 and was Privatdozent from 1854 to 1858. During the winter semester of 18561857, he gave the first course in Galois theory, to only two students one was Paul BACHMANN (18371920). He gave a second course in the following winter. However, the text of these lectures was not published until 1981. Dedekind lived 'bei dem stadtbekannten' Barbier Vogel and then 'im Hause Deppe' on Papendiek. (I'm not quite sure if these are names of buildings or of proprietors of lodgings??) [Gerke & Harborth, p. 659, but they give the date of the Galois lectures as 18541855 which does not agree with other sources.] (Christian) Felix KLEIN (18491925) was a student in 18691871, doing his Habilitation with Clebsch in 1871, then Dozent to 1872. He was professor from 1886 until 1913 when he retired due to illhealth. It was his advanced views on female education which led the government to allow some foreign women to enrol as an experiment in c1893. Grace CHISHOLM (Young), May Winston and Isabel Maltby were then allowed to start attending classes a bit later. Chisholm received her doctorate on "The algebraic groups of spherical trigonometry" magna cum laude in 1895. [Rothman.] Klein lived at Wilhelm Weber Strasse 3 [photo in Math. Intell. 6:2 (1984) 76]. Hilbert and Klein died and are buried in G?ttingen [Alexanderson]. Hermann Amandus SCHWARZ (18431921) succeeded Clebsch as Professor in 18751892. Otto H>LDER (18591937) and Arthur SCH>NFLIES (= Schoenflies) (18531928) were students of Schwarz. H?lder was later Dozent in 18861889. Sch?nflies was Professor of Applied Mathematics (Geometrical) in 1892-1899. Schwarz was succeeded by Heinrich WEBER (18421913) in 18921895. David HILBERT (18621943) succeeded Weber in 1895, becoming Emeritus in 1930. Hilbert had 69 doctoral students, including BLUMENTHAL, DEHN, F.BERNSTEIN, WEYL, SPEISER, HAAR, COURANT, HECKE, KNESER. It was here that Hilbert propounded the general theory of relativity in Nov 1915, five days before Einstein's announcement in Berlin. Hermann MINKOWSKI (18641909) came to a new chair in 1902, but died of appendicitis in 1909. Almost every 19C and early 20C German-speaking mathematician studied or worked for sometime at G?ttingen, including the following: M>BIUS (1813-1814); DEDEKIND (1850-1858); HANKEL (1860-1861); HEINE; LIE (1870); LINDEMANN; STUDY (c1890?); PAD( (18901891); FANO (postgraduate work with Klein, 18931894 [Giacardi & Roero, pp. 173176]); TIETZE (c1900); D)nes K>NIG (c1904); BIEBERBACH (19061910); HELLY; ZERMELO; POLYA (c1910 and/or 1912-1913); H. LEVY (19121914); CARATH(ODORY (19021905); SKOLEM (visiting BERNSTEIN in 19151916); VAN DER WAERDEN (early 1920s, Assistant in 1927-1928); FELLER (1925-1926); CHURCH (19271928?); K.MAHLER (to 1933); HEILBRONN (assistant to Landau in 19301933, but in 1933 his Doctorate was rejected because he was Jewish, and he left for Cambridge in 1933). Fritz JOHN and Kurt O. FRIEDRICHS were also exiled to the USA. Felix BERNSTEIN (18781956) was here to 1933. Helmut HASSE (18981979) was professor in 19341945. Carl Ludwig SIEGEL was professor in 19381940 but managed to get to the US, returning to G?ttingen in 19511959. Constantin CARATH(ODORY (18731950) came as a student in 1902, after two years at Berlin. He completed his thesis in Summer 1904 and even before his oral examination, Hilbert had asked him to work with him. He completed his Habilitationsschrift in Mar 1905, in his 10th semester of study, a record for German universities. After some years at small universities, he went to Bonn, Hannover and Breslau, then came to G?ttingen as Klein's successor in 1913, transferring to Berlin in 1918. [Behnke.] Erich HECKE (18871947) succeeded him in 19181919. Karl (or Carl) David RUNGE (18561927) was professor in a new chair of applied mathematics (the first such in Germany) from 1904 until becoming emeritus in 1924 besides his work in numerical analysis, he first noted numerical regularities in spectra, leading to the science of spectroscopy. Ludwig PRANDTL (18751953) was here. Edmund LANDAU (18771938) came as Minkowski's successor in 1909. In 1933, he was forced to retire and returned to his native Berlin. Emmy NOETHER (18821935) came as Hilbert's assistant in 1915, but was not permitted to do her Habilitation until 1919. She became a type of professor in 1922 and a little later got a teaching post. She was also dismissed and left in 1933. Richard COURANT (18881972) succeeded Hecke from 1920 until given 'forced leave' in 1933. He obtained a Rockefeller Foundation grant and built a splendid new Mathematical Institute in 1929 Otto NEUGEBAUER (1899 ) came to G?ttingen in 1922, already interested in ancient mathematics. His thesis was on Egyptian unit fractions. In 1927, he began lecturing on ancient mathematics and these lectures interested van der WAERDEN. He was Courant's chief assistant and was responsible for the library of the new building in 1929. He was one of the first to study Babylonian mathematics and produced his three volume Mathematische KeilschriftTexte in the 1930s, revealing a completely unexpected richness. He was the founder of Zentralblatt fGr Mathematik und ihre Grenzgebiete, first appearing in 1931. He refused to sign the loyalty oath to the Nazis and his friend Harald Bohr arranged an appointment in Copenhagen, to which he took Zentralblatt. However, he eventually resigned when Nazi sympathizers dismissed LeviCivita from the editorial board. In 1939, he sailed to America. Gustav HERGLOTZ (18811953) was appointed to succeed Runge in 1924, despite being a pure mathematician. Paul ALEXANDROFF came here often. In 1925-1927, Alexandroff and H.HOPF were both visiting and their discussions with Emmy Noether led to her recognition of homology groups. Max BORN was here and OPPENHEIMER studied with him in the late 1920s, getting his PhD here. Hermann WEYL (18851955) studied under Hilbert, obtaining his degree in 1910 and becoming Privatdozent in 1912, but left for ZGrich in 1913. He returned as Hilbert's successor in 19301933, then left for the Institute for Advanced Study. MACLANE studied here in 1931-1933 he boarded with Courant and later with Weyl. Paul BERNAYS, Harald BOHR, Peter DEBYE, Hellmuth KNESER, Paul KOEBE, Otto NEUGEBAUER, Alexander OSTROWSKI, Karl SCHWARZSCHILD, Arnold SOMMERFELD, Otto TOEPLITZ were also here as Dozents [Neuenschwander & Burmann]. Walter Karl Julius LIETZMANN (18801959) was Professor of Didactics of the Exact Sciences from 1934. He wrote numerous books on mathematical education and on popular mathematics, notably his Lustiges und MerkwGrdiges von Zahlen und Formen of 1922 which has gone through at least ten editions. Juergen MOSER (19281999) was a student from 1947, going to New York on a Fulbright Scholarship in 1950. He later returned to write a book on celestial mechanics with Siegel and to complete his PhD in 1955, when he returned to New York. Since 1945, G?ttingen has become the headquarters of the Max-Planck-Institut, the successor to the KaiserWilhelmGesellschaft, which is the principal research organization in Germany. HEISENBERG was a director(?). REIDEMEISTER (18931971) was professor from 1955. Emil ARTIN (1898-1962) spent a year here after his PhD in the 1920s and a term as Gauss Professor in 1956. Max Karl Ernst Ludwig PLANCK (18581947, Nobel Prize in Physics for 1918) is buried in G?ttingen [ MGG , p. 146]. Eugene (Jen) WIGNER (19021995) was here in the early 1930s, with Victor Frederick WEISSKOPF (19082002) as one of his graduate students. Weisskopf received his doctorate here in 1933. The Mathematical Institute has one of the finest collections of mathematical models and special cases display over 500 models [Neuenschwander & Burmann]. The University of of GREIFSWALD, MechlenburgVorpommern, was founded in 1456, but none of the early buildings survives. FUCHS was professor in 18691874. STUDY was professor to 1904. HAUSDORFF was professor in 1910-1921. At HAIGERLOCH, BadenWGrttemberg, is an Atom Museum (Atommuseum Haigerloch) explaining the work of HEISENBERG's group which created a nuclear reactor in 19441945. This reactor never went critical and apparently they were not equipped to stop a critical reaction. Fortunately this was as far as the German nuclear weapon program got! [ MGG , p. 147.] The University of HALLE, SachsenAnhalt, was founded in 1693. JnosAndrs [= Johann Andreas von] SEGNER (17041777) was at the University of HALLE, from 1755 [IHHS, p. 45; Neuenschwander & Burmann] until his death. He seems to be the first to publish on the ubiquitous Catalan numbers, in 1761, though Euler had mentioned them in a letter to Goldbach in 1751. Georg Simon KLFGEL (17391812) became Professor of Mathematics and Physics in 1787. His Mathematische W?rterbuch appeared in three volumes in 18031808 and was later extended by Mollweide and Grunert to 5 volumes with two supplements. He died in Halle. Karl Brandan MOLLWEIDE (17741825) was teacher of mathematics and physics at Halle in 18001811. KUMMER was a student in 18281831. Heinrich Eduard HEINE (18211881) was Professor at the University of Halle from 1856 until his death here. Hermann HANKEL (1839-1873) was born in Halle. C. G. NEUMANN was professor, c1860. Hermann Amandus SCHWARZ (18431921) was Dozent at Halle until 1869. Georg Ferdinand Ludwig Philipp CANTOR (1845-1918) came to Halle as Professor in 1869 and remained until his retirement in 1913 and his death (in the Nervenklinik) in 1918. In the decade from 1873, he produced his great works here. He founded the Deutsche Mathematiker Vereinigung and edited it proceedings for three years. In 1885, he built a house at Hndelstrasse 13 which is now occupied by a grandchild who has agreed to transfer it to the University. There is a rather worn 1970 plaque on it [Kert)sz, p. 21, with photo on p. 53 and in Stern]. In the old Lion Building of the University, there is a 1915 bust of Cantor in the Cantor H?rsaal on the 2nd floor (= 3rd floor in the US) [Kert)sz, p. 51 is a photo, also in Stern], near a portrait of GAUSS. In the centre of the suburb of Halle-Neustadt is a monument to several great citizens which includes a Cantor plaque showing the countability of the rationals [Kert)sz, p. 53, with photo on p. 54 and in Stern]. Cantor's tombstone is in the Giebichenstein cemetery in Friedenstrasse [photo in Kert)sz, p. 52, and in Stern]. ([Paine] reports they couldn't find it in 1992, indeed it reads as though they couldn't find the cemetery, but I saw the tombstone in 1988.) [Stern] says Cantor was buried in a now-vanished cemetery, but doesn't say whether the body was moved with the stone. PLFCKER taught at Halle for a time. HERTZ was at the University of Halle. Ludwig Otto HESSE (18111874) was professor in 18551856. Helmut HASSE (18981979) was professor in 19251930. ZORN taught here briefly in the early 1930s. Joachim JUNGIUS (15871657) was professor at HAMBURG in 16291657, where the JungiusArchiv shows he found several notable results, which he did not publish. [Lau et al.] The first element to be discovered by a known person was phosphorus, discovered by the Hamburg merchant and alchemist Hennig Brand in 1669 [H. P. H. Oliver; The Chemical Elements ; Chemistry Background Book, Nuffield Foundation, London, 1967, p. 6, with a painting of the discovery on p. 7]. The Kunstrechnungsliebende Societt or Kunstrechnungsliebende Gesellschaft Hamburg was founded in 1690 as a group of amateurs of mathematics. It has become the Mathematische Gesellschaft in Hamburg, by far the oldest extant mathematical society. Georg Simon KLFGEL (17391812) was born in Hamburg. Johann Zacharias DASE (18241861), born in Hamburg, probably was the first mental calculator who was a professional computer and is often considered the fastest and most extensive mental calculator on record. He could not learn conventional mathematics and had no intelligence in other fields. In about 1842, he used a new formula to compute ! to 205 places, 200 being correct. This was done (largely or entirely??) in his head, taking two months and was published in 1844. In 1847, he computed 7-place natural logarithms of the integers from 1 to 1,005, 000, though he may have used pencil and paper. This table was printed in Vienna, c1850. From 1849 until his death, the Academy of Hamburg supported him to compute prime factorizations of the numbers from 6,000,000 and he nearly got to 8,000,000. These were completed to 10,000,000 and published in 18621865. [Barlow, pp. 3538. Smith, pp. 98 & 221226.] Heinrich Rudolph HERTZ (18571894) was born in Hamburg. Hermann SCHUBERT (18481911) was professor at the Johanneum (a gymnasium ?) in Hamburg and died there. The University was founded after WW1. Wilhelm BLASCHKE (18851962) was Professor at the University in 1919-1962. Erich HECKE (1887-1957) was professor from 1919. REIDEMEISTER was Hecke's assistant, c1920. Emil ARTIN (1898-1962) was a Dozent from 1923 and Professor from 1926. In 1929, he married one of his students, Natalie Jasny. In 1937, he was dismissed (or left) because his wife was halfJewish and they went to America. He was here for a term in 1957 and then returned as Professor in 1958 and died here. [Richard Brauer; Emil Artin; Bull. Amer. Math. Soc. 73:1 (Jan 1967) 2743 & plate opp. p. 27.] ZORN did his PhD with Artin, finishing in 1930 and taught here briefly. VAN DER WAERDEN was a student(?) in 1926-1927. VON NEUMANN was a Privatdozent in 19291930. IYANAGA, HERBRAND, CHEVALLEY, WITT were here. Helmut HASSE (18981979) was professor from 1950 until becoming emeritus in 1966. He died in nearby Ahrensburg, qv above. The family of Hans ZASSENHAUS (19121991) moved here in 1916. He attended various schools, including the LichtwarkSchule, from which he graduated in 1930. He then entered the University, studying under Artin, Sperner, Hecke. He did his thesis under Artin, obtaining his doctorate summa cum laude in 1934. He then went to teach in Rostock, then returned as Artin's assistant in Jun 1936. He did his Habilitationsschrift in 1938. In 1940, he volunteered for the navy in order to avoid joining the Nazi party. In 1943, he became ausserordentlicher Professor at Hamburg and founded a new institute for applied mathematics. He also became director of the famous Mathematisches Seminar, but went to McGill in 1949. [Michael Pohst; In Memoriam: Hans Zassenhaus (19121991); Journal of Number Theory 47 (1994) 119.] Gottfried Wilhelm LEIBNIZ (sometimes Leibnitz) (16461716) came to HANNOVER (Hanover), Niedersachsen, to serve the Duke in 1676 as Court Librarian and remained till his death. He is buried in the Neustdter Kirche (St. John), HANNOVER, under a plain slab marked "Ossa Leibnitii". [Photo in Stein & Heinekamp, p. 19. I have a photo.] The Leibnizufer is nearby, along the river. The only extant version of his calculator is in the Niederschsische Landesbibliothek, Waterloostrasse 8. The calculator seems to be the seventh and last version (cf [Archibald (2), p. 88]), begun in 1693. Unfortunately, it doesn't work [Cohen]. It is in a safe and not on general exhibit, but serious visitors can apply to the Leibniz Archiv or the Leibniz Gesellschaft offices in the Bibliothek. (See [Stein & Heinekamp, pp. 104109, 120126 & 140142] for diagrams and photos, some in colour.) Leibniz's Nachlass is here and I saw the first usage of the integral sign in 1675 [reproduced in Stein & Heinekamp, p. 30] and some of his early work on binary and the medal he made about it. Leibniz was head of the precursor of this library. Initially Leibniz lived in the Leineschloss, but expansion of the library led to his moving in 1698 to a house with Hannover's most notable facade at the corner of the Kaiserstrasse. The house was destroyed in World War II. The name of Kaiserstrasse does not appear in current maps, so I'm not even sure where it was. The house was beautifully rebuilt in the 1980s as an academic guest house and occasionally open (Sunday afternoons??) museum in the Holzmarkt, not too far from where it was. [Anon., Countries, with a photo. Lehmann & Remmert, p. 37, photo on p. 38. Weimann has pictures, including one from 1825. Stein & Heinekamp, p. 76, reproduces an old print.] There is a relief at the City Hall [Lehmann & Remmert, p. 23]. There is a LeibnizTemple with a bust of Leibniz in the Georgegarten [etching in Stein & Heinekamp, p. 21]. Rather surprisingly, there is a major biscuit firm named Leibniz and their advertisements are common and the biscuits are even obtainable in England. I don't know if there is any connection. On the other hand, the fig newton (an American form of fig roll) is named for its native town of Newton, Massachusetts. William (originally Friedrich Wilhelm) (17381822) and Caroline (17501848) HERSCHEL were born in Hannover, where their father was a bandmaster in the Hanoverian Guards. William attended the Garrison School. At age 13 or 14, William joined his father and elder brother Jacob in the band of the Hanoverian Foot Guards, playing oboe and violin. In 1756, the regiment was stationed at Maidstone, England. After returning to Germany late in the year, Jacob and William left the army and went to England in 1757 Jacob returned to Hannover in 1759. Caroline went to Bath to study singing with her brother in 1772. After William's death, she returned to Hannover in Oct 1823 and lived with their brother Dietrich Herschel until his death three years later. Here she compiled her Zone Catalogue which received the Gold Medal of the RAS in 1828. She is buried in the Gartenkirchof. Another brother, Alexander, spent many years as assistant and mechanic to William and retired back here. [Thoday, item 9. Arago, pp. 258259, 263264. P. Moore (2). F. Brown. The latter two do not always agree with Arago.] Wilhelm JORDAN (18421899) was a geodesist and professor at Hannover from 1881. He is the Jordan of GaussJordan elimination, which he presented in the 4th ed. of his Handbuch der Vermessungskunde in 1895. Carl David Tolm) RUNGE (18561927) was professor in 18861904. LINDEMANN was born in Hannover [Gupta]. Constantin CARATH(ODORY (18731950) taught at the Technische Hochschule here in 19091910 [Behnke]. The University of HEIDELBERG, BadenWGrttemberg, was the first university in Germany, founded by Rupprecht I in 1386 (or 1385). XYLANDER (= Wilhelm HOLTZMANN) was professor at the University of Heidelberg, c1600. HESSE (18111874) was professor in 18561868. Heinrich WEBER (18421913) was born in Heidelberg and studied at the Lyceum and then the University, where he completed his doctoral thesis in 1866 and became Privatdozent, then Ausserordentlicher Professor in 18691873. Sonya KOVALEVSKAYA was the first woman student at the University of HEIDELBERG, c1869. Gustav Robert KIRCHHOFF (18241887) was professor of physics from 1850 until 1875 he and his colleague, the great chemist Robert Wilhelm Bunsen (18111899, monument in the FriedrichEbertPlatz), developed the spectroscope which Bunsen used to discover caesium and rubidium [H. P. H. Oliver; The Chemical Elements ; Chemistry Background Book, Nuffield Foundation, London, 1967, p. 11]. HELMHOLTZ was here from 1858 to 1871, developing his work on optics and starting on acoustics, producing his Sensations of Tone . P. DU BOIS-REYMOND was here he should not be confused with E. du Bois Reymond, the physiologist. Lazarus FUCHS (18331902) was professor from 1875. MENDELEEV was a student. HILBERT studied for a semester here, c1880. Moritz CANTOR (18291920), the mathematical historian, no relation to the set theorist, was at Heidelberg [Fraenkel]. HEILBRONN, BadenWGrttemberg, has a 16C Rathaus with a famous astronomical CLOCK [L.Schmieder; Translated and adapted by L. de Branges de Bourcia; A Comprehensive Guide to Heidelberg Its Castle and its Environs ; 21st ed., Druckerei und Verlag Dr. Johs. H?rning, Heidelberg, nd [c1955], p. 52]. Robert MAYER, the discoverer of the law of conservation of energy, was born in Heilbronn [ibid.]. Paul FINSLER (18941970) was born in HEILBRONN, BadenWGrttemberg. Georg S. KLFGEL (17391812), the first person to suggest that perhaps the Parallel Postulate could not be proven (in his 1763 doctoral dissertation, after examining 28 attempts to prove the Parallel Postulate and finding them all wanting), was a professor at HELMSTDT [Underwood Dudley; Mathematical Cranks ; Math. Assoc. of America, Washington, DC, 1992, pp. 144-145; Morris Kline; Mathematical Thought from Ancient to Modern Times ; OUP, NY, 1972, pp. 867-869]. This is the modern Helmstedt, Niedersachsen, east of Braunschweig. GAUSS did his dissertation here under PFAFF in 1799 [Neuenschwander & Burmann]. Karl MENNINGER (18981963), author of many popular mathematics books and the magisterial Zahlwort und Ziffer ( Number Words and Number Symbols ), was a school teacher in HEPPENHEIM. The only Heppenheim in my German atlas is Heppenheim an der Bergstrasse, Hessen, about 20km NNE of Mannheim. Hermann Amandus SCHWARZ (18431921) was born in HERMSDORF, Silesia, now Sobiecin, Poland. Wilhelm SCHICKARD (1592-1635) was born in HERRENBERG, BadenWGrttemberg, 30 km SW of Stuttgart, and went to the Lateinschule there [van FreytagL?ringhoff]. Hermann Csar Hannibal SCHUBERT (18481911) was a gymnasium teacher in HILDESHEIM, Niedersachsen, until 1887. Adolf HURWITZ (18591919) was born in Hildesheim. Ludolph van CEULEN's (1540-1610) monument in Leiden, Netherlands, (cf in Section 10) says he came from Hildeshim, but I don't know if it is this Hildesheim. In HUNFIELD, there is a school named for Konrad ZUSE (19101995), one of the earliest inventors of the computer, who lived nearby [Rochester & Gantz, p. 40]. This is probably HGnfeld, Hessen. The University of Bavaria was founded in INGOLSTADT, Bayern, in 1472, but moved in 1800 to Landshut and then again in 1821 (or 1826) to Munich, Bayern, where it is now the University of Munich, qv. However, the original building in Goldknopfgasse is now used by the Hoheschule [Pengelley & Pengelley, p.146]. Petrus APPIANUS (= Bienewitz or Bennewitz) (14951552) died at Ingolstadt. Christoph RUDOLFF (c1500c1545) was born in JAUER, Silesia, now Jawor, Poland. Michael STIFEL (c14871567) died in JENA, ThGringen. The University was founded in 1588 (or 1548). It is now known as the FriedrichSchiller University. The original university buildings are the Collegium Jenese. LEIBNIZ was here at some time, as was Hegel JnosAndrs [= Johann Andreas von] SEGNER (17041777) was a student, then practised medicine, then became Professor. Karl MARX received his doctorate here. Ernst HAECKEL (18341919) was Professor of Biology from 1858 and made beautifully symmetric drawings of marine life, e.g. radiolaria in the shapes of all the regular polyhedra, but there is some doubt as to whether all of these really existed. Gottlob Friedrich Ludwig FREGE (18481925) was professor at the University of Jena from 1879. In the mid 19C, Carl ZEISS and Ernst ABBE, both at the University, set up an optical factory based on their developments of the microscope and it has been one of the world's premier suppliers of optical and other instruments. There is an Optical Museum (Optisches Museum) in CarlZeissPlatz and a 1923 Zeiss Planetarium in the botanical garden, the oldest working planetarium in the world, designed by Walther Bauersfelt. This was the first geodesic dome construction, but it was then covered in a concrete shell. [Baister & Patrick, p. 144.] Kaiserwerth see DGsseldorf. KARLSRUHE, BadenWGrttemberg, had Germany's first School of Technology (Technische Hochschule ??) in 1825, which has now become the University. The city was laid out in 1715 with 32 straight lines radiating from the palace [Nigel Pennick; Leylines ; Weidenfeld & Nicolson (Orion), 1997, p. 15, with illustration]. Carl Fridolin Bernhard HIERHOLZER (18401871), the first to carefully prove that a graph with at most two odd vertices has an Euler path, was a student at Karlsruhe and later assistant to LGroth here in 1870 [Biggs, Lloyd & Wilson, p.217]. Wilhelm JORDAN (18421899) was a geodesist and professor at Karlsruhe in 18681881. He is the Jordan of GaussJordan elimination. Heinrich Rudolph HERTZ (18571894) was a student at the Technical High School. He later was Professor (of Physiology ??) in 18851889 when he demonstrated the existence of electromagnetic waves in 1887 [Ackermann, p. 368]. [Storer, p. 118] says he observed that radio signals were reflected by the pillars in his laboratory this is the ultimate origin of radar, see Sections: 2E: National Physical Laboratory; 3:Baird, WatsonWatt; 6-A: Daventry, Seaview; 8: Karlsruhe. KASCHAU see Kosice in Slovakia (Section 10). Jost BFRGI (1552-1632), co-inventor of logarithms, worked at KASSEL (then spelled Cassel) Observatory, Hessen, in 1590-1604 and 1612-1632. [But see Archibald (3), p. 15.] In the Astronomisches Kabinett of the Hessisches Landesmuseum is a reconstruction of Leibniz's binary calculator [Stein & Heinekamp, p. 120, has a photo]. There are numerous other globes, clocks, etc., including a small astronomical clock from the late 16C which is based on the Copernican system [ MGG , p. 172]. Helmut HASSE (18981979) was born in Kassel. Ernst STEINITZ (18711928) was professor at the University of KIEL, SchleswigHolstein, from 1920 until his death here. Hans Wilhelm GEIGER (18821945) was professor of physics in 19251929. In 1928, he and a colleague, W. MGller, improved his 1908 counter into what is properly the GeigerMGller counter [Sholl, p.74] cf Manchester in Section 6A. In 1933, Rudolph KFHNOLD developed an early radar system, detecting a ship 550 m away and then 11 km away. He even detected an aircraft which unexpectedly flew through his beam. Although the German government provided support, this project seems not to have been developed much further. [Storer, p. 118.] See Sections: 2-E:National Physical Laboratory; 3: Baird, WatsonWatt; 6A: Daventry, Seaview; 8: Karlsruhe. Hans ZASSENHAUS (19121991) was born in KOBLENZMOSELWEISS, RheinlandPfalz, but the family moved to Hamburg when he was four. ALBERTUS MAGNUS (1193 (or 1206) 1280) and DUNS SCOTUS (c12651308) gave lectures at K>LN (=COLOGNE or C?ln), NordrheinWestfalen, in the 1314C. Albertus retired from his bishopric on the grounds that it was too warlike to Cologne in 1262. THOMAS AQUINAS came here to study with him. His sarcophagus is in St. Andrew's (St. Andreas), a bit NW of the Cathedral (Dom) [ MGG , p. 104]. [Holmyard, pp. 111114.] The University was founded in 1388, apparently the second university in Germany, after Heidelberg (1386), but it was closed down by the French occupation in 1798 and not reopened until 1919, when Konrad Adenauer was mayor of the city [ MGG , p. 98]. Georg Simon OHM (17801854) was Professor of Mathematics at the Jesuit College here in 1817. Stefan COHNVOSSEN was at the University to 1933. The GermanoRoman Museum (R?mischGermanisches Museum), adjacent to the Cathedral (Dom) displays some Roman games and a Philosophers' Mosaic, showing the Seven Sages of Greece (one of whom was THALES) [ MGG , p. 100]. K>NIGSBERG , of the seven bridges, was the capital of East Prussia, but is now KALININGRAD in the USSR. My colleague Jeremy Wyndham has become interested in the seven bridges and has made inquiries which have turned up several maps of K?nigsberg and a list of all the bridges and their dates of construction (though there is some ambiguity about one bridge). The first bridge was built in 1286 and until the seventh bridge of 1542, an Euler path was always possible. No further bridge was built until a railway bridge in 1865 which led L. SaalschGtz to write about this in 1876 and to count the number of Euler paths. He got 192 starting from the island, but I recently wrote a program to find the number of paths in each case and discovered that he omitted two cases, leading to 16 paths, and there are actually 208 paths starting from the island. In 1905 and later, several more bridges were added, reaching a maximum of ten bridges in 1926 (with 4512 paths from the island), then one was removed in 1933. Then a road bridge was added, but it is so far out that it does not show on any map I have seen. Bombing and fighting in 19441945, especially carpet bombing by the RAF in Aug 1944, apparently destroyed all the bridges the Russians have rebuilt six or seven of them. I have computed the number of paths in each case from 1865 until 1935 or 1944, there were always Euler paths. The (Herzog Albrecht or Albertina) University of K?nigsberg was founded by Duke Albrecht of Prussia in 1544. One of the old city bastions, on the west, off modern Gvardeysky Prospekt, just north of the 11th Guards Army Monument, is called the Astronomers' Bastion perhaps it was used as an observatory?? There were Copernicus Strasse, Besselplatz and Besselstrasse in the area. Immanuel KANT (17241804) was born, lived and died here and was originally a cosmologist, expositing Newton's cosmology and producing a reasonable theory of the formation of the Solar System. He entered the University in 1740, studying mathematics, natural science and philosophy. His tomb is on the north side of the Cathedral. There is a Kant statue to the southeast of the University. He was buried in the graveyard of the University, but moved to a portico of the Cathedral in 1924, where it survived WW2. [John Noble, Nicola William & Robin Gauldie; Estonia, Latvia & Lithuania ; Lonely Planet Publications, Hawthorn, Australia, 1997, pp. 414, 415, 417, 419, 421.] In 1810, Friedrich Wilhelm BESSEL (1784-1846) was summoned by the King of Prussia to be Professor of Astronomy at the University and to supervise the construction of Observatory, becoming its first Director. In 1819, he developed and published Fourier series, three years before Fourier! In 1824, he first systematically studied the Bessel functions. In 1838, he made the first observation of a stellar parallax, hence of a stellar distance, of 61 Cygni, about 11 lightyears away. Its parallax is less than .3" (or .3' ??) of arc the aberration due to the Earth's motion is about 40'. He had started working on this about thirty years previously. Henderson, 1839, and Struve, 1840, made independent measurements of a stellar parallax. Carl Gustav Jacob JACOBI (1804-1851) was professor in 1827-1844. He persuaded the University to confer a PhD on STEINER in 1833. Gustav Robert KIRCHHOFF (18241887) was born in K?nigsberg and was a 21 year old student at the University when he formulated his famous laws of electric current flow [Biggs, Lloyd & Wilson, p.218]. Rudolf LIPSCHITZ (18321903) was born and studied here. HELMHOLTZ (18211894) was Professor of Physiology and General Pathology at the University in 1849-1855, studying the transmission of nerve impulses and starting his work on optics, including the Young-Helmholtz theory of colour vision. The University awarded an honorary doctorate to WEIERSTRASS in 1854 in recognition of his first paper of 1853. Heinrich WEBER (18421913) was Professor in 18731883. David HILBERT (18621943) was born near the city and his family moved into the city soon after. He attended school and university here, studying under Weber, getting his PhD in 1885. After a year of travel, he returned, took his Habilitation and did some lecturing for two years. (HURWITZ was Professor at this time.) Hilbert then did some more travelling. He met Gordan, and upon his return to K?nigsberg, he proved the finite basis theorem of invariant theory and then made it constructive. LINDEMANN succeeded Hurwitz as Professor in 18831893 [Gupta] and then was succeeded by Hilbert until 1895. [Neumann (2).] There was a copy of the Munich bust of Lindemann here but it is now lost. MINKOWSKI was a student from 1880. In 1881, as a freshman, he produced his solution to the Paris Academy's problem of the sum of five squares. The Academy then discovered that H. J. S. SMITH had solved the problem some years before, but found Minkowski's work sufficiently exciting to give him a prize despite the submission not being in French. Hilbert got him back and later he was Professor in 18951896. H>LDER was professor in 1896-1899. SCH>NFLIES was professor in 18991914. BIEBERBACH was Dozent in 19101913. BLASCHKE was Professor in 1917-1919. R. BRAUER, ROGOSINSKI, SZEG> were here. Konrad KNOPP (18821957) was Professor in 19201926. Kurt Werner Friedrich REIDEMEISTER (18931971) was professor in 19251933. Gabor SZEG> (1895 ) was professor in 19261935, fleeing to the USA. Juergen MOSER (19281999) was born in K?nigsberg and attended school there, leaving for G?ttingen in 1947. K>NIGSBERG, in the Duchy of Coburg, Upper Franconia, Bayern (NOT the one with seven bridges), was the birthplace of Johann MGller, known as REGIOMONTANUS (1436-1476). There is a plaque on the house where he was born. [Anon., 1976....] Gaspar SCHOTT (16081666), the prolific 17C writer on all fields of science and technology, ranging from mathematics to angels and sea monsters, was born in K>NIGSHOFEN. However, there are two of these, in Bayern and in BadenWGrttemberg, and my source is not specific. Max ZORN (19061993) was born at KREFELD, NordrheinWestfalen. NICHOLAS OF CUSA (14011464) was born in KUES (= Cues), now part of BernkastelKues, RheinlandPfalz, on the Moselle, below Trier (Treves). He suggested the earth rotated on its axis and revolved about the sun, proposed reforming the Julian calendar and attempted to square the circle. He left his library and instruments to the library of St. Nicholas' Hospice (Cusanusstift) he founded there in 1447. He specified that the hospice should house 33 poor people the age of Christ at his death, and this number is still adhered to. The four astronomical instruments of 1444 are the oldest German examples. In the chapel is a bronze copy of his tombstone in S. Pietro in Vincoli, Rome, and the tomb of his sister Clara Cryftz. [Sarton, pp. 14, 77 & 264. MGG , p. 80.] [Headlam(2), pp. 5152] reports that in 1451, the Cardinal came preaching through Germany, selling Indulgences like a cheapjack, lowering his price from time to time to get rid of his stock. LANDSHUT, Bayern, about 60km NE of Munich, is where the University of Bavaria was from 1800 to 1821 (or 1826), between being at Ingolstadt and at Munich. ALBERTUS MAGNUS (1193 (or 1206) 1280), Count of Bollstdt, was born in LAUINGEN, Bayern [Holmyard, p. 111]. Ernst STEINITZ (18711928) was born at LAURAHFTTE, Oberschlesien. This area is now part of Poland but I cannot determine the new name. The University of LEIPZIG, Sachsen, was founded in 1389 (or 1409??), apparently the third university in Germany, after Heidelberg (1386) and K?ln (1388). The 1409 date is based on the fact that in 1409, the constitution of the Charles University in Prague was changed to favour the Hussite Czechs and some 2000 students and many professors then emigrated and founded the University of Leipzig. REGIOMONTANUS was a student at the University from 1447 to c1450. Johann(es) WIDMANN (1462?-1498) was a student in 1480-1485 and then taught for some years, apparently giving the first German lectures on algebra in 1486. His 1489 arithmetic was the first printed book to use + and signs. He died in Leipzig. RHAETICUS (1514-1576) [= Rheticus = Retyk] came to teach in 1542 and remained until his death. Tycho BRAHE was a student of jurisprudence from about 1562. Gottfried Wilhelm LEIBNIZ (16461716) was born in Leipzig and attended the Nicolai school on the north side of the Nikolaihof in 16531661. He later studied at the University, receiving a Master's in 1664, but he was not awarded a Doctorate in Law because he was too young he was 20 at the time so he went to Altdorf and got his doctorate there in 1667. There is a statue in Universittstrasse, just south of the main university buildings [photo in Beckert & Schumann, p. 16]. (This is probably the statue formerly by the St. Thomas Kirche mentioned in [Alexanderson].) In 1682, the Acta Eruditorum was founded in Leipzig. This was the outlet for many of Leibniz's basic papers on the calculus. It ran until 1779. The University, formerly the Karl-Marx-Universitt Leipzig, has had many notable professors: MOLLWEIDE (18111825, first as Observer, then professor and Dean); M>BIUS (1816-1869 (or 1844?)); Carl Gottfried NEUMANN (18321925) was professor in 1869-1910; KLEIN (1880-1886); LIE (succeeding Klein, 1886-1898); H>LDER (1899-1930); HAUSDORFF (1901-1910); HERGLOTZ (1909-1925); BLASCHKE (1915-1917); VAN DER WAERDEN (1931-1945); KOEBE (1926-1945); E. HOPF (1937-1944); KHLER (1948-1958). For the first half of the 20C, the Mathematical Institute was located in an extant building at Talstrasse 35. Over the side entrance is a diagram of Leibniz, "Methodi tangentium inversa exempla", dated 11 Nov 1677, showing ( y dy [photo in Beckert & Schumann, p. 270]. Ernst CHLADNI (17561827) studied law here, receiving his degree in 1782, but then turned to science, particularly the study of acoustics, discovering Chladni figures and producing the first treatise on acoustics in 1787. M>BIUS (1790-1868) was a student in 1809-1813, studying under MOLLWEIDE. M?bius was Professor of Astronomy and Observer from 1816, Professor of Higher Mechanics and Astronomy in 18441868. (A source says he was in Jena from 1844??) He lived and died at an official residence in the Pleissenburg, since rebuilt as the Neues Rathaus. Wilhelm Eduard WEBER (1804-1891), the colleague of Gauss in developing electromagnetism in theory and practice (cf G?ttingen) was professor (of physics?) in 18431849. HANKEL moved to Leipzig as a 10 year old in 1849 and attended the Nicolai-Gymnasium. He was a student at the University in 1857-1860 and taught there in 1863-1867. KLEIN came as Professor in 18801886 and initiated the Mathematische Seminar in 1881. He lived on the north side of Shakespearestrasse, east of Hoffmannstrasse, in 1880-1885. VAN DYCK, HURWITZ, MOLIEN, HILBERT and STUDY came to study with Klein. Felix HAUSDORFF (1868-1942) came to Leipzig in c1871 and attended the Nicolai-Gymnasium in 1878-1887. He was a student at the University in 1887-1888, 1889-1891 and 1893-1895. He was a Dozent from 1895 and Professor in 1901-1910. Ludwig Otto H>LDER (18591937) was a student at the University in 1882-1884 and Professor in 1899-1930, becoming emeritus until his death here. PAD( was a student in 18891890. KOEBE was a professor. Werner HEISENBERG (19011976) was here from 1927, the youngest professor in Germany at the time. He received the 1932 Nobel Prize in Physics. TELLER was assistant to Heisenberg. Emil ARTIN (1898-1962) received his PhD here in 1921. Charles Edward SPEARMAN studied psychology here in 18971899 and returned to study and work in 19021907. The presence of Bartel Leendert VAN DER WAERDEN (19031996) in Leipzig through WW2 gave rise to an accusation of collaborationism, but [Beckert & Schumann, p. 240] and personal contacts at Leipzig say that there is no basis for such accusations van der Waerden was non-political and was under some restrictions as a foreigner and for his refusal to collaborate. The largest(?) German library is the Deutsche BGcherei in Leipzig. Founded in 1912, it hopes to accumulate all books in German and related materials. As of 1993, it had about 8 million books. Petrus APPIANUS (= Bienewitz or Bennewitz) (14951552) was born in LEISNIG, Sachsen. In LEMGO, NordrheinWestfalen, the Town Hall (Rathaus) has statues of noted philosophers and physicians on the facade, including ARISTOTLE [ MGG , p. 179]. Wilhelm Conrad R>NTGEN (18451923) was born at 1 Gnsemarkt, near the Moll Platz, (Remscheid) LENNEP, NordrheinWestfalen, but his family moved to Apeldoorn, The Netherlands, when he was three. There is a plaque on the house. The Deutsches R?ntgenMuseum, Schweimerstrasse 41, near the Moll Platz, is a large museum dedicated to him, established in 1930. It contains his library, a reconstruction of his laboratory in WGrzburg and lots of memorabilia. The birth house is used as the Museum's library and guest house. [Pengelley & Pengelley, pp.155-157.] The family of Johann KEPLER (15711630) lived at Marktplatz 11, LEONBERG, BadenWGrttemberg, about 15 km W of Stuttgart, in 15761579, when he was a boy. He was a student at the Lateinschule, previously the Beginenhaus and now the Museum fGr Vor und FrGhgeschicht, in 15761579 and later in 15821583. Kepler's mother was living in Leonberg in her old age when she was prosecuted for witchcraft by Lutherus Einhorn, who built the extant house at Pfarrstrasse 14. [Eberhard Walz & Bernadette Gramm; Historischer AltstadtfGhrer Leonberg ; 1991, with some handmade corrections to 1993, pp. 1213, 4448. Thanks to A. E. L. Davis for a copy of this material.] LIEGNITZ (now LEGNICA in Poland), Prussia, was the birthplace of Leopold KRONECKER (18231891). He attended the local school and the Gymnasium, where KUMMER was his teacher. After attending the University of Berlin in 18411845, he had to return and run the family estate for 10 years. [Perfect. Fraenkel.] Kummer taught here from 1831 to 1842 [Hensel]. Wilhelm ACKERMANN was at the Gymnasium in LFDENSCHEID, NordrheinWestfalen, about 60 km east of DGsseldorf. RIEMANN (18261866) was a student at the Johanneum in LFNEBURG, Niedersachsen [Ahrens, p. 16]. LUTHERSTADT WITTENBERG see Wittenberg, below. Otto von GUERICKE (16021686), engineer and mayor of MAGDEBURG, SachsenAnhalt, carried out his famous air pump and vacuum experiments here in the 1640s and 1650s. In 1660, he devised the first electrical machine, a ball of sulphur on a rotating shaft which generated an electric charge on a dry hand. He described these experiments in his Experimenta Nova (ut Vocantur) Magdeburgica de Vacuo Spatio of 1672. There is a monument to him in the front of the Town Hall (Rathaus) [ MGG , p. 189]. There are exhibits on his work in the Kulturhistorisches Museum, OttovonGuerickeStrasse 6873 [Baister & Patrick, p. 182]. At the Otto von Guericke Technische Hochschule in Magdeburg is a sculpture garden of mathematicians and physicists. A photo of the ARCHIMEDES statue is in [Pieper]. Lazare Nicolas Marguerite CARNOT (17531823) died in Magdeburg. MAINZ, RheinlandPfalz, was where Johannes Gensfleisch, known as GUTENBERG (1398?1468) started printing, c1450, the means whereby mathematics and knowledge in general have become so widespread. He was born in a vanished house at the intersection of Christofstrasse and Schusterstrasse. Due to political quarrels, he was exiled in c1428 and spent 14301444 in Strasbourg (qv in Section 7B) where he had developed all the techniques and equipment for printing by 1440, but no examples of Strasbourg printing are known. He left Strasbourg in 1444, but nothing is known of him until he reappears in Mainz in 1448 and begins setting up a printing house. In 1450, he borrowed money from Johann Fust, who foreclosed in 1455, taking over the entire shop and the employees, particularly Peter Schoeffer (or Sch?ffer) who married Fust's daughter, so that the first known printed books a Bible of 1456 and a Psalter of 1457 were published by Fust & Schoeffer, but it is clear that these works were well in hand under Gutenberg. The earliest known European printing is a letter of indulgence, printed here in 1454 or 1455 there is an example in the British Museum. ([Storer, p. 16] asserts that the oldest known printing is a fragment of a poem and part of an astronomical calendar produced by Gutenberg in 1448, but gives no further details.) There is a Gutenberg Museum at Liebfrauenplatz 5, with a reconstruction of his print shop, his original hand press and a Gutenberg Bible. [Ackermann, pp. 505506. Eastman, p. 142.] There is a statue in Gutenberg Platz. Gutenberg started printing with wooden blocks, before he developed the use of metal type. Far from realising the importance of the idea, these early printers simply thought they had a way of producing imitation manuscripts which could be sold at manuscript prices! Gutenberg made some 290 types for his famous Bible in order to simulate manuscript characters. About the same time, Costar was doing much cruder printing at Haarlem (qv under Netherlands in Section 10), but he did little, though one legend is that one of Costar's apprentices ran away to Mainz and told Gutenberg the ideas. In 1454?1457, Gutenberg was in Frankfurt, see above, but returned to Mainz and died there. By 1500, some 35,000 books had been printed. Archbishop Berthold, Elector of Mainz, enjoys the distinction of first establishing a censorship of printed books in 1486! Denis Papin (1647c1712) was professor at the University of MARBURG (an der Lahn), Hessen, from 1687. TYNDALL did his PhD at the University of MARBURG in 18491851 [Low, pp.111-112]. Heinrich WEBER was professor in 18841892. HENSEL was here. DAVENPORT spent some time here in c1932 [Rogers]. HASSE (18981979) was professor in 19301934. REIDEMEISTER (18931971) was professor in 19341955. There is a Mathematisch Physikalischen Institut at Marburg which contains a globe clock (Globusuhr) with the earliest known example of a gear system with a mobile gear (i.e. not having a fixed axis, generally called an epicyclic gear), built about 1575 for Landgraf Wilhelm IV of Cassel by his instrument maker Baldewin [H. von Bertele; The origin of the differential gear and its connection with equation clocks; Trans. Newcomen Society 30 (195557) 145155 and plates XXXIXXXV]. KEPLER (15711630) attended the Klosterschule or Protestant Seminary at MAULBRONN, BadenWGrttemberg, 40 km NW of Stuttgart, in 15861589 [Boll, p. 14; Eastman, p. 148]. Friedrich Wilhelm BESSEL (1784-1846) was born in MINDEN, NordrheinWestfalen. WILLIAM OF OCKHAM (or OCCAM) (12851347) was an adviser to the Holy Roman Emperor, LudwigIV, based in MFNCHEN (MUNICH) , Bayern, c1330, after escaping from imprisonment for heresy at Avignon. At some point, he was excommunicated. He died in Munich. Nicholas KRATZER (1487 ?, fl. 1523) came from Munich, but did most of his work in England. There are portraits of him by DGrer and Holbein. The ALTE PINAKOTHEK, Munich, contains several paintings of interest. Most notable is the famous 1500 selfportrait of DFRER. There are several other fine paintings by him. The Portrait of a Master Builder, by the Master of the Life of the Virgin, late 15C, shows him holding a dividers. There is also a de la Tour portrait of Mademoiselle Ferrand meditating on Newton I don't recall seeing this, but a catalogue shows her with a copy of the Principia behind her. The Bayerische Akademie der Wissenschaften was founded in 1759. Benjamin Thompson, Count RUMFORD, was chief adviser to the King of Bavaria about 17841792 and 17961798, becoming also Minister of War and Chief of Police. Among other things, he had the army round up all the beggars and put them in workhouses. He experimented with food for them potato and barley soup is still called Rumfordsuppe. He also turned a marsh into the Englischer Garden, where there is a Rumford memorial at the southeast corner and a Rumfordsaal. There is also a statue on Maximilianstrasse and there is a Rumfordstrasse just south of the city walls. It was in Munich that he made observations on the heat generated in boring cannon, leading to his assertion that heat is a form of motion. Joseph von FRAUNHOFER was at Munich and was the best optical glass maker in the world. In 1802, Wollaston had observed some dark lines in the sun's spectrum by repeating Newton's spectrum experiment with a slit rather than a pinhole. In 1815, Fraunhofer used improved equipment to find many more lines and recognised that different elements gave different lines, thereby founding spectroscopy. The dark lines are now called Fraunhofer lines. He also devised the split lens viewer for his heliometer. In 1824, he produced the first clockdriven telescope. There is a statue of him on Maximilianstrasse. The DEUTSCHES MUSEUM on the Museuminsel in Munich is the main German museum for the history of science, and perhaps the largest one in the world. It was founded by the engineer Oskar von Miller (1855-1934), in 1903, with the cornerstone laid in 1906. The actual Museum opened in 1925, with further buildings completed in the following years. There is a bust of von Miller in the entrance hall. The Museum pioneered the 'hands-on' approach to science exhibits. [Danilov, pp.19-20.] There are some 16,000 exhibits. The Ehrensaal (Hall of Fame) on the first floor has portraits and busts of: Albertus Magnus, Clausius, Copernicus, Diesel, Einstein, von Fraunhofer, Gauss (the same portrait as in Braunschweig I don't know which is a copy), von Guericke, Gutenberg, Hahn, Heisenberg, von Helmholtz, Hertz, Kepler, Leibniz, Julius Robert Mayer, Meitner, Ohm, Planck, R?ntgen, among others. Nearby are rooms devoted to the scientific instrument makers Georg Friedrich Brander (17131783) and Joseph von FRAUNHOFER (17871826), including a spectrum showing the dark lines, drawn and coloured by Fraunhofer. Fraunhofer's instruments were used by Galle in discovering Neptune and by Bessel in measuring stellar parallax. The Physics Department includes a reconstruction of Galileo's study, von Guericke's original air pump and hemispheres, some of R?ntgen's original Xray tubes, Hertz's apparatus for verifying the existence of electromagnetic waves, equipment used by Hahn and Meitner, etc. The Telecommunications Department has a reconstruction of the GaussWeber telegraph. On the third floor are galleries on measurement of length, weight and time. In 1988, the Computer Science and Automation Microelectronics exhibits were opened. This is an extremely rich collection, with many original devices and reconstructions of almost everything else it even has its own separate guidebook of 215 pages. In particular, they have von FreytagL?ringhoff's original reconstruction of Schickard's 1624 machine and reconstructions of Pascal's machine and of the Leibniz machine in Hannover (I don't know if they've made it work). They have an example of HAHN's 1774 fourfunction calculator. They have a rebuilt version of ZUSE's Z3 of 1941, widely accepted as the first 'general-purpose program-controlled calculator'. It only required conditionals to be a computer. [Augarten, p. 95.] They also have parts of Z1 and the complete Z4 (19421944). A number of automata have been moved here, including the late 16C Bear Driver, the c1540 Preaching Monk and the lifesize Trumpeter of 1810. A section is devoted to cryptography with two forms of the Enigma machine as well as many earlier devices. There is a splendid section of Technical Toys, in wood, stone, metal and plastic, with information about Friedrich FROEBEL and F. Adolph RICHTER. The Richter stone material was invented by Otto & Gustav Lilienthal, better known as aviation pioneers they sold the patent and their machines to Richter for 1000 marks to support their aviation experiments. The material might better be described as a fine brick which could be precisely moulded. Richter improved the stone and was producing puzzles from 1882 until the plant closed in 1964. Modern facsimiles are now being produced. See also Rudolstadt and Schweina, below, and Section 10: Netherlands: Alphen aan den Rijn. Among other exhibits are: Liebig's laboratory; an 1839 Daguerre camera; an 1860 Jacquard loom; the first selfexcited dynamo by Werner von Siemens in 1866; the first electric locomotive, again by Siemens in 1879; a number of other pioneering electrical devices; some of Lilienthal's gliders of c1885; the first motorcycle, by Daimler and Maybach, 1885; the first vehicle with a petrol engine Auto Number 1, by Carl Benz in 1886 (or 1885) {Actually Siegfried Marcus had a petrol car in Vienna c1875 cf Section 10: Austria: Vienna. Daimler was responsible for improving the petrol engine to real practicability, in particular he devised the carburettor, while Benz developed an adequate chassis for use with a patrol engine. [Storer, pp. 7579.]}; Lumi/re's first cinema camera of 1895; the first Diesel engine of 1897; the first German submarine, the U1 of 1906; one of the Wright Brothers' early biplanes, a TypeA Standard of 1909; several original early jet and rocket planes and rockets; Jacques Piccard's 1958 Bathyscaphe sphere; and an observatory and a planetarium. [DBS. Museum Guide. MGG , pp. 212213.] In the early 1970s, the length of galleries was estimated as 20 km. There is an astronomical clock in the gatehouse tower. The Bavarian State Library (Staatsbibliothek) in Ludwigstrasse is one of the largest in Europe with over 3M volumes (as of the early 1970s). The University was founded in Ingolstadt, Bayern, in 1472, then moved to Landshut, Bayern, in 1800 and then King Ludwig I brought it to Munich in 1826 (or 1821) and is formally the LudwigMaximilianUniversitt, located in Ludwigstrasse (or Leopoldstrasse). In the early 1970s, it had 25,000 students. The Technical University was founded in 1868. In the early 1970s, it had about 10,000 students. Von Miller was a student. Georg Simon OHM (17801854) was Professor of Mathematics and Physics in the mid 19C. HESSE (18111874) was professor at the Technische Hochschule from 1868. Klein was professor at the Technische Hochschule, 18751880. Siegmund GFNTHER (18481923) was Professor of Geography from 1886, but wrote several still useful books on the history of mathematics and science. There is a relief bust of Carl Louis Ferdinand LINDEMANN (1852-1939) in the Mathematical Institute of the University of Munich on Theresienstrasse, showing ! inside a square inside a circle. He was Professor from 1893 [Gupta]. He died in Munich and is buried in the Waldfriedhof. HERTZ was a student. Wilhelm Conrad R>NTGEN (18451923) was head of the Physical Institute at the University from 1900 to 1920 and continued to work until his death at his country house in Weilheim, near Munich. He received the first Nobel Prize in Physics in 1901. [Pengelley & Pengelley, pp. 155157.] Constantin CARATH(ODORY (18731950) was Professor at Munich in 19241950. He had a house in Rauchstrasse, Bogenhausen, a 30 minute walk from the University, via the English Garden. [Behnke.] He died here and is buried in the Waldfriedhof. Alfred PRINGSHEIM (18501941) was professor in 18861939, then fled to ZGrich. TIETZE was at the University. The family of Albert EINSTEIN (18791955) moved to Munich in 1880 and lived somewhere in Adelreiterstrasse. He attended the Leopold (Luitpold) Gymnasium from 1898 to 1895 the Gymnasium was at MGllerstrasse 3 until the Second War. [Whitrow, pp. 23. Eastman, p. 138.] Max von LAUE (18791960) was at Munich when he devised Xray crystallography in 1912, receiving the Nobel Prize in 1914. Heinrich Franz Friedrich TIETZE (18801964) was a student and later was professor from 1925 until his retirement in 1950, and continued to live here until his death [Biggs, Lloyd & Wilson, p.221]. WITTGENSTEIN's sister, Margarethe StonboroughWittgenstein, for whom he designed the Wittgensteinhaus in Vienna, was the subject of one of Gustav Klimt's notable portraits in 1905 this is in the Bayerische Staatsgemldesammlung. (Adolf) Abraham FRAENKEL (18911965) was born in Munich. HEISENBERG was here at some time. There is a fine 1540 astronomical clock in the Cathedral (Dom) of MFNSTER, NordrheinWestfalen [ MGG , p.217]. The clock casing is handsomely painted by members of the tom Ring family, excellent painters of the time, but whose work is not known outside the region. The works have been replaced several times, most recently in 1930. There is an example of the Three Rabbits pattern (cf under Paderborn, below) on a roof boss in the SW corner of the S transept, over the organ. My thanks to Michael Freude and Hanno Hentrich for remembering the existence of this and finding it. Since the Dom was much restored after the War, I thought it might be a postwar addition, but Hanno Hentrich checked in a MGnster history and photos showed this part of the Dom had survived, though the date of the boss is not stated in the material he had available. A local guidebook [Wolfgang Neumann & Ralf Schaepe; MGnster A City Guide ; NWVerlag, MGnster, 1998, p. 26] draws attention to the 5m high statue of St. Christopher near the entrance. The statue is holding a small real tree, with the trunk passing through his clenched hand. However, both the base and crown of the tree are larger than the hole through the clenched hand of the statue. This is very much like a classical 'impossible object', a typical example being a wooden arrow through a CocaCola bottle, with both ends of the arrow being much larger than the holes in the bottle. Christoph (or Cristof) GUDERMANN (17981852), of the Gudermannian function, was professor at the Theological and Philosophical Academy (now the University) in MGnster. WEIERSTRASS was sent here to prepare to be a school teacher and attended Gudermann's lectures on elliptic functions in 1839 the class shrank from thirteen students to one after the first lecture [Ahrens, p. 21; A. C. Baker]. KILLING was a student in 1865-1867, but there was no mathematician on the staff at the time. STURM was professor in 18781892. COURANT was professor in 19191921 (?). MGnstereifel see Bad MGnstereifel, above. In 1619, DESCARTES enlisted in the army of the Duke of Bavaria. On 10 Nov 1619, at NEUBERG on the Danube (presumably NEUBURG, Bayern, about 20km west of Ingolstadt), he found the cold, which he never liked, so bad that he locked himself in a heated room and began his contemplations. He and others consider this the most significant date of his entire life and the birthdate of analytic geometry! At the end of the winter, he continued his wanderings. [Scott, pp. 2 & 87.] NFRNBERG (= NUREMBERG ), Bayern, is best known as the home of Albrecht DFRER (1471-1528), Renaissance artist and geometer, but has had some other citizens of mathematical interest. In the Frauenkirche is a striking clock dating from 1356, renewed in 1509 and twice since [Headlam (2), p.256]. The first German papermill was established here by Ulman Stromer in 1390. (A source says this was the first papermill north of the Alps, but another source says Troyes, France, had a mill in 1348. Johann Sensenschmitt established printing in Nuremberg in 1470. Johann MGller, known as REGIOMONTANUS (1436-1476) came here in 1471 "because there I find without difficulty all the peculiar instruments necessary for astronomy, and there it is easiest for me to keep in touch with the learned of all countries, for Nuremberg, thanks to the perpetual journeyings of her merchants, may be counted the centre of Europe." He was also interested in the town's printing facilities. He set up an observatory, using instruments of his own design, assisted by Bernhard Walther this seems to be the first observatory in Europe. He installed a printing press in his house to print his own and similar works he was the first specialist printer of mathematical and astronomical works and also sold instruments. He produced his Kalendarium Novum in 1472. A source says he published the first almanac in 1474. Sixtus IV called him to Rome to assist in reforming the calendar in c1475 and he died of the plague there. One of his pupils was Martin BEHAIM, navigator and cartographer, who produced the first terrestrial globe in 14911493 which predicted the route of Vasco da Gama around Africa some six years later. [Headlam (2)] even says Behaim suggested to Magellan the idea of the Strait of Magellan, but I don't know if this means that they actually met or just that Behaim's work influenced Magellan this influence cannot have been through this globe as it does not show the New World. There is an 1890 monument to Behaim in Theresien Platz and his globe is preserved in the Behaim House, $giden Platz. A chandelier in the National Museum was dedicated to Behaim's memory by his son. [Headlam (2), pp. 59 & 282.] A striking clock was installed in the Lauferschlagturm in 1478 [Headlam (2), p. 132]. In c1500, Peter Henlein (or Hele) of Nuremberg is said to have invented the mainspring, or at least to have used it to make the first pocket watch in 1510 [Headlam (2), p. 214] or 1502, but the earliest surviving watches are from c1540 [F.A.B. Ward, p. 27]. As a consequence, the local watchmakers developed their own time system and Regiomontanus made tables for it. Headlam is not very clear, but it seems they used 24 hours of fixed length, but starting at sunset. Time of year was described by the time of dawn, e.g. "At the time of year when the day strikes 13." would seem to denote sometime in April. However Headlam's description also may indicate that they used variable length hours so there were 12 hours of day and 12 of night, which involves considerable fiddling of clocks. This system remained in use until 1806. [Headlam (2), p.257-259] Albrecht DFRER (1471-1528) was born and died in Nuremberg. He was born at his father's house, Winklerstrasse 20 [Headlam (2), p. 269] (or Burgstrasse 27 [Headlam (2), pp. 177 & 193]). He later bought the house from his brother and lived there until 1509, but it is long gone. In 14861490, he was an apprentice and presumably lived at his master's house, Burgstrasse 21, also gone. He was on his Wanderjahre in 14901494 and visited Switzerland. In 15051507, DGrer went to Venice, qv in Section 9B, to learn about perspective and he is known to have studied with Jacopo de Barbari. In 1509, he bought the house now called the DGrer House (DGrerHaus) on the corner at Albrecht DGrer Strasse 39, near the old North Gate (or Thiergrtnerthor) by the Castle, and lived there until his death. A drawing of the house is given as [Headlam (2), p. 173]. The house is today a museum. About the same time, he bought his father's house in Burgstrasse from his brother [Headlam (2), p. 193]. Albrecht DGrer Strasse runs into Albrecht DGrer Platz, north of St. Sebald's church, where there is a monument to him [Headlam (2), p. 175]. He is buried in grave 649 in the Johannes Cemetery, to the NW of the town, with a bronze plate on which is his famous monogram and the following inscription. Me Al Du Quicquid Alberti Dureri Mortale Fuit, sub hoc conditur tumulo Emigravit, VIII, idus Aprile, M., D. xxviii. The first line represents Meister Albrecht Durer. His Instructions how to use the Compass appeared in 1527, and his Proportions of the Human Figure appeared after his death. One of the major displays of DGrer's work is in the German National Museum (Germanisches Nationalmuseum), Kornmarkt 1 [Eastman, p. 137], though most of his works were sold by the city's merchants. This Museum has one of the few copies of KEPLER's tombstone inscription see under Regensburg, below. Gallery 65 is devoted to scientific instruments, including a watch from c1510 [ MGG , p. 221]. It also has a fine collection of early printed books, including some issued by Regiomontanus and first editions of DGrer's works [Headlam (2), p. 283285] [Headlam (2), pp. 285] says DGrer's drawing pen (Reissfeder) and Regiomontanus' astronomical instruments are in here along with other scientific instruments, old weights and measures, technical models, globes, early toys. The Museum contains: an early Piet!, c1500; the much damaged and inferior Hercules with the Stymphalian Birds (returned to the town by Ludwig I of Bavaria) [Headlam (2), pp. 188. 198 & 288]; much restored portraits of Maximilian, Charlemagne and Sigismund [Headlam (2), pp. 193194 & 288]; Descent from the Cross, known as the Peller altarpiece (also restored by Ludwig I, but perhaps no longer here??) [Headlam (2), p. 198 & 288]; four figures attributed to DGrer [Headlam (2), p. 281]; DGrer's frame for a picture sold to the Emperor [Headlam (2), pp. 193 & 281]; a number of wood and copper engravings [Headlam (2), pp. 282283] and several copies of works, including four Apostles with the original inscriptions retained [Headlam (2), p. 288]. [Headlam (2), pp. 196198] describes how most of DGrer's works were sold off, many to Emperor Rudolph, with the result that the best collections of his work are in the Albertina (in Vienna), the British Museum (via Sir Hans Sloane) and at Berlin (accumulated by the German government). The famous selfportrait was on a panel and the Town Council loaned to a local painter who split the front from the back. He then pasted his copy onto the front of the back piece and returned it to the town, who apparently never noticed the substitution, while he sold the original to King Ludwig I of Bavaria and it is now at Munich. A copy of his Interment of Christ and a poor picture by him of the Imhoff family are in St. Sebald's church. There is also a small wood carving said to be by him. [Headlam (2), pp. 237239]. The design of a stained glass window on the south side of the church of St. Lawrence is attributed to him and there is a Angels bringing the child Jesus to the Virgin with his monogram [Headlam (2), p. 247 & 254]. The north wall of the Rathaus Hall was painted to DGrer's designs by his pupils in 1521 [Headlam (2), pp.155157 & 195]. Part of DGrer's manuscript of Proportions of the Human Figure is in the Public Library and Record Office at Burgstrasse 4 [Headlam (2), p.263]. In 1527, DGrer produced a book, Instructions how to Fortify Towns, Castles, and Villages , and consequently the design of the round towers of the city walls has been attributed to him, though they were built some thirty years after his death and were based on older theories which his book had rendered obsolete [Headlam (2), p. 142]. Another famous citizen of the town was Hans SACHS (14941576), the Meistersinger. He composed a Meisterleid about the Josephus problem: Historia Die XV Christen und XV TGrcken, so auff dem meer furen [Ahrens (2), vol. II, pp. 132-133] gives the text. His house is in the Hans Sachs Gasse, with a plaque. There is a monument to him in Spital Platz. He is buried in the Johannes Cemetery and grave 503 is shown as his grave, though this is not certain. [Headlam (2), p. 215, 224 & 269.] Johannes SCH>NER came to Nuremberg from Bamberg in 1526. He taught mathematics and edited and published several works, including one of Regiomontanus in 1544. RHAETICUS was a pupil of his and addressed the Narratio Prima , the first printed description of Copernicus's work, to him in 1540. Wenzel (or Wentzel) JAMNITZER (or Jamitzer), was a famous Nuremberg goldsmith who produced Perspectiva Corporum Regularum in 1568. This includes many drawings of regular and semiregular polyhedra. He is buried in the Johannes Cemetery, grave 664, and he may have designed his own grave slab [Headlam (2), p.266]. [ MGG , p. 221] says the University of Nuremberg was the first German science university, founded in 1526, though it is shared with nearby Erlangen, about 20 km to the north, qv above. But [Headlam (2), p. 78 & 9192] says that a gymnasium was established by Melanchthon at this time in the $gidienkloster, but that Nuremberg was more interested in trade than study and the school moved to Altdorf in the late 16C. Headlam also says this was to remove the students from the distractions of the city, at the suggestion of Joachim Camerarius. See Altdorf, above, for the later development into a university in 1622 and its closure in 1809 as the new University of Erlangen developed. (Headlam seems to say the $gidienkloster burned down in 1699.) A new gymnasium was established in Nuremberg in 1633. [Headlam (2), p. 78 & 9192.] [Headlam (2), p. 132] says there is polytechnic school in the Landauerkloster and MGG may be confusing this or the present gymnasium with the earlier gymnasium ?? The famous Nuremberg printer J. Petreius printed COPERNICUS' De Revolutionibus for RHAETICUS in early spring 1543. Rhaeticus had to leave to take up a post at Leipzig and Andreas OSIANDER saw it through the press and added a prefatory note asserting that the ideas were merely hypotheses, in a vain attempt to forestall theological criticism. Tobias MAYER (1723?1762) worked for the Homann Cartographic Bureau in Nuremberg the 1750s. In 1757, he produced the first set of tables of the moon's position, assisted by a four year correspondence with Euler, who had developed the necessary equations. The tables were accurate to 1', which would be adequate to win the English Longitude Prize. The Board of Longitude awarded his widow 3000 and Euler 300. Georg Simon OHM (17801854) was Professor of Mathematics at the Polytechnic School here in 18331849. See also Altdorf, above. Friedrich Wilhelm August FROEBEL (or Fr?bel) (17821852) (see under Schweina below) was born in OBERWEISSBACH, ThGringen. OBERWOLFACH, near Hausach, BadenWGrttemberg, a small settlement in the Black Forest (Schwarzwald), is the site of the famous mathematics conference centre, established in 1944. The New Town Hall (late 15C) of OCHSENFURT, Bayern, 13 km SSE of WGrzburg, has a astronomical clock with striking figures [ MGG , p. 301]. Karl Theodor Wilhelm WEIERSTRASS (18151897) was born in OSTENFELDE, NordrheinWestfalen (then in Prussia). In the cloister (Kreuzgang) of the Cathedral (Dom) of PADERBORN, NordrheinWestfalen, is the Dreihasenfenster [Three Hares Window], where there are three hares, each with two ears, but there are only three ears all together. This is only visible from the outside, i.e. inside the cloister garden. Dr. Heribert Schmitz in the Archbishopric kindly sent information about this and I have since visited Paderborn. Much of the structure dates from the 13C, but the present form of the cloister dates from the early 16C and this is the date given on a postcard of the window that Dr. Schmitz sent me. The image is actually carved stone tracery in the arch over one of the triple windows of the cloister, and is about 3ft (1 m) across. The central stone image is supported only by the three rear feet of the hares which are on a circular rim the intermediate spaces are filled with leaded glass. Several of the photos show the bodies of the hares supported by metal rods, but there are presently no rods. It seems that some of the stone work has been cleaned or restored or even replaced, but I forgot to inquire about this. Other literature refers to the 'well known' window and says the symbol is an old landmark of the city one guide book shows three people dressed as hares who are a regular feature of parties. The Cathedral guidebook says the 'motif is also to be found in other buildings, but elsewhere is mostly smaller and less conspicuous', but no references are given and Dr. Schmitz's letter says that he knows of no other examples than Long Melford and the article by Schneider. St. Boniface, the Apostle of the Germans, came from Crediton, Devon, some 10 mi east of Dartmoor! Further, he consecrated a bishop at Paderborn. Schneider gives various interpretations of the symbolism of the three hares pattern: old German fertility symbols from the myths of the gods; the Easter rabbit as a symbol of the eternal power of nature; a symbol of the Trinity. In recent years, it has been connected to the patron saint of Paderborn, St. Liborius, by viewing his name as Leporius, which means 'hare man'. There is a Drei Hasen restaurant at 55 K?nigstrasse. Several local guide books give a rhyme: "Der Hasen und der L?ffel drei, / und doch hat jeder Hase zwei." [The hares and ears are three / and yet each hare has two[, you see].] [Paderborn Tourist Information]; Paderborn A short guide to the old city ; Paderborn, 1998, p. 13 & back cover] gives an English version of the rhyme: "Count the ears. There are but three. But still each hare has two, you see?" and I have now inserted 'you see' into my translation above. The pattern is printed on the outside covers of this booklet. [ MGG , p. 229. Hans Schneider; Symbolik des Hasenfensters in Nordwestchina entdeckt; Die Warte (Heimatzeitschrift fGr die Kreise Paderborn und H?xter) 32 (Dec 1981) 9.] See in Section 11 for other sites. The first university in Westphalia was founded in PADERBORN by Bishop Dietrich IV von FGrstenberg in 1614, but it was closed at some point, perhaps under Napoleon. Several schools were formed into a polytechnic in 1972 and this became the University of Paderborn in 1980. WEIERSTRASS (18151897) was a student at the Catholic Gymnasium Theodorianum in Paderborn in 18291834 [A.C.Baker]. This is located beside the Jesuitenkirche in Kamp Street [Verkehrsverein Paderborn]. Directly across from the steps to the Gymnasium is the only monument I know to a card game. In 1652, three men at an alehouse on the site of 66 Eckkamp created a new game which they named '66'. There is a stone relief showing three card players set in the wall. [Paderborn Tourist Information]; Paderborn A short guide to the old city ; Paderborn, 1998, pp. 89.] The Heinz NIXDORF MuseumsForum (HNF, FGrstenallee 7, D33102 Paderborn, NordrheinWestfalen, tel: 05251306600; fax: 05251306609; web: www.hnf.de .) was opened in Oct 1996. It was created by the will of Heinz Nixdorf (19251986), the computer manufacturer, as a computer museum with a broad interest in related fields. With the closure of the Boston Computer Museum, it is now the only major computer museum in the world. I found it very exciting, informative and pleasant and I highly recommend it to anyone wanting to understand computing and its relationship to other technologies. There is a massive Jacquard loom mechanism which was in use until the mid 20C and which runs. One of the prides of HNF is a version of Leibniz's calculator, the first calculator which could multiply. Leibniz made several versions, of which only one essentially complete example survives at Hannover (cf above), but no one had been able to make it work despite extensive study of it, its plans and what remains of other versions. However, HNF got a skilful engineer to work on it and he has produced the only known working model. They have two racks from ENIAC. They have an example of the first personal computer, the MITS Altair 8800 of 1975, and an example of the Apple I (of which only 200 were ever made in 1975). They have the onboard computer from Gemini II. There is one wall of about 800 different electronic calculators, including an example of the first model from HewlettPackard. c1967. The website has a virtual tour of the Museum. VOLTAIRE spent 17501752 at SansSouci, Frederick the Great's palace at POTSDAM, Brandenburg, now almost a SW suburb of Berlin, about 10 km from the city line. He lived in the Fourth Guest Room where some memorabilia and a replica of Houdon's bust of him can be seen (cf Voltaire in Section 7A2). [Eastman, p. 128. MGG , pp. 230, 232.] Carl Gustav Jacob JACOBI (18041850) was born in Potsdam and attended gymnasium there [Ahrens, p.20]. Hermann von HELMHOLTZ (18211894) was born in Potsdam incidentally, he was descended from William Penn on his mother's side. Hermann SCHUBERT (18481911) was born in Potsdam. In c1927, E. FREUNDLICH built an 'EINSTEIN Tower' (Einsteinturm) on Telegraph Hill in Potsdam, designed to measure the red shift of the solar spectrum as a test of the general theory of relativity. Freundlich had to leave Germany in c1933 before carrying out the experiment. The Nazis renamed the tower and converted it to other uses, but it has been renamed Einsteinturm. [Hans Reichenbach; Von Kopernikus bis Einstein ; Ullstein, Berlin, 1927; translated by Ralph B. Winn as: From Copernicus to Einstein ; Philosophical Library, NY, 1942; corrected ed., Dover, 1980, pp.99-101. Baister & Patrick, p. 77.] In QUEDLINBURG, SachsenAnhalt, there are several Nine Men's Morris boards carved on a pillar of the crypt of the Wipertikirche, probably from the 10/11 C [Gerhard Leopold; Skulptierte WerkstGcke in der Krypta der Wipertikirche zu Quedlinburg; IN: Friedrich M?bius & Ernst Schubert, eds.; Skulptur des Mittelalters ; Hermann B?hlaus Nachfolger, Weimar, 1987, pp. 2743; esp. pp. 37 & 43]. ALBERTUS MAGNUS (1193 (or 1206) 1280) was Bishop of REGENSBURG (= Ratisbon), Bayern, in 12601262, retiring because the job was too warlike [Holmyard, pp. 111114]. KEPLER (15711630) stayed in Regensburg in 1620-1622 and 1626-1628, as well as for several other shorter periods. In 1613, he made observations of sunspots from the Cathedral. In 1615, he stayed briefly at the Walderbacher Hof in Georgenplatz. In 16201622, he lived at Baumhackergasse 5, where one of his daughters was born. During 16261630, he stayed at Keplerstrasse 2 which has a plaque. He was on a visit here in 1630 when he died at the house of Hillebrand Billi in the Donauwacht, now Keplerstrasse 5. There is no record of which room was Kepler's. The house has a memorial plaque and was opened as a museum in 1962. It has a bust of Kepler, a 1590 celestial globe by Mercator, a 1603 celestial globe by Blaeu and numerous other contemporary items, including an elaborate astronomical table of 1600 and a wall calendar, both by Andreas Pleninger who was an acquaintance of Kepler, so Kepler probably helped with the designs. There are a number of original letters of Kepler and the original inventory of his Nachlass. [Gerlach & List, p. 36, with photo on p. 39. Seck, p. 46. Boll, with photos.] Previously a plaque was erected on no. 4 of the present Fischmarkt which was thought to be the house he died in. He was buried in the Petersfriedhof outside the walls, but the site was already destroyed during the siege of 1634. A copy of the inscription was made and is in the Germanischen Nationalmuseum NGrnberg. [Gerlach & List, p. 36 & 38. Seck, p. 46, with reproduction. Boll, pp. 2223.] There is a monument nearby. It is an open circular temple, based on that given on the title page of his Rudolphine Tables , with a bust on a pedestal in the centre, erected in 1808 [Caspar; Boll, p. 25]. Kepler's widow died in Regensburg in 1636 and was also buried in the Petersfriedhof. [Archibald (3), pp. 34 & 36. Boll.] The University of ROSTOCK, MechlenburgVorpommern, was founded in 1419, the first university in the Baltic region [ MGG , p. 248]. Nothing remains of its early buildings. Joachim JUNGIUS (15871657) was professor in the 1620s. He found notable results, but published little, so these results are not attributed to him. He founded the first scientific society north of the Alps at Rostock in 1622. There is a street named for him. [Lau et al.] There is a fine astronomical clock, dating from 1472, on the Marienkirche [Schukowski; MGG , p. 248]. [Baister & Patrick, p. 195] says it is behind the altar, was constructed by Hans DGtringer and rebuilt in 1643, "to take account of the latest scientific advances", probably meaning that it was converted to the Copernican system. Hans ZASSENHAUS (19121991) taught here in 19341936, writing the first draft of his Lehrbuch der Gruppentheorie . Von STAUDT came from ROTHENBURG (OB DER TAUBER), Bayern, and his descendents are still living there. He died and was buried in Erlangen, but the grave was moved to Rothenburg. RUDOLSTADT, ThGringen, was the home of Friedrich Adolph RICHTER and where he produced the famous Richter Anchor (Anker) Stone puzzles and building sets from 1882. The plant closed in 1964. In 1995, production restarted at: Modellbausteinspiele GmbH; Breitscheidstrasse 103, D07407 Rudolstadt; tel:03672-3111 10; fax 0367231 11 29; email: modellbau@ankerstein.de; web:www.ankerstein.de. See also MGnchen: Deutsches Museum, above; Schweina, below; and Section 10: Netherlands: Alphen aan den Rijn. [Biggs, Lloyd & Wilson, p.221] say Heinrich Franz Friedrich TIETZE (18801964) was born in SCHLEINZ, but I can't find this on my maps. Hermann HANKEL (18391873) died at SCHRAMBERG, near Leipzig. The only one I can find is in BadenWGrttemberg. SCHULPFORTA, SachsenAnhalt, is a school in the country south west of Leipzig, near Naumborg, where August Ferdinand M>BIUS (1790-1868) was born. His father was a dancing teacher there. M?bius attended the school in 1803-1809. Friedrich Wilhelm August FROEBEL (or Fr?bel) (17821852), the educational innovator, was the inventor of Kindergartens, advocated children's play blocks and inspired the Richter Anchor Stone Puzzles (cf MGnchen: Deutsches Museum, above) and Milton Bradley. On his grave in SCHWEINA, near Jena, ThGringen, is a monument with a sphere on a cylinder on a cube, designed by William Middendorf. There is a copy of this monument as a memorial near Marienthal. [Wieb); Wieb) (2) both of which include pictures.] Ernst Eduard KUMMER (18101884??) was born in SORAU (now ZARY in Poland). He attended the gymnasium there and later taught there for a year. [Hensel.] STAFFELSTEIN, Bayern, about 20 km north of Bamburg, was the birthplace of Adam RIESE and there is a plaque in the Town Hall [Berlet, p. VIII]. STETTIN was part of Prussia/Germany from 1720 to 1945. It is now SZCZECIN in Poland. Hermann GRASSMANN (18091877) was born and died here. His father was Professor of Mathematics at the Gymnasium and the son succeeded him. There is a 1994 plaque to him. STRLSUND, MechlenburgVorpommern, has "probably the oldest original, still running, astronomical clock in Europe" [Schukowski but he gives no date!]. In the late 19C, Ernst von HASELBERG was the City Architect. About 1887, he discovered the only magic hexagon and showed its uniqueness. He restored the facade of the City Hall. [Hans F. Bauch; Zum magischen Sachet von Ernst v. Haselberg; Wissenschaft und Fortschritt 40:9 (1990) 240242 & a cover side with a photo of the City Hall.] Albert Abraham MICHELSON (18521931) was born in STRELNO, now STRZELNO, Poland, SW of Toru. Georg Wilhelm Friedrich HEGEL (17701831) was born in STUTTGART, BadenWGrttemberg, where his house, at the corner of Torstrasse and Eberhardstrasse, is a museum. Otto H>LDER (18591937) was born in STUTTGART, BadenWGrttemberg. Hegelstrasse, Hegelplatz and Keplerstrasse are all adjacent to the University. See also: Esslingen, Herrenberg, Leonberg, Maulbronn, TGbingen, Weil der Stadt in this Section. Karl MARX (18181883), who dabbled in the foundations of calculus, was born at BrGckenstrasse 10, TRIER, RheinlandPfalz, where the birth house is a museum. He only lived here for a year, when the family moved to Simeonstrasse 8 where he lived until 1835 and stayed briefly in 1841 and 1842. [Eastman, p. 149, with photo.] [Eastman, pp. 399400] lists 12 further residences in three countries before he reached London in 1850. See also: Cues, above. The University of TFBINGEN, BadenWGrttemberg, 30 km S of Stuttgart, was founded in 1477 by Eberhard the Bearded, Prince of WGrttemberg [ MGG , p. 282]. The Rathaus has an astronomical clock said to have been made by a St?ffler or St?fler in 1511 [ MGG , p.282]. Michael MAESTLIN (15501631) was Professor of Mathematics and Astronomy at the University until his death. He taught the Ptolemaic system but seems to have provided the Copernican theory to those interested. Wilhelm SCHICKARD (1592-1635) was a student at the University, becoming Magister in 1611. He was later Professor of Biblical Languages from 1619, but he had interests in mathematics and astronomy, being a student and colleague of Maestlin and a friend of Kepler (he did copperplate engravings for Kepler's Harmonice Mundi ). He succeeded Maestlin as Professor of Mathematics and Astronomy in 1631. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624. The ravages of the Thirty Years' War prevented him from accomplishing much in his later years he had to flee from the Battle of TGbingen in 1631 and after the Battle of N?rdlingen in 1635. the town was overrun by troops bringing a plaque which killed Schickard and his entire family (except his mother who was killed by a soldier). In 1935, sketches of his machine were recognised among the papers of Kepler and Schickard by Franz Hammer. Due to the War, this information was not published until 1957. In 19571960, the TGbingen Professor Bruno Baron von Freytag-L?ringhoff was able to make a reconstruction of the machine. Several examples have now been made see: Section 2B: Science Museum; Section 8: Braunschweig, Weil der Stadt; Section 10: USA: New York Hayden Planetarium. There is a 1632 portrait of Schickard in the University Gemldesammlung [reproduced in Stein & Heinekamp, p. 55, and in von FreytagL?ringhoff]. This shows him holding the earliest known example of a Copernican planetarium (like an orrery). KEPLER (15711630) was a student of philosophy and theology in 1589(1588??)1594, becoming Magister in 1591. LHUILIER (17501840) was here in 17891795. C. G. NEUMANN was professor in 18651868. Lothar MEYER (18301895) was professor of Chemistry in 1864 when he worked out the idea of 'atomic volume' and observed some periodicity in the elements and produced a periodic table, but he did not use it to make predictions as Mendeleev did in 1869 [N. Coats; The Periodic Table ; Chemistry Background Book, Nuffield Foundation, London, 1966, p. 5]. HEGEL was a student. DU BOIS-REYMOND was a professor in 18741884. HANKEL was a professor in 1869-1872. RUNGE was a professor. H>LDER was a student to 1882 and a professor in 1889-1896. Hans GEIGER (1882-1945) was Professor of Physics in 19291936. KNOPP was professor in 19261950. He was a founder and the editor of Mathematische Zeitschrift in 19341954. The Cathedral (MGnster) at ULM, BadenWGrttemberg, has notable carved choir stalls from the late 15C which include a series of busts of classical philosophers and writers, including PYTHAGORAS apparently playing a lute. The Town Hall (Rathaus) has an astronomical clock. [ MGG , pp. 284285.] The Museum der Stadt Ulm (or Ulmer Museum) has the original standard volume vessel constructed by KEPLER (15711630), c1627 [Gerlach & List, p. 34, with photo on p. 35]. He lived here in 16261627 [Eastman, p. 397]. Johann FAULHABER (15801635) taught at Ulm. Descartes visited him here in 1630. Albert EINSTEIN (18791955) was born at Bahnhofstrasse 20, but lived there only for a year. The house perished in 1945. There was a street named after him during 19221933 and from 1945. [Whitrow, p. 1. Eastman, p. 137.] WEIL DER STADT, BadenWGrttemberg, about 20 km west of Stuttgart, was the birthplace of Johannes KEPLER (1571-1630). The birthplace in the Marktplatz was turned into a museum in 1940 at the instigation of the Kepler scholar Max Caspar. However, [Eastman, pp. 147148] says that the birthhouse was at Keplergasse 2, that it burned down in 1648 and that the present building dates from about 1648, but is probably similar to the previous house on the site. There are some models demonstrating Kepler's laws and the Ptolemaic, Copernican and Brahean systems, models of Kepler's star polyhedra, of his solar system "Mysterium Cosmographicum" based on the regular solids, of his volumetric measurements of wine casks, of his Ulmer Messkessel (see under Ulm, above) and of SCHICKARD's calculator. There is a copperplate engraving of Galileo. There is a bust of Kepler in the museum and a monument with a life-size seated figure in the market place. The pedestal of the monument has small statues of COPERNICUS, Michael MAESTLIN [= MSTLIN] (Kepler's teacher), BRAHE and BFRGI and some reliefs showing episodes of Kepler's life. [Caspar. Archibald (3), p. 36. Postcards from A. E. L. Davis. Gerlach & List.] Kepler lived here until 1577 when his family moved to Leonberg, qv above. WETZLAR, Hessen, is the home of the Leitz firm of photographic and optical equipment makers, who introduced the 35mm camera in 1924 [ MGG , p. 293]. Gottlob FREGE (18481925) was born in WISMAR, MechlenburgVorpommern. The University of WITTENBERG, SachsenAnhalt, was founded in 1502. Luther came here in 1508 and became Professor of Theology in 1512. On 31 Oct 1517, he started the Reformation by nailing his 95 Theses on the door of the Schlosskirche. Georg Joachim RHAETICUS [= Rheticus = Retyk] (1514-1576) was professor of mathematics from 1537 [Sarton, p. 36; Ahrens, p. 34]. In 15391541, he went to Frauenberg (qv in Section 10: Poland) to study with Copernicus. He described Copernicus's work in a letter, known as the Narratio Prima , published in Dantzig in 1540. BRAHE lived in Melanchthon's house at Collegienstrasse 60, in 15981599 [Sarton, p. 66; Eastman, p. 115]. In 1817, the University was combined with that in Halle. The city is now also called Lutherstadt Wittenberg. Ernst Florens Friedrich CHLADNI (17561827) came from Wittenberg and was Professor of Physics at Breslau, qv above. WOLFENBFTTEL, Niedersachsen, 12 km S of Braunschweig, was the seat of the Dukes of Braunschweig and LGneburg from the 15C until 1753. Duke Augustus the Young founded a library (HerzogAugust Bibliothek) here in 1572 which was the largest and most important library in Europe during the 17C. Gotthold Ephraim Lessing, the noted German writer, was librarian here in 17701781 and discovered the Greek text of Archimedes' famous Cattle Problem, which he published in 1773. The University of WFRZBURG, Bayern, was founded in 1582. Athanasius KIRCHER (16021680) was at WGrzburg in the 17C. Gaspar SCHOTT (16081666) died at WGrzburg. Wilhelm Conrad R>NTGEN (18451923) followed his mentor August Kundt and became was assistant at the University of WGrzburg in 1872 (or 1871) but was not offered a post. He then worked at Strasbourg and Giessen, but returned in 1888 as Professor of Physics and Head of the Physikal Institut, then Rector of the University in 1894. There he discovered Xrays on the evening of Friday 8 Nov 1895 'at a late hour when assistants were no longer to be found in the laboratory'. He investigated the phenomenon in secret, taking an Xray of his wife's hand, and first announced it in a paper, "Ein neue Art von Strahlen", to the WGrzburg PhysicalMedicalSociety on 28 Dec and it appeared in their 1895 proceedings. By January he was famous. In the next year some 50 books and 1000 papers appeared on the subject! A journal devoted to the subject was founded in May 1896. The techniques of barium meals and enemas were developed in 1896. He left WGrzburg for Munich in 1900, shortly before receiving the first Nobel Prize in Physics in 1901. He donated the prize money to the University of WGrzburg. [Bowers. Darius, p. 4849. Pengelley & Pengelley, pp. 155157.] The Physikal Institut is at R?ntgenring 8b and has a plaque on the outside. R?ntgen's laboratory is now a modern physics laboratory, but the Institut has three display cases of memorabilia, including the Xray of his wife's hand, his Nobel Prize certificate and a commendation from the German Physics Society, signed by Einstein and Planck. A lecture room that R?ntgen used is preserved more or less as in his day. [Pengelley & Pengelley, pp. 158159.] There is a copy of the Freiburg bust of LINDEMANN at the University. See also Ochsenfurt, above.  9. MONUMENTS IN ITALY. 9-A.FIRENZE (FLORENCE) , Toscana (Tuscany). 9A1.GALILEO.  In Florence, GALILEO (1564-1642) is virtually an industry. Unfortunately there is considerable confusion about some dates and events in his life due to inaccurate early accounts of his life by Viviani and Gerardini see [Segre] for a discussion of some points. He lived with his family somewhere near S. Croce from about 1575 to 1589, though he spent some time about 1579 as a novice at the monastery of VALLOMBROSA about 33 km east of Florence. In 15811584, he was a student at Pisa and then Professor from 1589 (or 1585) until 1591. After leaving Pisa, he returned to Florence in 1592, before going to Padua for 15921610. During 16051606 (or summer 1605), he was tutor to Cosimo de' Medici, eldest son of Grand Duke Ferdinando I, who was later Grand Duke Cosimo II, at the Medici villa near the present day Villa Demidoff in PRATOLINO, 12.5 km north of Florence [Macadam, p. 234]. He returned to Florence from Padua in about September 1610 as Mathematician to the Grand Duke and stayed with various friends until 1617 [Bonelli (1), pp. 5-7]. In 1610-1613, he was at Duke Filippo Salviati's villa 'Le Selve', which still (1957) stands at Signa, in the southwest suburbs of Florence [Bonelli (1) has a photo facing p.15; Scandone has photos on pp. 2223]. It was probably here that he discovered the phases of Venus in Oct/Dec 1610 (though [Andrade (2) says this occurred just after his appointment in summer 1610, when he might have still been at Padua) and sunspots in early 1611 (using a 'pinhole camera' or using his telescope as a projector). Ptolemy had already noted that in his system Venus could never show more than half an illuminated surface, whereas Copernicus's theory implied that it would have a complete set of phases. The lack of these had been raised as an objection to Copernicus, but Galileo soon saw that Venus did have a full system of phases this was the first observational verification of the Copernican system. Sunspots had been observed by the ancient Chinese and by Harriot and Fabricus in the previous two years. Galileo noted that they showed the rotation of the sun. In 1612, he produced his Discorso ... intorno all cose che stanno in su l'aqua , a treatise on floating bodies. [Eastman, p. 336] says he lived at 19 Via della Costa di San Giorgio with his mistress and children until 1617. He lived from 1617 to 1631 at the Villa dell' Ombrellino in Bellosguardo, a bit southwest of the city [Baedeker, p. 552; Fahie, pp. 156-157 & plate XLIV, opp. p. 157]. GASSENDI visited him here in 1620 [Fahie, p. 33]. This was restored as a 'trade centre' in 1988. There is a plaque beside the gate to the villa recording that Galileo and Ugo Foscolo (a noted Italian poet) lived here and that there were many other distinguished visitors or residents including James Fenimore Cooper, Hawthorne, the Brownings, Henry James, Hans von Bulow, Clara Schumann, NIGHTINGALE and Violet Trefusis (to 1973). There seems to be no objection to one's walking through the gate and up to the villa where there are large memorial busts and plaques to Galileo and Foscolo on the side of the house facing a terrace with wonderful views over Florence. (I have photos.) He lived from 1631 to his death on 8 Jan 1642, virtually under house arrest after 1633, in Villa Gioiello [now Villa Galileo] (bust and inscription facing the street and inscription over the door from the courtyard I have photos, but the exterior inscription is not legible), No. 42, Via del Pian de' Giullari in the southern suburb of Pian de' Giullari (or Piano dei Giullari). (The location is often called Arcetri, but Arcetri is actually the next hill/village, about a mile to the north.) [Fahie, pp. 158-160 & plate XLV, opp. p. 160. Photos in Bonelli (1); Scandone, pp. 38 & 40; P. Moore (4), p. 11.] It is sometimes said that he came here to be close to his two daughters, Maria Celeste and Arcangela, who were nuns in the nearby Convent of San Matteo. He published Dialogo ... sopra i due Massime Sistemi del Mondo Tolemaico e Copernicano ( Dialogue concerning the Two Chief World Systems ) in 1632, leading to his trial in 1633. He produced Discorsi e Dimostrazione Matematiche intorno ! due Nuove Scienze ( Dialogues Concerning Two New Sciences ) here in 1636 and smuggled it out for publication at Leyden in 1638. The two new sciences are the strength of materials and the dynamics of a particle. In 1637, he discovered the libration of the moon. About 16371641, he invented the pendulum clock and his son Vincenzio made a start at building one [Miniati et al., pp. 60 & 189190; p. 189 shows a 1658 drawing by Viviani from Vincenzio's description], but it was some years before an example was completed probably by Huygens in 1657 (cf under Netherlands in Section 10). By 1638, he was completely blind. Vincenzo VIVIANI (16221703) was his amanuensis here, living in the house from 1639, and HOBBES visited Galileo here. Milton visited him in 1638 and looked through the telescope, leading to his lines in Paradise Lost , Book I (though the geography is a bit off). ... Like the moon, whose orb Through optic glass the Tuscan artist views At ev'ning, from the top of Fesole [sic!] Or in Valdarno, to descry new lands, Rivers or mountains in her spotty globe. Milton also mentions his visit in his Areopagitica . Evangelista TORRICELLI (16081647) came to assist him in late 1641, but Galileo died a few months later. The house has been recently bought by the state and is being restored (already in 1985 [Eastman, p. 337] and still going on in 1994, but the work has been suspended due to more important needs) for use by the Observatory. I am grateful to the Observatory Director, Prof. Franco Pancini, for permission to visit the house and to his secretary, Fern Bongiani (sp??) for showing me around it in Sep 1994. It is not in a state for casual visitors there are several large holes in the ground and several rickety steps. Serious visitors can be admitted ask at the Observatory (see below), but it is advisable to write or telephone in advance, while the restoration continues. Nearby in Arcetri(?) is the Torre del Gallo (or Torre al Gallo), often said to have been used as an observatory by Galileo, though there is no firm evidence for this. The Torre dates from perhaps the 9C. Gustavo Galletti bought the Torre in 1846 and it passed to his son Count Paolo Galletti in 1876. The Count made a collection of documents, paintings, etc. relating to Galileo and Florence in the Torre, but the Torre was reconstructed in 19041906 and the collection seems to have been dispersed [Fahie, pp. 30-31]. The ground floor included Sustermans' portrait of Galileo, a portrait of a Galileo Galilei who was an ancestor of our man in the mid 15C, a portrait of Alessandro Galilei (see under Santa Croce, below, and Rome in Section 9B), a dossier of unpublished documents from 15881592. The second floor had the Museo Galileiano, including busts, portraits and letters, etc. of Galileo and those connected to him. Especially notable were a telescope attributed to Galileo and the letter from the Inquisition to announce the result of the trial of 22 Jun 1633, the drafts of the inscriptions on Viviani's house as submitted for approbation, portraits of Viviani and Torricelli, Viviani's will. There was also a microscope attributed to Galileo, with the signature of his relative Antonio Galilei, but we know Galileo never really pursued microscopy. The description of the collection is given in [Cesare da Prato; La Torre al Gallo e il suo Panorama ; Estratto dal giornale fiorentino La Vedetta; Tipi dei successori Le Monnier, Firenze, 1891]. A photo of the collection is given in [W. Alfred Parr; Galileo's tower at Florence; Knowledge 22 (Jul 1899) 157]. (A May 1900 article by Parr notes that the Torre is still owned by Count Paolo Galletti.) The Torre seems to be in private ownership, but is currently (1991 & 1994, see above) being restored by the state. It may eventually be open. The Observatory of Arcetri (Osservatorio Astrofisico di Arcetri "Giorgio Abetti") is nearby. It is a national research centre located within the Institute of Physics complex whose entrance is at the bottom of the other side of the hill at Largo FERMI 5. The Observatory is on a height with a splendid view. It originated as part of the museum/institute La Specola (see below) and thus has links back to the time of Galileo, though the present complex was only built in 18691872. It has some Galilaeana [Fahie, p. 37]. [Scandone, p. 57] shows a painting of Galileo dictating to Viviani located at the Observatory, but this may now be in the Museo di Storia della Scienza [Miniati et al., p. 62], though I didn't notice it in 1991. Piazzale Galileo, Viale Galileo, Viale Torricelli and Via Viviani are in the same area. Galileo bought his natural son Vincenzio a house at No. 11 Costa S. Giorgio (formerly called Via della Costa) in 1629 [Fahie, p. 160 & plate XLVI, opp. p. 161]. In 1634, Galileo bought the adjacent house and Vincenzio moved into the remodelled building in about 1636. Galileo stayed in this house on his visits to town and for a brief period in 1638-1639, when two Dutch merchants brought a letter and a gold chain from the States-General of Holland as thanks for his 1637 (or 1616?) proposal to use the moons of Jupiter to determine longitude [Fahie, pp. 93-95]. [Bonelli (1), pp. 10, 21, 23-24, with some photos.] The house is now numbered 17, 19 and 21 and has a commemorative mural and plaques [photo in Scandone, p. 24 and I have a photo]. [Hare, p.211] asserts that the garden of this house has a sundial of Galileo. Galileo's two natural daughters became nuns at San Matteo in Arcetri [Scandone, p. 56]. Because of Papal objections, Galileo's body was concealed in (or adjacent to) the Chapel of Novices (later in the Medici Chapel??) in SANTA CROCE. ([Pengelley & Pengelley, p.164] say it was in the churchyard.) In 1674, an inscription was put over the tomb [Bonelli (1) has a photo of this site]. Galileo's last pupil, VIVIANI (16221703), left money for a monument. In 1737, Galileo's remains were translated to the North Aisle and Viviani was interred beside him (see below) [Bonelli (1), p. 26]. A large monument, including a bust and statues of Geometry and Astronomy was erected [Fahie, pp. 142143; I have photos]. During the translation, some bits were removed as relics, including at least both index fingers (sic, but the bones in the Museo di Storia della Scienza are the middle finger of the right hand), the right thumb and a vertebra [Fahie, pp. 128 & 149]. [Dave Dutton; Horrors ; Futura, London, 1989, p. 136] states that three fingers were taken by a Gori. In the middle of the nave in front of the tomb is a tomb slab of another Galileo Galilei, a 15C Florentine physician and ancestor of the scientist [Macadam, p. 175]. There is also a monument to an Alexandro (Alessandro) Galilei (16911737), 'mathematico et architecto clarissimo' in the Bardi Chapel at the end of the north transept (I have a photo). (He designed Castletown House in Co. Kildare, Ireland, in 17221732 (see Section 6E2), the altar of the Cathedral in Cortona and the facade of San Giovanni Laterano in Rome.) In 1994, I could find no trace of Viviani and one of the priests could not find him listed in their catalogue of graves. [Hare, p. 86] indicates that Viviani was buried near Galileo in the Medici Chapel. His son Vincenzio lived in the Costa S. Giorgio house until his death and is buried in S. Lucia in Via de' Bardi, below Costa S. Giorgio [Bonelli (1), p.27]. Galileo's condemnation by the Inquisition was officially cancelled in 1992. There was a copy of the Pisa statue of GALILEO in the entrance of Fratelli Alinari, Via Nazionale [Fahie, p. 132], now 15 Largo Alinari, but I didn't see it on a quick visit in 1991 and a telephone call got a response that it was no longer there. SUSTERMANS' house in Piazza degli Unganelli, near Arcetri, has a plaque commemorating him as 'the painter from life of the portrait of the renowned GALILEO' and commands a superb view of Florence [Fahie, p. 35, misspells it as Uganelli; I have a photo]. The plaque seems to spell the artist's name as Subtermans, but it may be a  or the carver has miscarved the  as a b. For the TRIBUNE OF GALILEO, see LA SPECOLA in Section 9A2. Vincenzo VIVIANI (16221703), the last pupil and amanuensis of Galileo, made the facade of his house at 11 Via San Antonino (formerly Via dell'Amore), near S. Maria Novella, into the first public GALILEO monument in 1693. There is a bust over the door with small plaques underneath showing a mariner observing Jupiter's moons and sunspots and another observer watching the trajectory of a cannonball, with a broken beam nearby (Galileo studied the strength of beams). [Fahie, pp. 154-156 & plate XLIII, opp. p. 156, which is from an old engraving. I have photos.] Viviani wrote the first life of Galileo Racconto istorico della vita ... in 1654, but he made a revised version at some time and added a letter about the pendulum in 1659. The first printed version of 1717 had some editorial corrections. Viviani is our earliest source for the stories of the swinging lamp in Pisa Cathedral and dropping weights off the Tower of Pisa. The only other contemporary biography of Galileo is by NiccolA Gherardini, a local priest and friend, and doesn't mention these stories, though it does repeat two other legends or exaggerations. Unfortunately there is no other contemporary evidence for the Pisan events. See under Pisa and Padua in Section 9B for more details. [Segre.] In 1997?, a large modern monument to Galileo was erected at the south end of Ponte San Niccolo. Florentine friends say it is quite ugly. See also: Duomo, Museo di Storia della Scienza, Santa Croce, La Specola and Uffizi in the next Section.  9A2.OTHER MATERIAL IN FIRENZE (FLORENCE)  For the mathematician, Florence is also particularly notable as the place where PERSPECTIVE was invented and developed. The history of perspective has been confused by partizans of various inventors, but the principal progenitor was the goldsmith, sculptor and architect Filippo BRUNELLESCHI (1377-1446) in or just before 1413. Leon Battista ALBERTI (1404-1472), polymath and architect, was the first to write a text on perspective, first in Latin and then in his own translation into Italian: De Pictura (1435) & Della Pittura (1436). (A fine translation by Cecil Grayson from the Latin is available, with good Introduction and notes by Martin Kemp [Alberti]. Other architect followers of Brunelleschi were Donatello (13861466), Michelozzo Michelozzo (1396-1472) and Giuliano da Sangallo (1445-1516). Numerous works of these are in Florence and exemplify the famous dictum (just invented by myself?) that "Architecture is mathematics turned into stone." MASACCIO (cf Santa Maria Novella, below), Donatello (13861466), Fra Angelico, Domenico Veneziano, Ghiberti and Paolo UCCELLO (13971475) were among the first artists to make use of the ideas in their works. The ideas rapidly spread throughout Italy. PIERO DELLA FRANCESCA wrote on perspective De Prospectiva pingendi ; Luca PACIOLI, Botticelli, Mantegna, LEONARDO DA VINCI and many others studied it and Albrecht DFRER took the ideas to Germany in the early 16C. Florence abounds in works displaying the new geometric ideas. INSTITUTIONS The ACCADEMIA DEL CIMENTO was one of the earliest scientific academies in 16571667. Though shortlived it was influential. It met in the Pitti Palace [Pengelley & Pengelley, p.162]. The dome of the DUOMO was the first large dome since Roman times and is the masterwork of Brunelleschi assisted by the mathematician Giovanni di Bartolo [Franci & Toti Rigatelli]. It was built surprisingly quickly in 14181436. The facade was only designed and built in the late 19C. Around the central rose window are four medallions of GALILEO (lower left), TOSCANELLI, VESPUCCI and FICINO. Galileo had often been consulted on the maintenance of the structure. In 1497 (or 1468??), Toscanelli installed a gnomon attached to the window sill of the southern window of the lantern at the top of the dome which passes a beam of light at the summer solstice onto a mark on the floor, 300 feet below. This was installed to study the obliquity of the ecliptic and it is said to show that the dome has not shifted in nearly 500 years. There is a commemorative plaque near the floor mark in the north transept. [Fahie, pp. 113-115]. The floor mark and plaque were not accessible in 1991, apparently due to restoration works. [W. Alfred Parr; The great gnomon at Florence; Knowledge & Scientific News 2:13 (Dec 1905) 287290] has photos of the gnomon and the floor. There are two concentric circles in the floor, but the inscription in the smaller one was already worn away in the mid 18C. On the larger, and later, circle is the date MDX PRIDIE ID IUNII (= 12 Jun 1510) which was the date of the solstice then because the Gregorian reform had not yet happened. However, these are not quite on the meridianline, but correspond to about a minute and half before noon. In the mid 18C, Leonardo XIMENES laid out a meridian line some 30 ft long and had protective brass plates made to cover the floor marks. He also replaced Toscanelli's gnomon with a duplicate, but it was removed and replaced for repairs to the lantern some years later and was not recalibrated until 1893! It is said that the beam shows that the dome has not shifted, but Parr notes that the image of the 1 inch hole is actually four feet in diameter and is so affected by atmospheric perturbation and the expansion of the dome in the sunlight that it is too unsteady and inconsistent to have any real astronomical or constructional significance. On the north side on the Duomo is the lifesize fresco of an equestrian monument to Giovanni Acuto (Sir John Hawkwood) painted by Paolo UCCELLO in 1436 to show the power of the new technique of perspective. Ghiberti's second set of panels for the east(?) door of the Baptistery also display the power of perspective. The north side of the Campanile had a set of five panels with relief figures representing the Liberal Arts by Luca della Robbia, but these have been moved to the Museo dell'Opera del Duomo at No. 9 Piazza Duomo, and have been replaced by copies. The contents include the following. 2: Plato and Aristotle representing Philosophy. 4: Ptolemy representing Astrology (or Astronomy). 5: Euclid (or Pythagoras) representing Geometry. This museum also contains equipment used in erecting the dome and Brunelleschi's death mask. The [Istituto e] MUSEO DI STORIA DELLA SCIENZA (Piazza del Giudici 1, I50122 Firenze; tel:055-293493) is just up river from the Uffizi, indeed adjoins it. It has a great deal of material relating to Galileo, Torricelli and Viviani. Bonelli (3) observes that Galileo manufactured and distributed a considerable number of instruments (e.g. over fifty examples of his geometrical and military compass were made) and these instruments were prized during his lifetime, so it is surprising that the only known extant examples are in the Museo. There is a new, detailed, and profusely illustrated catalogue [Miniati et al.], which should be consulted for details of the exhibits. [Pengelley & Pengelley, pp. 162164] summarise the material. The museum contains two of GALILEO's early telescope tubes (14X & 20X) [photos in Scandone, p. 33; Miniati et al., p. 73; Bonelli (2)], the objective lens through which he first saw the moons of Jupiter (already accidentally cracked when he presented it to Grand Duke Ferdinando II, and now mounted in an ivory frame) [photos in Scandone, pp. 27 & 33; Miniati et al., cover & p. 61; Bonelli (23)], his geometrical and military compass [photos in Miniati et al., p. 61; Bonelli (23)] and his right middle finger bones mounted in a reliquary [photo in Bonelli (2)]. [Bonelli (3)] says the lenses presently in the telescopes are not definitely known to be due to Galileo. In the 1966 flood, the then Museum director, Professoressa Bonelli, carried the telescopes to safety. There are also lodestones [photos in Miniati et al., p. 63; Bonelli (23)] and other materials used by Galileo and models of instruments and machines devised by him e.g. an 1877 version of his pendulum clock [photos in Miniati et al., p. 61; Bonelli (2)], a modern copy of his thermosocope [photos in Miniati et al., p. 61; Bonelli(2)]), a water pump, two microscopes sometimes said to be made by Galileo himself, an astrolabe of 1584, attributed to Egnazio Dante, that was used by him [photos in Miniati et al., p. 45; Bonelli (2)]. There are also a chair, a telescope stand and the feet of a bed which are supposed to have belonged to him [photos in Bonelli(2)]. Fahie [p. 141] quotes a letter referring to the death mask of Galileo 'in the Florentine Museum', but there is no further reference to it and it is not mentioned in [Miniati et al.]. Where is it?? Mario Velucchi writes that it is not at the Domus Galilaeana in Pisa. One source claims that the Museo has some of the Torricelli/Viviani barometers, but I don't find this in Miniati et al., perhaps it is a confusion with the hygrometers, below. The Museum also has the following. Hygrometers by VIVIANI (16221703), who was a major developer of this instrument [Miniati et al, pp.168171], and a number of his compasses and instruments, including a microscope one of those sometimes claimed to be made by Galileo [Miniati et al., pp. 109 & 120]. A compass set supposed to have belonged to Michelangelo [Miniati et al., pp. 1617]. Lenses and a telescope by TORRICELLI (16081647), from the 1640s [photo in Miniati et al, p. 75]. The large 'burning glass' given to Cosimo III and used by DAVY and FARADAY to burn a diamond in 1814 [Miniati et al., p. 182 with photo on p. 183]. Sundials on various polyhedra. Some mechanical demonstrations for falling bodies: inclined plane, brachistochrone and the tautochrone property of the cycloid. Two versions of Samuel MORLAND's calculating machine (1664 & 1670). An automaton writing hand from 1764 [photo in Miniati et al., p. 221]. Various portraits generally copies (e.g. Holbein's portrait of Kratzer and Sustermans' portrait of Galileo). The earliest Islamic celestial globe, from Valencia, 478 AH = 1085 AD. A fine library. A room on the history of cartography. The clock of the PALAZZO VECCHIO was installed with (or modified to) a pendulum in 1667 under the direction of Viviani [Miniati et al., p.191]. The Dressing Room is decorated with 16C maps [ MGG ]. The basilica of SANTA CROCE contains tombs and memorials of many distinguished Italians. For us, the most notable is the tomb of GALILEO (1564-1642), just to the left of the entrance. It is flanked by statues of Astronomy and Geometry. Before burial here, the body was in a sacristy of the Medici Chapel, at the south end of the transept. It is usually said this was because the Church would not permit a public burial and monument, but a guide book to Santa Croce asserts this was "for other reasons, mainly financial". The church also has the tombs of Leon Battista ALBERTI (whose ashes were brought from Rome and put in the family vault), Eugenio Barsanti (18211864, inventor of an internalcombustion engine), Ghiberti, Michelangelo, Rossini and memorials to Cherubini, Dante, FERMI, Machiavelli, MARCONI, Raphael, Paolo TOSCANELLI (del Pozzo), Amerigo VESPUCCI, Da VINCI. [Gustavo Cocci; Santa Croce Temple of the "Glories of Italy" ; Bonechi, Florence, nd [1980s?]. Deborah Singmaster, personal communication, 1998.] VIVIANI (1622-1703), qv in Sections 9A1 & 2, is supposed to be buried near Galileo. On the south side of the church are its cloisters. In one of the rooms of the Minor Refectory, a branch of the Inquisition condemned Cecco D'ASCOLI to death [Hare, pp. 8990]. Luca Pacioli lived in the monastery for much of 14991506. The upper part of the facade of SANTA MARIA NOVELLA was designed by ALBERTI in 1458. It has a meridian and a quadrant erected in 1572 and 1574 by Egnazio (or Ignazio) DANTI (15361586), Court Astronomer to Cosimo I. [Miniati et al., p. 39] says the church also has a gnomon by Danti. A recent glance makes me think the quadrant and the gnomon are the same object at the right of the facade, while the object at the left looks like an armillary sphere, but could be a sundial, which is called a meridiana in Italian. Bruno Giovanetti & Roberto Martucci [ Architect's Guide to Florence ; Butterworth, London, 1994, p. 46] describe these as an armillary sphere on the left and a sundial on the right. [P. Stefano Orlandi, revised by P. Isnardo P. Grossi; Historical Artistic Guide of Santa Maria Novella and her Monumental Cloisters ; Edition S. Becocci, Florence, 1984, p. 4] says the object on the right is a marble quadrant, while the object of the left is a bronze meridian. Inside the church is the 14251426 fresco of the Trinity by MASACCIO (= Tommaso di Giovanni or Tommaso Guidi) (1401-c1438), one of the first showpieces of the new geometry of perspective. Off the Chiostro Verde (Green Cloister) is the Capitolo or Capellone degli Spagnoli (Chapter House or Spanish Chapel), with fine frescoes by Andrea di Bonaiuto in the late 1360s. On the left wall is the Triumph of St. Thomas Aquinas and an Allegory of the Sciences. The bottom half of the wall has fourteen compartments depicting the Sacred Sciences and the Liberal Arts, represented by seated allegorical women with historical figures in front of them. Third from the left is Knowledge with Aristotle. From the middle to the right are the Quadrivium (Arithmetic with Pythagoras, Geometry with Euclid, Astronomy with Ptolemy, Music), followed by the Trivium. Arithmetic is signing two and holding a multiplication table (still known as the Table of Pythagoras in some places). Geometry is holding a compass and set square. Astronomy is holding an astrolabe and pointing to the sky. [Orlandi, op. cit., pp. 6071.] Those interested in the history of mathematics should pay respects at the grave of Antonio Magliabechi (1633-1714), in the floor to the right of the first bay of the west aisle, in front of the tomb of Antonio Strozzi [Orlandi, op. cit., p. 40]. Magliabechi had a prodigious memory, being able to recall hundreds of books word for word and being regularly consulted as a living reference library. He became librarian to Grand Duke Cosimo III. Magliabechi was a noted bibliophile and authors of his time frequently presented him with copies of their works. His collection was bequeathed for public use and is a major part of the old works in the Biblioteca Nazionale. It includes one of the four main manuscripts of Fibonacci's Liber Abbaci , indeed the early 14C version used by Boncompagni for his printed edition of 1857, the only printed edition ever produced of this major work. Magliabechi's collection also includes the manuscript Trattato d'Aritmetica attributed to Paolo dell'Abbaco, c1370, and the two manuscripts: Libro di ragioni and Liber habaci of Paolo Gherardi, 1327 & 1327? the first has been called the earliest vernacular treatment of algebra. At Via Romana 17 (formerly 19; note there are two doors labelled 17), the Palazzo Torrigiani was formerly, from 1775, the Museo di Fisica e di Storia Naturale and had an observatory, whence its name of LA SPECOLA. The observatory was originally part of the Museum of Science and Natural History in a wing of the Pitti Palace, c1700. It moved here in 1789 and to Arcetri (cf in Section 9A1) in 1872.) The building is now the home of several biological departments of the University and a zoological museum including the greatest collection of wax anatomical models. It was here that DAVY and FARADAY burned a diamond in 1814 using the great 'burning glass'. In a niche by the staircase is a large statue of TORRICELLI. On the first floor is the 18391841 TRIBUNE OF GALILEO, with paintings illustrating his life and a statue. It was commissioned by Grand Duke Leopold II and inaugurated during the Third Meeting of Italian Scientists. It took me some years to get into the tribune, but it is now (1998) open on Sunday mornings as part of a visit to the zoological museum, which is now open most mornings. Fahie [pp. 144-151 & plates: XXXVIII, opp. p. 133; XXXIX, opp. p. 140; XL, opp. p. 141; XLI, opp. p. 148] gives an extended description of it "one of the noblest, certainly, the most evocative and inspiring monument ever raised to the memory of mortal man". It was opened in 1841 as part of the third congress of Italian scientists. The Tribune has a frescoed ceiling showing the invention of the pendulum, the presentation of his first telescope to the Doge of Venice [photo in Scandone, p. 32] and the dictation of his final thoughts on the laws of motion. There are also busts of his students: CASTELLI, CAVALIERI, TORRICELLI and VIVIANI and basreliefs of various scientists including ALBERTI, CASSINI and VIVIANI. In the vestibule and hall are further frescoes showing LEONARDO, VOLTA (lecturing to an audience that includes LAGRANGE), Galileo (experimenting with an inclined plane) and Viviani. Fahie also describes several items which have since been removed to the Museo di Storia della Scienza. [W. Alfred Parr; A temple of Science; Knowledge 23 (May 1900) 103104] describes the Tribune and its contents, though most of the contents have been moved. The UFFIZI GALLERY contains many portraits, notably GALILEO (1564-1642) done from life by Sustermans, 1635 [Fahie, Frontispiece; Scandone, cover & p. 55]. Part of the Third Corridor was the Sala delle Matematiche in the 1718C and its ceiling has a fresco on astronomy and mathematics showing GALILEO, TORRICELLI, PAOLO MATEMATICO (= Paolo dell'Abbaco) [Fahie, p. 82; Miniati et al., pp. XIXII]. There is a statue of GALILEO in the ninth niche of the outer wall of the portico under the Uffizi. The Gallery contains one of the three large panels of the 'Battle of San Romano' by Paolo Uccello, c1456, which have strong perspective lines formed by the broken lances. The other panels are in the National Gallery, London (Section2-B) and the Louvre, Paris (Section 7A1). Amerigo VESPUCCI was a member of one the great Florentine families his cousin by marriage Simonetta Cattaneo Vespucci was a celebrated beauty, immortalised in Botticelli's paintings of 'The Birth of Venus', c1487, and 'Mars and Venus', c1483 the latter shows little wasps ('vespucci') circling the head of Mars. The University of Florence was founded in 1348 (or 1321) and opened on 6 Nov 1349 [R. E. Taylor, pp.138 & 294; Pengelley & Pengelley, p.161]. In 1499, Lorenzo de' Medici reorganized the universities of Pisa and Florence into a joint operation, with only philosophy and philology in Florence. Luca PACIOLI came to teach in 1499 and taught at both Florence and Pisa until 1506 [R. E. Taylor, pp. 250 & 293300]. INDIVIDUALS Paolo (di Piero) DELL'ABBACO (or Abaco, sometimes called Dagomari) (c1281-1367 (or 1374)), born in nearby Prato, was the best known teacher of, and writer on, mathematics in 14C Italy. He owned two houses in Via Maffia, near Santo Spirito, one of which may be the one now numbered 15. He endowed the two chapels flanking the chancel in Santa Trinita and was buried there, but no trace of the tomb remains. [Arrighi, p. 7. Van Egmond]. Van Egmond [p. 9, note 35] cites 1589 and 1793 descriptions of the tomb. He ran his school in the church of S. Trinita and the school continued under his pupil and successor, Antonio de' MAZZINGHI (13531383?), who was born and died in Florence. In his will, dell'Abbaco asked that his astrological books and instruments should be placed in the monastery of S. Trinita 'until there appeared in Florence another astrologer approved by four masters.' After some debate, this was awarded to the young de' Mazzinghi. GIOVANNI DI BARTOLO succeeded de' Mazzinghi. [Franci & Toti Rigatelli.] Leon Battista ALBERTI (1404-1472), polymath and architect, was the first to write a text on perspective, first in Latin and then in his own translation into Italian: De Pictura (1435) & Della Pittura (1436) [Alberti]. He came to Florence in 1434 and spent much time here thereafter. He was a Canon of the Cathedral and held the benefice of the nearby town of Borgo San Lorenzo. Architectural works of his are in Florence, Rome, Mantua and Rimini (see Sections 9A2 and 9B). He designed the upper part of the facade of Santa Maria Novella (qv above) in 1458 and the Palazzo and Loggia Rucellai in 1446. (The Rucellai commissioned the completion of the facade of Santa Maria Novella He also designed the Rucellai chapel in S. Pancrazio.) His De Re Aedificatoria of c1450 emphasised the role of mathematics in architecture. He also wrote the first Italian grammar, Regule lingue florentine . Other scientific works of his were Ludi matematici (simple measurement problems); Elementa picturae (simple geometry applied to painting); Descriptio urbis Romae (partly a measured survey of the city); De statua (including a device for scaling and transferring measurements); De Componendis cifris (an effective coding device) [Kemp, pp. 56]. [R. E. Taylor, p. 93] says he is credited with inventing the camera obscura though IbnalHaytam described a version in c1010. He lived in the Palazzo Alberti, 1 via de' Benci, Florence. He died and was buried in Rome, but his ashes were soon conveyed to Florence and placed in the family tomb in Santa Croce [R. E. Taylor, p. 108]. Filippo BRUNELLESCHI (1377-1446), Renaissance goldsmith, sculptor and architect, discoverer of the principles of perspective, is buried in the recently opened crypt of the Duomo in Florence. Sadly he does not lie under his dome, but he is near the west door and the Baptistery which was the site of the proof of his principles in c1413 he made a perspective view of the Baptistery as seen from the door and devised a mirror viewer so one could compare his view with the reality. [Kemp, p. 21] says he also made a view of the Palazzo de' Signori (=Palazzo Vecchio). There is a bust of him in the Duomo by his pupil and adopted son, Andrea Cavalcanti, called 'Il Buggiano' (I wonder why?). His death mask is in the Museo dell'Opera del Duomo at No. 9 Piazza Duomo and his works are on every hand, most notably the cupola of the Duomo, built in 14181436. The cupola of the Cappella Ridolfi in S. Jacopo sopr'Arno is said by Vasari to have been a trial for the Duomo sadly this chapel was destroyed in the 18C. He also built the Spedale degli Innocenti (1419), rebuilt San Lorenzo (1425) and added the Old Sacristy (1423), rebuilt Santo Spirito (1435), built the Cappella dei Pazzi (14291443), rebuilt the Palazzo Pitti (c1444). 'Built' is perhaps a misnomer as the actual work often did not start immediately it frequently was not completed until long after the architect's death and indeed sometimes did not even get started until then! Later rebuilding and additions may make the architect's work hard to appreciate, but modern restoration works have generally attempted to remove these in order to make Renaissance work appear as it was intended. Cecco D'ASCOLI (??1327) was a physician and astrologer who had written a commentary on Sacrobosco's De Sphaera Mundi . A jealous colleague had him condemned by the Inquisition (see S. Croce above) and he was burned outside the Porta Santa Croce, in the area called Africa (after a stream of that name). [Hare, pp. 8990.] There is a Largo FERMI near the Istituto di Fisica near Arcetri. There is a recent monument to Fermi in Santa Croce. There is a Via FIBONACCI in northeast Florence, north of the Stadio Comunale, not far from Piazza Edison, Via Galvani, Via Marconi, Via Pacinotti and Viale Volta an electrifying area! GIOVANNI DI BARTOLO ( c1440) succeed de' Mazzinghi as head of the abacus school founded by Paolo dell'Abbaco. He assisted Brunelleschi in designing the dome for the Duomo (= S. Maria del Fiore). He also taught astrology at the University of Florence. [Franci & Toti Rigatelli.] LEONARDO DA VINCI (14521519) stayed in Via de' Gondi, c14671469 [Eastman, p. 398]. He was apprenticed to Verrocchio and spent roughly 1467-1477 at Verrocchio's studio in Via dell'Agnolo [Sarton, p. 221]. [I could find no indication of this in 1991 another book claims the studio was part of the Casino Medici, on the NW side of Piazza San Marco, where Michelangelo studied.] He then took lodgings on his own until 1482. On Monte Ceceri, in Fiesole, are two monuments to the first human flight, by a friend of Leonardo in a craft of Leonardo's design. One, on the top, commemorates its launch: Pigliera'il primo volo / Il grande uccello / Sopra del dosso / Del suo magno cecero / Empiendo l'universo / Di stupore, / Empiendo di sua fama / Tutte le scritture. / E gloria eterna / Al logo dove nacque // Leonardo da Vinci. The other monument is on the Via Maiano, close to the Pensione Bencist near Via Beato Angelico, where the craft, killing the 'aviator'. Later Leonardo returned to Florence and stayed in the Servite monastery attached to Santissima Annunziata, Piazza Santissima Annunziata, in 15001506. During this time he painted the 'Mona Lisa'. [Eastman, p. 343.] Guglielmo LIBRI (18031869) was born in Florence and died in adjacent Fiesole [Giacardi & Roero, p.139]. LUCHA DI MATTEO (1356c1435) was one of the bestknown abacus teachers of his time, with a school on the Lungarno between Ponte a Santa Trinita and Ponte all Carraia [Franci & Toti Rigatelli]. Florence NIGHTINGALE (18201910) was born in Villa La Colombaia (plaque), Via Foscolo, a bit SW of the Porta Romana. She lived there for about a year. There is a memorial to her in the cloisters of Santa Croce. [Macadam, pp. 239 & 179. Eastman, p. 351.] Luca PACIOLI (c14451517) came to teach at the university in 1499 and taught at both Florence and Pisa until 1506, living in the monastery of Santa Croce [R. E. Taylor, pp.250 & 293300]. He and da Vinci had left Milan together and came to Florence, originally lodging in the same house [R. E. Taylor, p. 250]. He spent most of 15001507 here [Fennell, p. 16]. He may have taken some time out to teach at Bologna. He was formally admitted to the Santa Croce chapter of his order in 1505 [R. E. Taylor, p. 299]. There is a plaque to Evangelista TORRICELLI (16081647) in the Cloisters of S. Lorenzo, on the way into the Laurentian Library. He came to Florence in 1641 and acted as assistant to Galileo for his last three months, then succeeded him as Mathematician to the Grand Duke and Professor at Pisa. In 1644, Torricelli, assisted by Viviani, demonstrated the pressure of air, apparently first published in 1663. Where did they do the experiment?? Paolo del Pozzo TOSCANELLI (13971482) lived at 16 Piazza Pitti [Macadam, p. 201], across from the Palazzo Pitti, and there is a plaque [I have a photo]. His world map and accompanying Letter showed a large Asia and a small Atlantic Ocean and proposed that one could reach the Indies by sailing west. This encouraged Columbus. There is a Via Toscanella behind his house. Francesco TRICOMI (18971978) was Professor of Algebraic and Infinitesimal Analysis at the University in 19251926 (or 1928) [Giacardi & Roero, pp. 190191]. Amerigo VESPUCCI (14541512) was born in one of the Vespucci houses in Borgo Ognissanti. He is said to have made four voyages to the New World. He reported sighting the South American mainland on 16 Jun 1497, a week before Cabot reached North America, which led to his name being attached to the New World in Martin WaldseemGller's Cosmographi% Introductio of 1507 but many authorities doubt that Vespucci ever made this voyage. WaldseemGller realised that he had overrated Vespucci's accomplishments and removed the name from later versions of his map, but it was too late. His cousin, Simonetta Vespucci, was a celebrated beauty, immortalised in Botticelli's paintings his 'Mars and Venus' in the Uffizi shows little wasps ('vespucci') circling the head of Mars. Florence's airport, in the NW suburb of Peretola, is named Amerigo Vespucci. Vincenzo VIVIANI (16221703) lived at 11 Via S. Antonino, see Section 9A1. He also was Mathematician to the Grand Duke.  9-B.ELSEWHERE IN ITALY.  Italy is divided into 20 regions (e.g. Toscana = Tuscany) and subdivided into 94 provinces (e.g. Firenze = Florence). I don't have an atlas giving the provinces of Italian cities and provinces are named for the principal city in them, so the province gives no additional information for most of the entries below. The MGG gives the regions and I have now added them, though some towns are not in the MGG and I have had to estimate their region from a small scale map. AGRIGENTO (Agrigentum), Sicilia, was the home of EMPEDOCLES (504/443 or 490/430), the physician and philosopher who asserted everything is made of the four elements: earth, air, fire, water. He is said to have leaped into MT. ETNA in order to become a god! Francesco FA  DI BRUNO (18251888) was born in ALESSANDRIA, Piemonte [Giacardi & Roero, pp. 144146]. In AMALFI, Campania, there is a Piazza Flavio Gioia commemorating the supposed perfecter of the mariner's compass [ MGG ], which would have been c1000. Connoisseurs of pattern will know that the floors of old cathedrals in Italy are generally covered in mosaics in elegant geometric patterns One style is known as Cosmatesque after the Roman family of Cosmati who did such work in the 1214C; other styles are called Opus Alexandrinum, Opus Sectile, Opus Reticulatum, Opus Spicatum, etc. Indeed, the floor of the Sistine Chapel in Rome is one of the finest such floors in the world, though few visitors ever examine it! In ANAGNI, Lazio, about 50 km ESE of Rome, the Cathedral has a fine Cosmatesque floor with sections in the form of the fourth stage of the Sierpiski gasket! [Etienne Guyon & H. Eugene Stanley; Fractal Forms ; Elsevier/NorthHolland for Palais de la D)couverte, 1991, colour photo on back cover with caption inside] say that the Cathedral and the floor were built in 1104, that the pattern was pointed out by Rachel Stanley, aged 10, and that it may be the oldest manmade fractal object! However, other guidebooks indicate the floor may be c1235 and there are certainly many other possible floors if anyone finds an earlier example, please let me know. [ MGG ] says that the pavement is in the crypt and that it also has fine 13C frescoes including scenes from the lives of men of science, but only mentions Galen and Hippocrates. Anchiano see Vinci, below. Vito VOLTERRA (18601940) was born in ANCONA, Marche [Giacardi & Roero, pp. 153154]. St. ANSELM ( 1109), the theologian whose existence proof of God continues to bemuse students, was born in AOSTA, Valle d'Aosta [ MGG ]. Cesare BURALI FORTI (18611931) and Francesco SEVERI (18791961) were born in AREZZO, Toscana [Giacardi & Roero, pp. 168170 & 180181]. The Badia of SS. Flora and Lucilla has an illusory dome painted on a canvas over the crossing. It was done by Andrea Pozzo in 1702. [ Arezzo A City Guide ; Edizione Turchini Ennio, no other details given, [bought in 2001], p. 35, with photo.] A labyrinth carved on a rock wall in the Tomba del Labirinto possibly dates from -2500 to 2000, probably the oldest surviving example [Fisher, pp. 12 & 2526, with photo on p. 12]. [Fisher] says this is in Luzzanas, Sardinia, but this is a name for an uninhabited area of fields and hence does not show up on any ordinary map. This is certainly the most difficult to locate monument that I have ever visited. A contact at the University of Sassari, Professoressa Silvana Diana Corrias, managed to find an archaeologist who knew where it was, but said we would need local guidance. It is near the village of BENETUTTI, Sardegna, about 19 km NW of Nuoro. If you drive west from Benetutti to the adjacent villages of Bultei and Anela, you come to the Terme Aurora. The Tomba is about a kilometre due north. The road crosses a small river and there is a Terme San Saturnino on the other side. In Benetutti we were told that staff at the Terme can direct one to the site, but we found that they are closed on Sundays needless to say, we arrived on a Sunday. The area is uninhabited the farmers seem to live in town. We did find a few farmers, carabinieri and other locals, but none of them knew where the Tomba was. Making further inquiries in the town, we were directed to the farmyard and stables across the road from the Terme Aurora, but were told that no one would be there until after siesta when the shepherd would come to milk his sheep, etc. (We had already discovered that no one was at this site.) We arrived just as he did and after some discussion, he led us back along the road about a mile, then across two fields to a gate. He pointed to a pile of rocks about a quarter of a mile further on. He said he had never gone into the cave as he was afraid of the frogs we think he meant bats. He left us and we walked across the field to the pile of rocks, where there was nothing. But I remembered that the chap had said something like 'beyond' the pile and a young man in town had said his class did a project on the Tomba and had mentioned it was by the river, which was another fifty yards or so, where there was a mound rising a bit above the river bank. As we approached, we saw the mound was of stone and there were two round holes in it, about three ft across, and filled with growth. We walked around and over the mound, which dropped down about 15 feet to the stream. The upper floors of the Terme Aurora are clearly visible, about a kilometre to the south. No other openings in the mound were apparent, so we examined the northern opening which had less dense shrubbery, mainly a small fig tree. The hole was about three ft deep. I dropped into it and got out my trusty Swiss Army knife and cut away the growth and found an opening about two ft square cut into the rock. I cleared away the growth around the opening and looked in to see a dry room. I had a small flashlight (torch) and crawled in to a room about eight foot square and three feet high with openings at the back and immediately to the left. And there, beyond the opening to the left, was the labyrinth carved on the stone!!! We only saw two bats. One stopped for a bit in the corner they are really very sweet beasts. I wonder why the carving is attributed to perhaps -2500. I imagine the style of the cave and perhaps some associated artifacts point to that date. But there was some modern graffiti on the same wall, so it's quite possible that the cave has been visited many times since it was made and the labyrinth could have been carved 100 years ago by some bored shepherd. The stone seemed to be limestone. It must not be too hard as one doesn't go carving chambers in really hard rock. I have seen it asserted that one can tell the nature of the tool that carved a pattern in rock e.g. whether it was steel, iron, bronze, copper or bone. I don't know if such analysis has been applied here. To locate the Tomba, it is advisable to get the 1 : 25,000 map of the area produced by the Istituto Geografico Militare, Foglio 481, Sezione III Bono. An isolated building is marked where we think the pile of stones was presumably it is a collapsed shelter. If so, then the universal map reference of the mound is 32TNK10587621. With the map as a guide, one could walk NNW along the river by the Terme Aurora there was construction there and the map shows another terme. This is the Rio Mannu and one would go downstream about 700 m, to where the Mannu joins the Rio Tirso. Then one could go up the Tirso to the NNE about 800 m. However, we didn't see enough of this route to know whether it is passable. It seems unlikely that one could find the Tomba without some local assistance. On the map, we found Luzzanas written across the fields between the road and the river!! However, this area doesn't seem to have any inhabitants! There is even a Nuraghe de Luzzanas about 1/4 mi to the NE of the mound. My thanks to Ann Maury for inspiring us to go to Sardinia with her, for getting the information from Prof. Corrias, for her intrepid interrogation of the locals and for later obtaining the detailed map. For more details see my article "The oldest labyrinth in Sardinia" [Caerdroia 30 (1999) 1721] or a version on Adrian Fisher's website: www.mazemaker.com . BERGAMO, Lombardia, has a 15C clock on the Bell Tower in the Piazza Vecchia [ MGG ]. [M. J. W. Rogers; Dalton and the Atomic Theory ; Chemistry Background Books, Nuffield Foundation, 1966, p. 8] shows a bust of AVOGADRO at the technical institute in BIELLA, Piemonte, about 45 miles NNE of Torino. BOLOGNA , EmiliaRomagna, has the oldest university in Europe, founded in 1088. In the 13C, it already had 10,000 students. Cecco D'ASCOLI (??1327) was a physician and astrologer at the university. He wrote a commentary on Sacrobosco's De Sphaera Mundi which led to a reprimand by the religious authorities in 1324. He then went to Florence where he was burned as a heretic in 1327. [Hare, pp. 8990.] Leon Battista ALBERTI was a student at the University c1420. He studied jurisprudence and probably graduated in canon law in 1428, but he must have studied optics and mathematics as well [Kemp, p. 3]. COPERNICUS (14731543) came here to study canon law in 14961500, but he devoted much time to the study of astronomy. His first extant astronomical observation was made here the time of the occultation of Aldebaran by the moon on 9 Mar 1497. He may have lodged in Via San Giuseppe [Eastman, p. 333]. In 1500, he was lecturing on astronomy and mathematics in Rome. [Armitage, pp. 6465. Rudnicki, pp. 45.] Scipione FERRO (or del Ferro or dal Ferro) (14651526) was professor in 1496-1526. He solved the cubic, with no x2 term (or with no x term), in c1500 or by 1506 or c1515. He communicated this solution to his pupil Antonio Maria FIORE, who challenged Tartaglia with it in 1535. Tartaglia then solved both forms and later communicated them to Cardan. Cardan and Ferrari heard about Ferro's solutions and came to Bologna in 1542 to read them, leading Cardan to publish the solutions and to initially attribute them to Ferro. Luca PACIOLI (c14451517) taught here for some time during 1500 and 1506 [Giusti, p. 40; Fennell, p.16]. [R. E. Taylor, pp. 299300] suggests it was during JunJul 1501 and cites an author who suggests that DGrer studied under Pacioli in Bologna in 1506, apparently based on a comment of DGrer in 1506 that he was going to Bologna to see the leading authority on perspective. Sebastiano SERLIO (14751554), the noted Italian architect, was born in Bologna. Cf under Sheldonian Theatre in Section 5A. Rafael BOMBELLI (15261572) was born in Bologna and was a student at the University. During his stay in Bologna, 1562-1571, CARDAN (15011576) lived in Via de Gombru (=? Gombruti), then in the Palazzo Ranuzzi in Via del Galera and then near S. Giovanni in Monte (in the SE quarter) [Cardan, pp.17, 82, 85, 309]. Lodovico FERRARI (15221565) was born and died in Bologna [Masotti, p. 26]. Bonaventura CAVALIERI (15981647) was Professor here. Giovanni Domenico (or Giandomenico) CASSINI (16251712), the first of the Cassinis (cf under Paris, Sections 7A1 & 2), was Professor of Astronomy in 1650-1669, filling the post previously held by Cavalieri. The Church of S. Petronio has a 220 ft long meridian line set out by him in 16531655 [ Blue Guide to Northern Italy , 1971, pp. 370 & 377], improving on the one set out by Egnazio DANTI in 1575. Danti produced the first astronomical treatise in Italian, in 1569, much enlarged in 1578. He described the gnomon and meridian line in a broadside sheet (Horblit Catalogue, lot 263) Usus et Tractatio Gnomonis Magni quem Bononiae ipse, in Divi Petronii Templo ... Confecit , of 1576. He later went to Rome to work for Pope Gregory XIII, the calendar reformer. The function of the line was to prove a theory of the solstice and to determine the exact date of the vernal equinox. The line runs along the left side of the church from just inside the central door. (Normally one would call the left side the north side, but here the church has its altar toward the south.) A source says Domenico Guglielmini assisted Cassini. On a visit in 1695, Cassini had to repair this as the dome had settled. [Anon: Eloge de Monsieur Cassini]. It had to be adjusted in 1776. The hole through which the sun shines is so small and distant that a goodsized image of the sun is projected on the floor. [Angelo Raule; La Basilica di San Petronio a Bologna ; extract, translated by Gina L. Bedeschi Pincherle, as: The Basilica of Saint Petronio ; Editcomp, Bologna, nd [1990s], pp. 11 & 14.] In 1665, Cassini discovered the great red spot on Jupiter and determined Jupiter's rotational period this seems to have been done while he was at Citt!dellaPieve in Tuscany. In 1667-1669, he determined the rotational period of Mars and in 1668, he produced the first detailed table of the motions of the moons of Jupiter. In 1664, he first detected the irregularities of the moon's outline, as conjectured by Galileo. Toward the middle of the left side of the church is a pair of clocks which keep four different times. The guide book is not too clear: the left one keeps 'the mean time of Central Europe and the real time of the Bologna Meridian', while the other keeps 'the mean time of the meridian of Bologna which was used from 1857 to 1893, and the time according to ancien[t] Italian clock, in which hours were counted beginning from the evening' [Raule, op. cit. above, p. 6]. There is a statue of the Bolognese Pope GREGORY XIII, the calendar reformer, of the doorway of the Palazzo Comunale. The Instituto delle Scienze di Bologna was established in 1714 by Luigi Ferdinando Marsili. It supported Newton's work and Marsili visited London in 1722 and was made an FRS with Newton as his sponsor. They began publishing their De Bononiensi Scientiarum et Artium Instituto atque Academia Commentarii in 1731. Vincenzo RICCATI (17071775), son of Jacopo Riccati (see Padua, below), was a Jesuit, Professor of Mathematics at the University of Bologna from 1739, who developed the hyperbolic functions in 1757, using the notations Chx and Shx. Maria Gaetana AGNESI (17181799) was the eldest child of Pietro Agnesi, who became professor of mathematics in Bologna. She was a prodigy, speaking half a dozen languages by her teens and being the star of Conversazione, where the purity of her Latin impressed visitors. When her mother died, c1740, she withdrew into raising and educating her 20 siblings. Her Instituzioni Analitiche vol. 2, of 1748, was the first systematic text on calculus and both volumes were models of clarity which were widely translated and used as textbooks. She was appointed Professor of Mathematics and Natural Philosophy by the Pope to replace her ill father in 1750, but never taught, though the University kept her on its roll until 1796. About 1750, she decided to devote herself to the needy, eventually becoming director of a hospital for poor women, the Pio Albergo Trivulzio or Luogo Pio in Milan. [Perl, pp. 5262. Sister Mary Thomas ! Kempis; The walking polyglot; Scripta Mathematica 6 (19391940) 211217.] Luigi Aloisio GALVANI (17371798) was Professor of Anatomy here when he discovered 'animal electricity' c1786 (published in 1791). He was ousted from his post when he refused to swear allegiance to Napoleon. There is a Piazza Galvani. Luigi CREMONA (18301903) was the first Professor of Higher Geometry from 1860. Eugenio BELTRAMI (18351900) was professor from c1860. Cesare ARZEL  (18471912) was at Bologna from 1880, becoming Professor of Higher Analysis in 1884. Among his students were Bortolotti, Vitali and Tonelli. [Martini.] Salvatore PINCHERLE (1853-1936) was professor from 1882 and died here. Federigo ENRIQUES (18711946) was Professor of Geometry in 18961923. Guglielmo MARCONI (18741937) was born in the Marescalchi Palace, 5 Via Quattro Novembre, Piazza Roosevelt. His mother, Anna Jameson, was Irish and his upbringing was very British. He was a student at the University. In 1894, he read about Hertzian waves and realised they could be used for communication. He soon developed wireless telegraphy at his grandparents' Villa Grifone, in nearby Pontecchio (now PontecchioMarconi) in 18941895, signalling over a mile and then further in 1895. The Italian government was not interested, so he and his mother went to England in Feb 1896. He is buried in the Camposanto. [Eastman, pp. 344345.] The Bologna Airport is named for him. Beppo LEVI (18751961) was Professor of Mathematics until 1938, when he had to leave because of his religion and went to Argentina. Francesco SEVERI (18791961) did postgraduate work here under F. Enriques, c1901. [Giacardi & Roero, pp. 168170.] Francesco TRICOMI (18971978) was a student of chemistry at the University, but soon moved to doing physics at Naples [Giacardi & Roero, pp. 190-191]. During 19241926, Dirk STRUIK spent nine months in Italy and visited Bologna, where he was shown some 16C MSS which initiated his interest in the history of mathematics [Tattersall]. Borgo San Lorenzo see under Alberti in Section 9A2. Borgo Sansepolcro see: Sansepolcro. The BORROMEO family have been a noble family in northern Italy since the 15C. The famous Borromean Rings form part of the family coat of arms. The Golfo Borromeo and the Borromean Islands are in Lago Maggiore, off the town of Stresa, Piemonte. In the 16 and 17C, the Counts of Borromeo built a baroque palace and gardens on the main island, Isola Bella. The Borromean rings can be seen in many places in the palace and gardens, including the sides of the flower pots! Although the Rings have been described as a symbol of the Trinity, I don't know how they came to be part of the Borromean crest, though the guide book describes some of the other features of the crest. (Thanks to Alan and Philippa Collins for the information and loan of the guide book.) Antonio Genesio Maria PANIZZI (17971879) was born at BRESCELLO in the Duchy of Modena. He fled, under sentence of death, to England in 1823 and became Principal Librarian (i.e. Head) of the British Museum where he instigated and built the great Reading Room. NiccolA TARTAGLIA (1499?1557) was born in BRESCIA, Lombardia, and lived there until c1517. In 15481549, he spent a year and a half teaching in Brescia at S. Afra, S. Barnaba, S. Lorenzo and at an academy in the area of Rezzato. There is a statue of him in the piazza by Santa Maria Calchera. [Masotti (2), pp. 1718, 38 & 55] In the Ateneo di Brescia is a model (bozzetto) for a monument to Tartaglia showing him holding a sheet with X3Ġ+PX= Q [Masotti (2), frontispiece & p. 55]. The Civici Musei has the only known example of a Byzantine astrolabe, dated 15 Jul 1062. NICHOLAS OF CUSA (14011464) became Bishop of BRESSANONE, TrentinoAlto Adige, in 1450. Tradition says BOETHIUS (c475c523 or 455524) was buried in CALVENZANO, Lombardia, near Melegnano, 10 km SE of Milan, and a plaque was erected there in 1947 [Masotti, pp. 68]. CAPRESE MICHELANGELO was the birthplace of Michelangelo and there is a museum on the site. Rather surprisingly, this has a small room dedicated to the astronomer Giovanni Santini (17871877). He was born in the adjacent hamlet of Lama in Caprese and was Professor of Astronomy at Padua in 18131857, establishing the observatory there and becoming Rector of the University in 1824. His main work was on comets and determining their orbits. The exhibit is mostly photographic, but has some actual instruments. Cassino see: Montecassino. Guido FUBINI (18791943) was professor at CATANIA, Sicilia, in 19031906 [Giacardi & Roero, pp.185-186]. On a visit in 2001, I found several examples of puzzle grills in CITT  DI CASTELLO, Umbria. Some are on the left side of the Cassa di Risparmio di Citt! di Castello, in Via Mario Angeloni (I didn't check the right side). Another was in Via G. Marconi and another was just inside the restaurant Amici Miei, Via del Monte 2. Also I saw three clocks on the Piazza Matteotti facade of the Palazzo dell'Podest!. One had the usual Roman numerals (except it used VIIII instead of the more common IX). Another had 12 divisions, but only labelled every other one, using Roman numerals I through VI. The third had sixteen divisions, with every other one labelled with the following letters: T, G, +, S, O, I (possibly L), P, M. Also in Via G. Marconi is a bracket or console with a triple head, viewable from three direction. Alessandro VOLTA was Professor of Physics at COMO, Lombardia, in 17751779. About 1km west of CORTONA, Toscana, on the road toward Sodo, is the Tanella (s Tomb) of PYTHAGORAS. This is an Etruscan tomb variously dated 4C and [ MGG ]. I was rather mystified how Pythagoras came to be thought to have been in this area and I wondered if someone misinterpreted Crotone (see below) as Cortona at some point. On a visit to Cortona in Sep 2001, I found that this is the standard explanation! A local guidebook claims the two names are similar in Greek and dates the tomb as 4C. The placard at the tomb dates it to the period 250/100. The 6th Room in the Museum of the Etruscan Academy has a large ivory chess board. The 8th room has two celestial globes from c1700. The altar in the Cathedral (Cattedrale) was designed by Alessandro Galilei in 1731. (Cf under Santa Croce in Section 9A1. GERARD OF CREMONA (11141187), the greatest of the translators of Arabic texts, was born in CREMONA, Lombardia. He spent most of his working life at Toledo, Spain, but may have returned to Cremona to die. Cf Toledo, Spain in Section 10. [Holmyard, pp. 104106.] There is a fine astronomical clock on the campanile by the cathedral, dating from 1471, but altered several times [ MGG ]. CROTONE, Calabria, is on the site of Croton, to which PYTHAGORAS migrated, c-531, and established his mystic brotherhood. Legend says he developed his theory of vibrating strings after hearing the sound produced by blacksmiths' hammering. He was later forced out and retired to Metapontum (now METAPONTO, near Bernalda, about 30 km west of Taranto) where he died. [Crosland, vol. 3, p. 159.] [HM 25:1 (1998) 99] reports that William S. Anglin visited Crotone and only found a street and a correspondence school bearing Pythagoras's name. JunIchi Yamashita [letter of 4 Oct 1996] visited Metaponto in 1992 and found nothing relating to Pythagoras. Giovanni Francesco PEVERONE (15091559) was born in CUNEO, Piemonte. His Due brevi e facili trattati, il primo d'Arithmetica, l'altro di Geometria ... of 1558 included solutions of some problems of games of chance, in particular the famous 'problem of points'. [Giacardi & Roero, pp. 117118.] Spinetta, a village three miles from Cuneo, is the birthplace of Giuseppe PEANO (1858-1932). He studied at the local school before going to Turin at age 12. A plaque has recently been placed on the house. The local Liceo Scientifico is named after him and there is a bust of him in the entrance. [Anon., Commemoration.] Elea see Velia, below. "An extraordinary ancient coloured mosaic representing the manner of death of A[RCHIMEDES] ... came originally from the city of HERCULANEUM ..." [Archibald (2), p. 65]. This is ERCOLANO, Campania. I don't know where this mosaic is, but much of the material from Herculaneum is in Naples. There is a fine floor mosaic labyrinth in the tepidarium of the baths [ MGG ]. Mt. Etna see Agrigento, above. Evangelista TORRICELLI (16081647) was born near FAENZA, EmiliaRomagna, perhaps in the village of Modigliana. There is a monument to him in Faenza [Andreas Hinz, letter of 26 Mar 1987]. In the Piazza Maggiore of FELTRE, Veneto, NNE of Bassano, is a statue of Panfilo Castaldi, an early printer sometimes claimed to have preceded Gutenberg [Buckley & Robinson, p. 355]. COPERNICUS (14731543) received his doctorate (of Canon Law) at the bishop's palace in FERRARA, EmiliaRomagna, in May 1503 [Ramsauer, pp. 24-25], though his studies had been done at Bologna and Padua. Federico COMMANDINO (15091575) was a student of philosophy and medicine at Padua in 15341544, but took his medical degree at Ferrara. Fiesole is included under Firenze (Florence), Section 9A. THOMAS AQUINAS (c12251274) died in the guest house of FOSSANOVA Abbey, Lazio [ MGG ]. Marco POLO (12541324) was a prisoner in Palazzo San Giorgio, Piazza Capricamento, GENOVA (GENOA), Liguria, when he dictated his Travels . The palace has been restored to 13C style, but is occupied by the city harbour board and has no traces of Marco's stay. [Eastman, p. 355.] Leon Battista ALBERTI (1404-1472), architect, the first to write a text on perspective, was born in Genoa where his family was in exile from Florence [Kemp, p. 3]. Christopher COLUMBUS (who always signed himself Cristobal Colon, 14511506) was probably born inside the old eastern gate, Porta dell'Olivella, where his family lived until 1455. The area has been completely rebuilt. He was baptised in Santo Stefano. In 14551470, he lived in the House of Columbus, 37 Vico di Morcento, where two floors of the original five floor house remain. The municipal Museum in the Town Hall, 9 Via Garibaldi, has some fragments of the skeleton found in Santo Domingo in 1877 and some manuscripts by him. [Eastman, p. 333. MGG .] However there are other locations which claim to be Columbus's birthplace see Calvi in Section 7B. Cf Sevilla, Spain, in Section 10, for more details on his remains. James SMITHSON (1765-1829), whose legacy founded the Smithsonian Institution, died in Genoa and was buried in the British Cemetery. When the land was needed in 1903, Alexander Graham Bell came and removed the remains to the USA, where they were reinterred in a crypt in the Institution. [Gunther (3), p. 279. Grosvenor.] See United States: Washington in Section 10. Supposedly, as he lay dying, he requested his friends to do a postmortem "and find out what ails me; for really I am dying to know what my disease is myself." Gino LORIA (18621954) became Professor of Higher Geometry in 1886, teaching until 1935. He had a strong interest in the history of mathematics, publishing Storia delle Matematiche in three volumes, 19291933, and editing Bolletino di bibliografia e storia delle scienze matematiche for many years. He left his library to the Biblioteca Speciale di Matematica which he founded. [Giacardi & Roero, pp. 177178.] Guido FUBINI (18791943) was professor here in 19061908 [Giacardi & Roero, pp. 185186]. CAUCHY tutored the Bourbon heir in exile in Prague and G?rz (now GORIZIA, FriuliVenezia Giulia, in 1833-1838. There is a collection of capacity measures in the Tower of the Porta Romana, GUBBIO, Umbria. Herculaneum see Ercolano, above. F. ENRIQUES (1871??) was born in LIVORNO (LEGHORN), Toscana [Giacardi & Roero, p. 173]. NICHOLAS OF CUSA died in LODI, Lombardia, in 1464 [Sarton, p. 14]. In LUCCA, Toscana, there is a fine labyrinth carved on the pillar of the entrance to the Cathedral of S. Martino. Luzzanas, Sardinia see Benetutti, above. Cesare ARZEL  (18471912) taught at the Lyceum in MACERATA, 18701878, with a year on leave at Pisa in 18721873. VOLTERRA was one of his students. [Martini.] In MANTOVA (MANTUA), Lombardia, Leon Battista ALBERTI designed the churches of San Sebastiano (1459) and Sant' Andrea (14701471, completed after his death) [Kemp, pp. 67]. There is a fine panelled wooden ceiling in the form of a labyrinth in the Stanza del Labirinto in the Palazzo Ducale. Some of the finest perspective and trompe l'oeil effects of the Renaissance are by Andrea MANTEGNA (14311506) in the Palazzo Ducale and Sant' Andrea and by Giulio ROMANO in the Palazzo del Te. Gino LORIA (18621954) was born in Mantova [Giacardi & Roero, pp. 177178]. Gino FANO (18711952) was born in Mantova [Giacardi & Roero, pp. 173176]. In 1971, David Singmaster was on an underwater archaeological expedition directed by Honor Frost investigating some concretions off Capo San Teodoro, on the north side of the Punic ruins on the island of Motya (Mozia), about 12km N north of MARSALA, Sicilia, when he discovered the remains of a ship where sand had been removed by winter storms and currents. This turned out to be a Carthaginian warship, from about 250, making it the first Carthaginian ship and the first classical era warship to be discovered. It was excavated by Honor Frost in 19711974 and conserved. In 1972, a smaller fragment of another ship was discovered next to the first, with more of its prow and a movable ram the first remains of a ram to be discovered. The prow (probably of the second ship) has been reconstructed at the Archaeological Museum, Via Boeo, Marsala. [DBS see also: Sunday Times Magazine (22 Jul 1973); Intl. J. Naut. Arch. 1 (1972) 113117 & 2(1973) 3349; Maria Grazia Griffo Alabiso: Marsala ; Lions Club Marsala, 1984, pp. 2526 & plates IXXI; Aramco World (NovDec 1986) 29. MGG-Italy(1995) , p.273.] At MASER (or Mas/r), Veneto, ENE of Bassano, is the Villa Barbaro (or (di) Maser), one of Palladio's finer villas, of 15571558, built for the brothers Daniele and Marcantonio Barbaro. Daniele BARBARO (-c1570) was a noted intellectual of his day. He and Palladio travelled to Rome to study Roman architecture and Palladio assisted Daniele in his edition of Vitruvius. Daniele also wrote on geometry and perspective, including his La Practica della Perspectiva of 1569, which probably inspired the mosaic starlike dodecahedron at San Marco, Venice, qv below. He was later Venetian ambassador to London, then Patriarch of Aquileia and official historian of Venice. He undoubtedly assisted both Palladio in the design of the villa and Paolo Veronese in the decorative frescoes which feature trompe l'oeil effects. At the ends of the wings of house are colossal dials the western one is a sundial, but the eastern one is marked with signs of the zodiac and is probably the wall equivalent of a meridian line. [Buckley & Robinson, pp. 352354. MGG-Italy(1995) , pp.228229.] Francesco MAUROLICO (= Maurolycus) (1494 or 1498 -1575), one of the first users of mathematical induction, taught at MESSINA, Sicilia, and died there [Sarton, pp. 84-85]. Giovanni Alfonso BORELLI was Professor of Mathematics at the University in 16391656. Gino FANO (18711952) was professor of algebra and analytic geometry in 18991901 [Giacardi & Roero, pp. 173176]. Beside the Cathedral is a 60m tall Campanile with an astronomical clock made in Strasbourg in 1933 and believed to be the largest in the world [ MGG-Italy(1995) , p.274]. Metaponte see Crotone, above. BOETHIUS (c475c523 or 455524) lived in MILANO (MILAN) , Lombardia. See also Calvenzano, above. [Masotti, pp. 68.] The earliest mechanical clock of which reasonable knowledge exists was set up in Milan in 1335 and had a striking mechanism [F. A. B. Ward, pp. 20 & 48]. One of Andrea MANTEGNA's most remarkable uses of perspective is his Dead Christ in the Pinacoteca di Brera. The late 15C architect BRAMANTE produced a fine illusionistic false apse in the Church of S. Maria by ('presso') S.Satiro [Converso, p. 34]. Luca PACIOLI (c14451517) was professor here in 14961499. He was inspired to start his Divina Proportione on 9 Feb 1498 and completed it on 14 Dec 1498, though it was not published (in an expanded form) until 1509 [Masotti, pp. 1819; Giusti, p. 40; Fennell, pp. 1215; R. E. Taylor, pp. 231232, 235, 251 (noting the erroneous 1497 in the printed version)]. The period in Milan was the high point of his career, being a leading member of the glittering intellectual court of Lodovico Sforza. He lived at the monastery of San Simpliciano, writing his Divina Proportione , and De Viribus Quantitatis here [R. E. Taylor, pp. 230231]. He was a good friend of LEONARDO DA VINCI (14521519) who drew the pictures for Pacioli's book. Pacioli is our leading witness to Leonardo's work at this time, particularly the Last Supper in the Refectory of the Monastery of Santa Maria delle Grazie during 1495-1497, and he may well have advised on the perspective of the painting. Certainly Pacioli stimulated Leonardo's interest in perspective and it is possible that Leonardo's famous drawing of the proportions of the human body was inspired by Pacioli's comment on classical architecture; "For in the human body they found the two main figures ..., namely the perfect circle and the square." Pacioli seems to have made models of the polyhedra illustrated in his book, though we don't know if Leonardo used these for his drawings. A set was probably given to Pacioli's earlier patron, the Duke of Urbino, in 1494. Another set was paid for by Florence in 1504. [Fennell, pp. 1215.] The Biblioteca Ambrosiana (Ambrosian Library), 2 Piazza Pio XI, has a major display of Leonardo's drawings and notebooks. The Galleria Leonardesca of the vast Leonardo da Vinci Museum of Science and Technology, 21 Via San Vittore, displays models of his designs. Leonardo lived in Milano in 14821499 and 15061513. [Eastman, pp. 343344 & 398.] There is a large monument to Leonardo in the centre of the Piazza della Scala, facing the famous opera house [Converso, pp. 2021, 25]. In the BRERA GALLERY is one of PIERO della Francesca's great paintings: Madonna and Child, with Saints and Angels, done about 1472. The second saint from the right, St. Peter Martyr, distinguished by the gash on his head, has been identified as Luca PACIOLI. See also under Perugia, below. [R. E. Taylor, pp. 118119.] CARDAN (1501-1576) spent his early childhood in Milan in the Via dell'Arena near the present Ponte Ticinese. He later lived near the Castle; in Via dei Rovelli; near S. Michele di Chiusa; near Porte Orientale and in Via Cinque. [Cardan, pp. 85-86 & 308-309.] He is buried in S. Marco [Cardan, p. xiii]. After Cardan's publication of Tartaglia's solution of the cubic, a public disputation was held between Ferrari and Tartaglia on 10 Aug 1548 at S. Maria del Giardino dei Minori Osservanti [Masotti, p. 28; Masotti (2), p. 29]. Giovanni Francesco PEVERONE (15091559) died in Milan [Giacardi & Roero, pp. 117118]. There is a statue of CAVALIERI in the Brera Palace [Masotti, p. 41]. There is a street and a school named for Maria Gaetana AGNESI (1718-1799), who was born in Milan and later was director of a hospital for poor women, the Pio Albergo Trivulzio or Luogo Pio. She was buried in a common grave outside the Roman gate with no monument. Monuments have been erected to her in and on the hospital. [Deal. Sister Mary Thomas ! Kempis; The walking polyglot; Scripta Mathematica 6 (19391940) 211-217]. The facade of the Galleria Vittorio Emanuele has statues of COLUMBUS, GALILEO, LEONARDO, MARCO POLO, MICHELANGELO, VOLTA, etc. [Fahie, pp. 137-138]. There is a statue of La Matematica in the Sala di Lettura Pio XI of the Biblioteca Ambrosiana [Masotti, p. 2]. There was a statue of Francesco BRIOSCHI (18241897) in the Palazzo della Canonica [Masotti, p. 87]. He was a founding professor at the University of Milan in 1862. EINSTEIN spent 18951896 in Milan [Eastman, p. 390]. Enrico BOMBIERI was at Milan when DAVENPORT visited in 1965. While Davenport was visiting Florence and Venice, Bombieri developed his large sieve, meeting Davenport at the station with his manuscript produced in four days without going to bed. [Rogers.] The Leonardo da Vinci Museum of Science and Technology opened in 1953 at 21 Via San Vittore (see above), but the Civic Collection of Applied Arts in the Castello Sforzesco, Piazza Castello, includes clocks and scientific instruments [Converso, p. 68]. Paolo RUFFINI (17651822) was at the University of MODENA, EmiliaRomagna, c1821. MONTECASSINO is the site of one of the great monasteries, founded by St. Benedict in 529 and the mother house of the Benedictine order. CASTELLI (15771644), the pupil of Galileo and teacher of Torricelli, was here. The University of NAPOLI (NAPLES), Campania, was founded in 1224 by Emperor Frederick II of Sicily. In the Museo Nazionale Capodimonte is the marvellous portrait of Luca PACIOLI (c14451517) with geometric models, by(?) Jacopo de' Barbari, probably in 1495. This is the earliest extant real portrait of a mathematician, done in Venice about the time of publication of his Summa de Arithmetica in 1494. The books depicted are his Summa and the first printed Euclid of 1482. Nick Mackinnon argues that the youth on the side is Albrecht DFRER, possibly a self portrait, and that the glass rhombicuboctahedron was done by LEONARDO. [Mackinnon (3). Reproduction in Giusti, p. 5. Fennell, p. 10, with reproduction.] [R. E. Taylor, pp. 200205] discusses the painting, saying he long thought the young man might be DGrer, but that the painting is done with great accuracy and the young man has blue eyes, which DGrer did not. Pacioli taught here in the 1490s for some time, possibly completing his Summa here, though he certainly worked on it while it was being printed in Venice [Fennell, pp. 1112]. R. E. Taylor [pp. 169 & 330331], cites a passage in De viribus quantitatis [ff.93v94r] where Pacioli refers to one of his pupils in 1486 in Naples, but on p. 169, Taylor interprets this as saying this may have been a pupil in 1486 who was later in Naples, while on p. 331, Taylor says this proves that Pacioli was in Naples in 1486. Giordano BRUNO (15481600) was born in Naples. Giovanni Battista della PORTA (15431615) was Neapolitan. He observed the effect of a pinhole lens and invented the camera obscura which he described in 1597 (though some feel Leonardo da Vinci had the idea earlier [Storer, p. 37] states that Leonardo mentioned it c1500). [Scott, p. 30.] The earliest scientific academy in Europe was the shortlived Academia (??sp) Curiosorum Hominum in Naples in the 16C. Mary SOMERVILLE (1780-1872) died in Naples and was buried in the British Cemetery at Santa Maria della Fede which has been recently restored [Richard Owen; A foreign field that remains 'a tranquil corner of England'; The Times (13 Jun 2000) 24]. (Thanks to George Duckworth for this article.) Francesco TRICOMI (18971978) was born in Naples and did part of his undergraduate years here, first doing physics, then mathematics, graduating in 1918 [Giacardi & Roero, pp. 190191]. Ernesto CES RO (18591906) was professor from 1891. There is a meridian line in the marble floor of the Grande Salon on the first floor of the National Archaeological Museum [Jan Lukas; Naples ; Spring Books (Hamlyn), London, 1965, p. 116]. [Timbs (2), p. 69] says that in one of the museums of Naples, there is a Roman statue of Atlas (the Farnese Atlas) holding a celestial globe on which one can identify 42 of the 47 constellations known to the Romans. [Lukas, ibid., p. 116] shows what is probably this statue in the Grande Salon. I believe this is the earliest representation of Atlas holding the heavens ??check. The Museum also has a bust of SOCRATES and a mosaic from Pompeii of The Academy of PLATO. See also: Ercolano, above. The 13C commentator on Euclid, CAMPANUS (c12151296), was named Novariensis, indicating that he came from, and was probably born in, NOVARA, Piemonte. He is often forenamed Johannes, but this first appeared in the 16C with no known evidence. It was his c1270 edition of Adelard of Bath's translation of c1130 that was the first printed Euclid in 1482. The University of PADOVA (PADUA) , Veneto, was founded in Sep 1221, the second oldest Italian university (this excludes the school of Salerno). Bishop Jordanus of Padua invited William of Gascogne, professor of Decretals at Bologna, to come to Padua. William invited Peter the Spaniard to follow him and Peter did. [R. E. Taylor, p. 138] says a group of Bolognese professors left Bologna due to political discord and went to Padua. [Pengelley & Pengelley, pp. 170171] say the Bolognese professors left because there was not freedom to teach in Bologna. The University is centred around the intersection of Via Roma and Via 8 Febbraio, where the main building is the Palazzo del Bo [Pengelley & Pengelley, p.168]. ALBERTUS MAGNUS was here in 1223 when he joined the Franciscan Order. GALILEO taught here in 15921608 see below. [Foligno, pp. 147152.] The university has the oldest botanic gardens in Europe, started in 1545 [Buckley & Robinson, p. 289]. Jacopo di'DONDI ( 1359), a professor at the University, and his son Giovanni built an Atraraum, one of the first astronomical clocks, here in 13481364 (or 13441364 or 13641381, one source says the clock was present in 1343). The clock tower was greatly damaged in the early 15C and the tower and the clock were reconstructed in 14271434 from the original plans and the new clock was started on 16 Jun 1434. This tower and clock are extant (as of 1910), to the north of the Cathedral, though the clock was repaired in 1529 and slightly altered in 1688 and 1838. [Pengelley & Pengelley, p.172] say there is huge preCopernican clock in the Piazze dei Signori, which must be the Dondi clock. Dondi was later called Jacopo dell'Orologio. He was buried near the Baptistery and an inscription can be seen there. Giovanni published a treatise on clocks in 1365. There is a modern facsimile of the clock in the Science Museum, London. Leon Battista ALBERTI attended school in Padua from c1414 [Kemp, p. 3]. The SALONE or Sala della Ragione is one of the principal sights of the city. Its interior fresco decoration, from c1420, is based on astronomical themes and sunlight falls on the appropriate zodiacal signs during the year [Foligno, p. 291]. [ MGG ] says the frescoes include representations of the Liberal Arts and the Trades, so I would expect some mathematical topics to be included. Lorenzo and Cristoforo Canozii da Lendinara started printing in Padua in 1461 with a reprint of the Gutenberg Bible [Foligno, pp. 163164]. The first Italian printers were in Venice in the same year. REGIOMONTANUS was Professor of Astronomy at the University of Padua, c1462. COPERNICUS (14731543) was a student of medicine and philosophy at the University of Padua in 1501-1503 (though some sources refer to four years), possibly studying with Girolamo FRACASTORO [Armitage, p. 67; Hoyle, p. 20; Rudnicki, pp. 56]. Though he completed his course in Canon Law here, he officially graduated from Ferrara, for reasons not known. [Pengelley & Pengelley, pp.170171] say there is a bust in the Hall of Rectors and a fresco in the Room of Forty, both in the Palazzo del Bo. CARDAN (15011576) was a student at the University in 1524-1525 and a Rector [Cardan, pp. 12-13 & 298]. Federico COMMANDINO (15091575) was a student of philosophy and medicine in 15341544, but took his medical degree at Ferrara. John CAIUS (15101573), refounder of the Cambridge college, was a student of medicine here. After Pisa, GALILEO (1564-1642) was Professor of Mathematics at the University of Padua from 1592 to 1610. Since Padua was part of the Republic of Venice, Galileo was less constrained by the Church than he would have been elsewhere. His wooden Lecture Stand is preserved in the anteroom of the Great Hall (= Aula Magna) of the Palazzo del Bo [Photos in Gasparotto, p. 83 and Scandone, p. 14], where he lectured to up to a thousand students [Andrade (2), p. 3]. [Eastman, p. 337] says his chair and wooden lectern are in the University Museum, Via 8 Febbraio. [Pengelley & Pengelley, p.171] say his podium is in the Room of Forty, adjacent to the Aula Magna. There is a bust in the Aula Magna [Fahie, p. 128 & plate XXXII, opp. p. 109; Foligno, p. 175]. [Pengelley & Pengelley, p.170] say there is a bust in the adjacent Hall of Rectors. William Harvey is believed to have attended Galileo's lectures and may have been inspired by Galileo's studies of water motion [Wymer, p. 1:9]. Here Galileo made his water pump in 1594, his first thermometer in 1597 (or 1593 or 1592) (the invention of the thermometer is indeterminate Santorio and Drebbel produced examples about the same time; [A. Brown, p. 30] says 1593), his proportional compass in 1596 (publishing an instruction manual: Le Operazioni del Compasso Geometrico et Militare in 1606, his first book) and his first telescope in May 1609. About 1599, he wrote Della Scienza Meccanica on the lever, pulley and screw, but this was never published by him, though Mersenne published a French translation in 1634 [Andrade (2), p. 3]. He set up a workshop to make and sell his proportional compasses and, later, lenses and telescopes [Andrade (2), pp. 34]. Galileo never claimed to have discovered the telescope, but he devised his own in May 1609 and immediately recognised its potentialities. '... being in Venice, I heard news that the Count Maurizio (of Nassau) had been presented by a Dutchman with an eyeglass by which the far distant objects could be seen as perfectly as if they were very near, and nothing more was said. As I went back to my residence in Padua, I thought over this problem, and the first night after my return I solved it and the following day I built the instrument .... I immediately proceeded to build a more perfect one, which I brought to Venice six days later, ....' [From Il Sagittore (1623), quoted in Scandone, pp. 4445. See under Venice, below, for more about this telescope which could magnify 9 times. Scandone, pp. 4546 continues with Galileo's account of his deductions and experiments.] His first telescope magnified three times. He soon discovered the necessary relationship between focal lengths and that spectacle lenses could not give any greater power, so he learned how to grind his own lenses. By midAugust he had an 8 or 9 power telescope which he took to Venice on 23 Aug. By November he had a telescope which magnified 20 times and he later achieved a magnification of 32 times. He began to observe the sky with the 20 power telescope in Nov 1609. By January 1610, he discovered that stopping down the aperture gave clearer images. He soon discovered the multitude of faint stars (e.g. in the Milky Way), the mountains and 'seas' (his terminology) of the moon and the fact that planets appeared as discs, but the stars did not. (Thomas Harriot had carefully observed the moon through a 6 power telescope and drawn a map of it some months before Galileo, but he did not publish his results.) His first description of his observations was in a letter of 7 Jan 1610 and includes a diagram of his observation 'only this evening' 'at the first hour of the night' of the first three moons of Jupiter though he didn't realize they were moons until he reobserved over the next few days and recognized them as moons on the 11th and that there was a fourth moon on the 13th. He suggested naming them the Cosmian or Cosmica or Medicean Planets, and the Medicean court felt the last was best. Galileo had already started printing his findings with the word Cosmica. In March 1610 he announced his findings in Sidereus Nuncius , dated 12 March. He sent an unbound copy to grand Duke Cosimo on the 13th and, on the 19th, he sent a bound copy and his telescope, reporting that all 550 copies of the book were already sold! In the book, he deduces that the mountains on the moon are about four miles high. He has not enough data to determine the periods of Jupiter's moons, but indicates they range from about a day to about two weeks. In July he discovered the rings of Saturn (he thought there were two moons they weren't identified as rings until Huygens in 16551656). He also observed the phases of Venus about this time one source says this was in Oct/Dec 1610, which would have been in Florence, but [Andrade (2) says it occurred just after his appointment to Pisa in the summer, hence he might have still been at Padua. The phases of Venus show that it is orbiting around the sun this was the first observational verification of the Copernican system. He observed 40 more stars than the visible 7 in the Pleiades. He also devised the first(?) microscope, though he didn't pursue microscopical studies. There is dispute about the priority of the microscope, but a colleague mentions Galileo's work already in 1610 and another colleague gives a more detailed description in 1614 the earliest definite information about the Jansens' microscope is in 1619 and they didn't make a claim for priority until 1655 cf under Netherlands in Section 10. In the Piazza Vittorio Emanuele (formerly Prato della Valle) is a statue of Galileo [Fahie, p. 131 & plate XXXII, opp. p. 109]. He lived in a small house in Via dei Vignali, apparently still extant, near the church of S. Giustina [Maria Luisa Righini Bonelli; Vita di Galileo ; Nardini Editore, Florence, 1974, p. 57; information from Mario Velucchi]. A legend recounted by by Viviani and Gherardini is that Gustavus Adolphus, later King of Sweden, was one of Galileo's pupils at Padua. There is no evidence that Gustavus was ever in Italy and he was only 16 when Galileo left Pisa in 1610. However, there were two other Swedish princes named Gustavus who spent some time in Italy and may have studied at Padua, so there may be a grain of truth in this story. [Segre.] [Foligno, pp. 284285] says there is a modern plaque on the tower of the Ponte dei Molini (at the north end of Via Dante) incorrectly asserting that Galileo made some of his astronomical discoveries here. Sadly, Foligno doesn't mention any place where Galileo lived in Padua. James GREGORY spent 16631668 in Italy and in 16651668 he was at Padua, lodging with Dr. Caddenhead, the Scottish Professor of Philosophy. It was here that he wrote Vera Circuli et Hyperbolae Quadratura and Geometriae Pars Universalis , the first of which was published here in 1667. [H. W. Turnbull & Bushnell; Boag.] In 1678, Padua awarded the first degree (in philosophy) to a woman, Elena Lucrezia Cornaro (= Corner) Piscopia. The fact that she was a descendent of Doges of Venice may well have had something to do with the award the next woman to get a degree was over fifty years later at Bologna. [Buckley & Robinson, p. 285.] Jacopo (or Giacomo) Francesco RICCATI (16761754), of Riccati's differential equation, was at the University. For his son Vincenzo (17071775), see Bologna, above. Nicholas BERNOULLI (1687-1759) was a professor at Padua, c1720. Guido CASTELNUOVO (18651952) was a student at the University, studying under G. Veronese and graduating in 1886 [Giacardi & Roero, pp. 171173]. Francesco SEVERI (18791961) was professor of projective and descriptive geometry from 1905 to 1922, and also became director of the School of Engineering [Giacardi & Roero, pp. 168170]. Francesco TRICOMI (18971978) was Severi's assistant in 1918 and followed him to Rome [Giacardi & Roero, pp. 190191]. There is an observatory in a 13C tower near Ponte Nuovo di Ferro [Foligno, p. 306]. Michael SCOT (c1175c1235) was Court Astrologer to Emperor Frederick II of Sicily from 1227 and the main seat of the court was in PALERMO, Sicilia. He is best remembered as an astrologer and alchemist, but he was the person who proposed problems to Fibonacci for the Emperor and Fibonacci dedicated the second edition of the Liber Abaci to him. It was in Palermo that Giuseppe PIAZZI observed Ceres on the night of 1 Jan 1801. He could only get three fixes on it. GAUSS developed his technique of determining the orbit and OLBERS (or Zach ??) relocated it a year later. Cesare ARZEL  (18471912) was Professor of Algebra in 18781880 [Martini]. Ernesto CES RO (18591906) was born in Palermo and was professor in 18861891. The 13C Baptistery at PARMA, EmiliaRomagna, is a 16gon [ MGG ]. (Buildings in the shape of ngons, with n > 8, are not common; there is a 22sided piano factory in London.) Giovanni Battista BENEDETTI (15301590) lectured on philosophy and mathematics at the court of Duke Ottavio Farnese in Parma, in 15581567, before going to Turin, qv below [Giacardi & Roero, p.118]. Francesco SEVERI (18791961) became professor of projective and descriptive geometry at the University in 1904, but left for Padova a year later. [Giacardi & Roero, pp. 168170.] BOETHIUS (c475c523 or 455524) died in PAVIA, Lombardia, and there are a grave and relics in S. Pietro in Ciel d'Oro. But another tradition gives Calvenzano, qv above. [Masotti, pp. 68.] The University of Pavia is ancient, but I only have 11C as a date which would predate Bologna and Padua which are the two oldest Italian universities. Further [Helen Waddell; Medieval Latin Lyrics ; (1929), 4th ed, (1933); Penguin, 1952, p. 339] says the University celebrated its eleventh centenary in 1925. Leonardo da VINCI was a student. [ MGG .] The 11C (or 14C) tower by the Duomo collapsed in Mar 1989, killing four people cf Pisa, below [ MGG ]. I have a note that Giovanni di'Dondi built an astronomical clock here, but I think this is a confusion with the clock at Padova, qv above. CARDAN (= Cardano) (15011576) was born in the town [Cardan, p. vii, though Sarton, p. 32, says Milan]. He was a student in 1520-1523 [Cardan, p. 12] and lived there for much of his life. He vaguely specifies several places, lastly near S. Maria in Pertica, in the NE quarter near the castle [Cardan, pp. 85 & 309]. See also Sacco, below. I have recently seen the assertion that the potato was introduced to Europe by Hieronymus Cardan, a monk but somehow I doubt if this is our man! Girolamo SACCHERI (16671733) was a professor, c1730. Alessandro Giuseppe Antonio Anastasio VOLTA (17451827) was Professor of Physics from 1779. Foreign Member RS, 1791; Copley Medal RS, 1794. From 1794 (or 1792), he followed up Galvani's report of 'animal electricity' and soon discovered the real situation. In 1800, he invented the 'voltaic pile' and described it in a letter to Sir Joseph Banks as PRS. Banks showed it to two colleagues who promptly made an example and used it to decompose water for the first time. Napoleon called him to Paris to see his experiments and struck a medal in his honour. Volta was a Senator for Lombardy. He was commemorated on the 10,000 lire note. There is a bust of Felice CASORATI at the University [Masotti, p. 90]. Francesco BRIOSCHI (18241897) was professor in 18521861. Giovanni Domenico CASSINI (16251712) was born in PERINALDO, Liguria, near Nice and San Remo [Anon: Eloge de Monsieur Cassini]. The University of PERUGIA, Umbria, was founded by a papal bull of Clement V in 1308 [R. E. Taylor, pp.138139]. Luca PACIOLI (c14451517) was the first mathematics lecturer at the University, in 1477-1480 [Giusti, p.39] and taught here again in c1490 [Fennell, pp. 1112]. [R. E. Taylor, pp. 118, 127128] says that Pacioli states in his Summa that he was here in 14751480 and 14861488. Taylor [p. 141] says that in 1475, he lectured to a class of 150. He was again here in 1510 [R. E. Taylor, pp. 367368]. In the Galleria Nazionale dell'Umbria is another of PIERO della Francesca's paintings: The Polyptych of St. Antony of 1470. [R. E. Taylor, pp. 118120] claims that the leftmost saint 'is the same as' the St. Peter Martyr in the picture in the Brera, Milan, qv, and hence is a picture of Luca Pacioli. However, a standard work on Piero's art says the saint is St. Antony of Padua, and I cannot see any sign of a gash on the head in my poorish pictures. In the Piazza di S. Lorenzo is a fine early Renaissance fountain with panels by Niccola and Giovanni Pisano, including the sciences and arts, with Geometry among these. In 1498 or 1499, Giovanni Battista Danti (c14771517) is supposed to have made several flights using 'wings'. His major flight was over the town square, but a strut broke and he crashed onto the roof of St. Mary's Church. This is first reported in 1652. [Gordon Stein & Marie J. MacNee; Hoaxes! Dupes, Dodges & Other Dastardly Deceptions ; Visible Ink Press, Detroit, 1995, p. 123.] Angelo GENOCCHI (18171889) was born, studied and taught Roman law at PIACENZA, EmiliaRomagna, there being no scientific faculty in Piacenza. After the uprisings of 1848, he fled from the impending Austrians to Turin. [Giacardi & Roero, pp. 143144.] PIENZA, Toscana, was the home of the Piccolomini family which produced Popes Pius II and III. Pius II decided to rebuilt his native town as a Renaissance city and was probably assisted by ALBERTI [Kemp, p. 7]. In PISA , Toscana, the Leaning Tower continues to lean but hasn't come down yet. It is 191 or 189 ft (58 m) high, with a diameter of 49 ft (15 m) and was built in three stages during 11731350. The first stage was 1173-1178 and stopped in the middle of the fourth level, at 34 or 35 ft (10.5 m), due to tilting toward the north. In 12721278, the builders tried to compensate for the tilt and added three levels, but the tower began to tilt to the south. Though the tilt increased, work was resumed and the bell chamber was added in 13601370, with a final tilt of about 1.6o to the south. Not only was the tower tilting, it was sinking. By the 19C, it had sunk 3 m and the tilt had increased to about 5o and various attempts began to be made to stabilize it, often resulting in greater tilt. In particular, the 1838 excavation of the area around the tower to reveal the original base caused a lurch of .5 m. In the late 20C, it was tilting at about 5.5o, while computer simulations predicted collapse at 5.44o! The top overhung the base by about 19 ft (5.8 m) or more than 17 ft, having increased from 13 ft in the 1930s. The overhang was increasing at about 1.5 mm per year. When I lived in Pisa in 19721973, the Tower was open and quite terrifying as there were few guard rails. At the time, there were reports of work being done to stabilize it, but when I walked over to look, there was no sign of any work. Numerous other reports have appeared and some 500 proposals for the Tower were made. The tower was closed to the public in 1990 after the tower of Pavia, qv above, collapsed without warning in Mar 1989, killing four people. From about 1990, a commission (the 18th?) considered what to do. John Burland, a civil engineer specialising in soils at Imperial College, London, was on this, having just worked on the problems of the Jubilee Line Extension under the tower of Big Ben. He advocated removing soil from under the north side of the tower's base. Strengthening bands were put around the tower in 1992. Some 600 tonnes of lead weights were stacked on the north side in 1993 or 1994 and this certainly stabilised the tower. By 1995, Burland had tested his ideas on a full weight model. The commission produced plans to encase the entire foundation in concrete and anchor it to the bedrock, leaving soil removal for later consideration. The concrete process was started in 1995 and abandoned in Sep 1995 when it caused an extra 1.5mm tilt over the night of 6 Sep. The soil extraction process was approved in Aug 1996, but then the commission was disbanded and reconstituted a year later, requiring reexamination of all possibilities. In autumn 1998, soil extraction was reapproved. They decided to first attach cables from bands about 20 m (or 72 ft) above the ground to an anchor about 100m to the N. This will provide stability while excavation removes some soil. In Feb 1999, soil extraction started. There was a slight move to the south after two weeks, but this soon came back and was recognised as the normal response to cold weather! In early 2000. it was announced that the preliminary work had reduced the lean by 3 cm and that it was intended to bring it back to the lean it had in c1700. By May 2000. the tower had moved back 20 cm and the lead was removed. In Sep 2000, it was announced that it had been brought back 23 cm and was currently moving 1.5 mm/day, with the intention of producing a move of 45 cm (=o) by removing 15 m3 of the soil. The extraction process stopped on 6 Jun 2001, having removed some 70 tons of soil, a rate of about 100 l of soil per day. A report of 16 Jun 2001 said that the tower had been brought back 40 cm to a lean of 4.1 m, reversing about 300 years of lean. Further the tower now seems to be stable. The lack of guard rails is an obstacle to reopening the tower to the public, but there was a grand ceremony on 16 Jun 2001, the feast of Pisa's patron saint, S. Ranieri. The key of the tower was returned to its guardians. [Philip Willan; Huge cables to take strain of leaning tower; The Guardian (12 Dec 1998) 15. Bruce Johnston; Pisa hoping for miracle as work starts on tower; The Daily Telegraph (12 Dec 1998) 7. Leaning tower going straight; The Guardian (8 Jan 2000) 19. Tim Radford; Tube lesson helps save Pisa's tower; The Guardian (8Sep 2000) 8. Equinox program, Jul 2001.] Few readers will need to be reminded that Pisa was the home of Leonardo Pisano (c1170>1240), known as FIBONACCI (though this name only became popular in the 19C). Leonardo was born in the Quartiere di Mezzo. We have only one contemporary reference to Fibonacci which only records that the Comune of Pisa was granting him an honorarium of 20 pounds per year. A plaque containing it and an appropriate heading was erected in the entrance to the Archivio di Stato in 1865 [Bonaini; photo in Arrighi (2), p. 15]. There is also a deed of 28 Aug 1226 in which Leonardo and two relatives buy some land and buildings near S. Pietro in Vincoli, outside the city. Despite this paucity of contemporary information, there is a handsome statue of him! When I lived in Pisa in 1972-1973, this was in the Giardino Scotto in the Fortezza by the Bastione di San Gallo on the Lungarno Fibonacci, not in the Camposanto as described in [Alexanderson], and the Paines confirmed that there was no statue in the Camposanto in 1992. In 1999, Mario Velucchi reported that the statue was moved (or returned?) to the Camposanto Monumentale, Galleria Est, by 1997. [I have my own photo; Arrighi (2), p. 19, gives another; there is a closeup in The Fibonacci Quarterly 26:2 (May1988) 130, which also says the statue is in the Giardino Scotto.] The base of the statue, erected in 1859 [Arrighi (2), p. 16], reads as follows. A Leonardo Fibonacci Insigne Matematico Pisano Del Secolo XII My wife tutored English while we were in Pisa and one student said her exam was in the Aula Fibonacci. When asked if she knew who Fibonacci was, the student replied that he must have been some Risorgimento hero! In the Camposanto is (was?) a 15C tomb "Sepulcrum Pieri quondam Barthalomei de Bonagiis et eius heredum" which may contain some descendents of Fibonacci's brother Bonaccingo [Bonaini]. Mario Velucchi [email of 28 Aug 1999] reports that the Church of S. Nicola, via Santa Maria 2, has a handsome winding stairs believed to be related to some work of Fibonacci. (?? Get details) There is a Centro per la Conservazione e lo Studio degli Strumenti Scientifici in the Department of Physics, Piazza Torricelli 1 [Velucchi, ibid.]. The University of Pisa was chartered by Pope Clement VI in 1343 [R. E. Taylor, p. 138]. [Pengelley & Pengelley, p.175] claim it has 12C origins. Its main building is on Via XXIX Maggio and the internal courtyard dates from the 15C, so Galileo would have known it. [Pengelley & Pengelley, p.175]. In 1499, Lorenzo de' Medici reorganized the universities of Pisa and Florence into a joint operation, with only philosophy and philology in Florence. Luca PACIOLI came to Florence to teach at the university in 1499 and taught at both Florence and Pisa until 1506 [R. E. Taylor, pp. 293300]. Pisa is the birthplace of GALILEO (15641642) and the airport is named for him. There is a commemorative plaque on a house where he was born in Borgo Stretto, at the corner of Via Mercanti [Bonelli (1), p.3; I verified this in 1991 and have a photo]. Other sources say the site is unknown or claim other sites in and near Pisa, but Mario Velucchi writes that these are certainly wrong. The exact date is probably 15Feb 1564, though this is complicated by the fact that different Italian cities used different starting points for their years and Viviani seems to have recorded the baptismal date rather than the birth date see [Segre] for a discussion of this. He lived there until about 1575, when his family moved to Florence. [Eastman, p. 336] says the family house was near the Porta Fiorentina and he lived there until c1572. In 1581-1584, he was a student of medicine at the University of Pisa, but seems to have studied a lot of mathematics and did not get a degree [Bonelli (1), pp. 3-4; Pengelley & Pengelley, p.174]. The stories of the timing of the lamp in the Cathedral and of dropping weights off the Leaning Tower are first mentioned by Viviani in 1654, but the only other contemporary biography of Galileo, by NiccolA Gherardini, a local priest and friend, doesn't mention these stories, though he does repeat two other legends or exaggerations [Segre]. Fahie [pp. 119-120] claims he dropped weights off the Tower in 1590-1591; [Eastman, p. 337] says he reputedly dropped a cannonball and a bullet in 1585. [Ackermann, p. 681, quoting a lecture of Andrade] says he dropped a lead weight and a wood weight and saw that the wood dropped more quickly at first but was overtaken by the lead!!. (This is not in [Andrade (2)].) Modern scholars claim that Galileo knew enough about air resistance to know that the heavier body would fall faster and hence would not have performed the experiment, at least not in public, though a student of Galileo did try it c1640. Nonetheless, the comment that lighter objects dropped faster at first dates back to Galileo so a group in the 1980s decided to retry to experiment and confirmed Galileo's observation! Fortunately high speed movie cameras now exist and analysis showed that the difference was due to muscle fatigue in the hands of the people holding the balls and the more tired hand opened less rapidly. [Keith Devlin; Tall tale stands corrected; The Guardian (28 Jun 2001) S2.] Galileo's notes on motion, De Motu may have been written at this time and they refer to bodies falling from towers. Further, other Pisan professors did similar experiments in 1612 and 1641 and it appears to have been a popular sport throughout Europe in the 17C pedestrians tended to avoid walking near towers in this period. Stillman Drake, perhaps the greatest student of Galileo, feels that Galileo must have done some form of the experiment and may have written about it to his Pisan successor c1641, at which time Viviani was his amanuensis. [Segre.] Cf Stevin at Delft, Netherlands, in Section 10. The notorious 'Lamp of Galileo' in the Cathedral was hung on 20 Dec 1587, sometime after his discovery of the pendulum in 1581 [Ross & Erichsen, p. 161] or 1583 [Bonelli (1), p. 27; Viviani, according to Segre] or 1581-1582 [Fahie, p. 135]. (I have a photo.) Galileo doesn't mention the idea until 1602. [Tremayne, pp. 2021] says the lamp was made by Battista Lorezo [sic, but probably a misprint for Lorenzo], that the swing was probably caused by a draught and that it stopped swinging when it was electrified. [Andrade (2), p. 2] asserts that Viviani states the Galileo was eighteen at the time and that the lamp is by Possenti. He adds that Galileo used the idea to make a pulsilogium, a device for timing the pulse, which was much used. In 1589 (or 1585), Galileo became Professor in Mathematics at the University, but resigned in 1591 due to disagreements with other professors. [Eastman, p. 336, with photo on p. 337] asserts that he lived at 26 Via Santa Marta, now the Domus Galilaeana, a centre for the history of science which has some memorabilia. One of the stories given by Viviani and Gherardini is that Galileo had to leave Pisa after disagreeing with Giovanni de' Medici, an illegitimate son of Grand Duke Cosimo I, about plans for dredging the port of Livorno (= Leghorn), but there seems to be no other evidence for this. However, when he was appointed Mathematician to the Grand Duke in 1610, he was also made Professor at Pisa. TORRICELLI (16081647) likewise held both posts as successor to Galileo. A statue of Galileo was in the Great Hall of the University building, La Sapienza [Ross & Erichsen, p. 325. Fahie, p. 132 & plate XXXIV, opp. p. 117], but I don't recall ever seeing it. There is a Lungarno Galilei. The arches of the Ponte di Mezzo are cycloidal, commemorating Galileo's suggestion of the use of the cycloid for bridges. Giovanni Alphonso BORELLI (16081679) was professor of mathematics at Pisa, but his work was on the application of mechanics to movements of the body [Guthrie, pp. 197198]. Guglielmo LIBRI (18031869) became professor of mathematical physics at Pisa in 1823. But he retired from teaching after one year and was made professor emeritus. After the uprisings of 1831, he fled to Paris. [Giacardi & Roero, p. 139.] The first Congress of Italian Scientists took place in Pisa in 1839. Enrico BETTI (18231892) was Professor of Algebra in 1857, then Professor of Higher Analysis from 1859. He died in Pisa. Pisa also has a monument to Ulisse DINI (18451918) with a statue (I have a photo) in Via Ulisse Dini, both near the Scuola Normale Superiore. He was born and died here. Salvatore PINCHERLE was a student at the Scuola Normale Superiore, 1869-1874. Cesare ARZEL  (18471912) was a student at the Lyceum, then at the Scuola Normale Superiore from 1861, completing four years later with a dissertation under Betti. He also attended lectures of Dini. He spent a later year here in 18721873. [Martini.] Luigi BIANCHI (18561928) taught at the Scuola Normale Superiore in the late 19C. Vito VOLTERRA (18601940) was a student at the Scuola Normale Superiore, graduating in 1882 and becoming assistant to Betti. In 1883, he became professor of rational mechanics at the University of Pisa. In 1893, he left for Turin. [Giacardi & Roero, pp. 153154]. Cesare BURALI FORTI (18611931) was a student in 18641867, taking courses from Dini and Betti [Giacardi & Roero, pp. 180181]. Francesco SEVERI (18791961) did postgraduate work here under E. Bertini, c1902. [Giacardi & Roero, pp. 168170.] L. BIANCHI was at Pisa, Guido FUBINI (18791943) was a student at the Scuola Normale Superiore and studied under Bianchi, Dini and E. Bertini. He graduated in 1900 and did his teaching qualification in 1901 and became an assistant, leaving in 1903. [Giacardi & Roero, pp. 185186] BLASCHKE studied here. Enrico FERMI (19011954) did his thesis here, graduating in 1921. He began publishing at age 19. BETTI was born near PISTOIA, Toscana. At POMPEII, Campania, there are several labyrinths, including a notable one showing Theseus and the Minotaur in the House of the Labyrinth (Casa del Labirinto) and an example scratched on a pillar in the House of Lucretius and inscribed "Labyrinthus hic habitat Minotaurus" [Fisher, pp. 27 & 3637, with diagram on p. 27]. In the market place is a bench with standard volume measures [Ripley's Believe It or Not! , 8th series; Pocket Books, 1962, p. 78]. POMPOSA ABBEY, EmiliaRomagna, was the home of Guido D'AREZZO, the inventor of the musical scale in the 12C? [ MGG ]. Pontecchio(Marconi) see Bologna, above. Paolo DELL'ABBACO (12811374) was born in PRATO, Toscana. The Church of San Vitale, RAVENNA, EmiliaRomagna, has a 6C mosaic labyrinth [Pennick, p. 117; but Fisher, p. 41, dates this to 1584 ??]. Leon Battista ALBERTI (1404-1472), architect and first writer on perspective, moved to RIMINI, Emilia-Romagna, where he converted the exterior of the Church of San Francesco Rimini into the Tempio Malatestiano in 14461460. There is a medallion portrait, considered to be Alberti, on the back of the balustrade of the first chapel to the right. The third chapel on the right is the Chapel of the Planets and is decorated with representations of the planets and the zodiacal figures, many beautifully carved by Agostino di Duccio. The third chapel on the left is the Chapel of Liberal Arts, with sculpted figures depicting Architecture (with rod and plumb line), Philosophy, Mathematics, Astronomy (with astrolabe and plumbline), Geography (observing a pendulum), Education, Geometry and either Painting or Arithmetic (with a little board, apparently either a palette or a writing board). Alberti died in Rome; I have a recollection that he was buried in Rimini in this Tempio, but the guide book lists all the burials in the Tempio and Alberti is not named, nor does the guide book say anything about Alberti being buried in Rimini ??. [Giuseppe Pecci; A Guide to the Tempio Malatestiano With Some Notes on the Principal Monuments of Rimini ; Translated by Mary Boni D'Orazi; Stab. Tip. Garattoni, Rimini, 1957, pp. 11, 21, 3244.] In ROMA (ROME) , Lazio, there are numerous streets, piazzas, etc., named for the Greek mathematicians and philosophers. The Pincio Gardens and various museums have putative portrait busts of them as well as more recent persons such as GALILEO. Archimedes, Aristotle, Euclid, Plato, Ptolemy, Pythagoras and Zeno (perhaps more) are all portrayed (?) in one of Raphael's finest compositions, the School of Athens in the Stanza della Segnatura in the Vatican. Moving from the mythical to the real, one of the more unexpected monuments in Rome is the PYRAMID of Gaius Sestius (died 43), adjacent to the Porta San Paolo. The base is 100 ft (30 m) square and it is 121 ft (37 m) high. The Roman obelisk in the Campo Martio has been identified as a sundial. GERBERT (c950-1003), who helped introduce the Arabic numerals to the West, rediscovered Boethius' work on geometry and later became Pope Sylvester II in 999, is buried in S.Giovanni Laterano with an epitaph in the south aisle. [Masson, p. 315] says it is a modern (1909) monument, erected by a Hungarian to commemorate the Pope's giving the iron crown to St. Stephen I, the first Christian king of Hungary. According to Eves [Eves, vol. I, pp.84-85], he predicted he would die in Jerusalem, but died in S. Croce in Gerusalemme, about half a mile east of S. Giovanni Laterano. He made a pendulum escapement and is said to have invented the striking clock. The oldest pavement labyrinth in a church is in the chapel of San Zeno in the church of Santa Prassede [Pennick, p. 116]. The floor of the Sistine Chapel has one of the finest geometric mosaic pavements, in Opus Alexandrinum, but visitors rarely examine it. A friend told me he used to walk around looking at the floor and people would interrupt him to say the Michelangelos were on the ceiling. He would answer "Michelangelo Schmangelo this is the finest mosaic floor in the world!" After a bit other people would start looking at the floor! Some authorities say Abraham ibn EZRA (10921167) died in Rome. The University of Rome was established by Pope Boniface VIII in 1303, though it claims some origin in 63 [R. E. Taylor, pp. 138, 388389]. NICHOLAS OF CUSA (or Cusanus or Cusano) (1401-1464), a learned cardinal who criticized the Ptolemaic system, suggesting the earth revolved about the sun, proposed the reform of the Julian calendar and tried to square the circle, is buried in a monumental tomb in San Pietro in Vincoli [Masson, p. 369]. Cf Kues in Section 8. PEURBACH stayed with him. Leon Battista ALBERTI (1404-1472), architect and first writer on perspective, came to Rome as a secretary to the Papal Chancery in 1432. He went to Florence in 1434, but was often in Rome until his death there. His Descriptio Urbis Romae of 1434 was the first systematic study and measured survey of the ruins of ancient Rome. [Kemp, pp. 46.] (I have a recollection that he is buried in Rimini??) PACIOLI (c14451517) stayed with him for about a year from 1470 and later taught here, c1514 [Giusti, p. 39; Fennel, p. 8, 19 & R. E. Taylor, p. 91, give 1471]. PACIOLI later became attached to Cardinal Francesco della Rovere and lived at his palace adjacent to the basilica of S. Pietro in Vincoli. The Cardinal became Pope Sixtus IV in 1471 and his nephew Giuliano became a cardinal (later Pope Julius II) and took over the palace and Pacioli. Pacioli was again here in Rome in 1489 and 1514. [R. E. Taylor, pp. 104106, 118, 160, 388393.] REGIOMONTANUS (14361476) came to Rome to assist with calendar reform and died of the plague [Sarton, p. 70]. [Gyles Brandreth; 1000 Firsts and Lasts The Greatest Book of Quite Amazing Facts ; Carousel, 1985, p.103] says the first gold brought back from the New World by COLUMBUS was used to gild the ceiling of Santa Maria Maggiore. But cf Toledo, Spain, in Section 10. COPERNICUS (14731543) spent a year in Rome, mostly in 1500, lecturing on astronomy and mathematics and recording the eclipse of the moon on 6 Nov 1500 [Armitage, p. 65; Rudnicki, p. 5]. There is an Astronomical and Copernicus Museum at 84 Viale Parco Mellini, with some memorabilia [Eastman, pp. 333334.] The first known lecture on Copernicus's unpublished theory was given in Rome by a Widmanstad at the request of Pope Clement VII [Harold Spencer Jones; Copernicus The Selby Lecture, 1943 ; Press Board of the University of Wales on behalf of the University College of South Wales and Monmouthshire, 1943, p. 13]. In 15131516, LEONARDO DA VINCI (14521519) lived in the Belvedere Pavilion of the Vatican [Eastman, 343]. In 1514, he seems to have worked on making a telescope his diary has the entry "Make lenses in order to see the Moon large" and he ground some lenses in secret, but we don't know if he made anything usable [P. Moore (4), p. 8]. The Rome Airport, at Fiumicino, is named for him and has a large statue of him. CARDAN (15011576) came to Rome in 1571 and lived in Piazza San Girolamo, near Porta del Popolo, then in Via Giulia, near S. Maria in Monserrato. He died in Rome in 1576 and was buried in S. Andrea, but was later moved to Milan (qv above). [Cardan, pp. xiii, 17, 85-86, 309.] Pope GREGORY XIII had a Torre dei Venti (or Quattro Venti) built at the Vatican as an observatory. This contained the Sala del Calendario, which had a meridian line on the floor which demonstrated that the calendar was seriously off from the heavens and is probably where the discussions took place which led to the promulgation of the Gregorian Calendar in 1582. [P. W. Wilson; The Romance of the Calendar ; George Allen & Unwin, London, 1937, pp. 141142.] The observatory fell into disuse in the 19C and was converted into living apartments after 1870. In the 1880s, the observatory was reestablished on the 9C Leonine Tower at the top of the Vatican Hill. Since then it has removed to Castel Gandolfo. Gregory's tomb in St. Peter's has reliefs illustrating the establishment of the new calendar [ MGG ]. About 1575, Egnazio (or Ignazio or Egnatio) DANTI (15361586) came to Rome as Geografico Pontificio to Gregory XIII cf under Bologna. In 1578-1581, the Galeria delle Carte Geographiche in the Vatican was painted, under Danti's the supervision. He probably did most of the designs. At some time he became Bishop of Alatria. Giordano BRUNO (15481600) advocated various heretical doctrines, including Copernicanism and the idea that there were infinitely many inhabited worlds. In 1576, he fled from the Inquisition and wandered abroad until 1591, when he was lured back to Italy and soon betrayed to the Inquisition (cf under Venice, below) and tried. He was imprisoned in the Castel S. Angelo and/or the Tor di Nona, adjacent to the S end of the Ponte S. Angelo, and refused to recant. He was burned at the stake in the Campo dei Fiori on 17 Feb 1600. There is an 1887 statue of him in the Campo. In Feb 2000, it was reported that the Pope would soon apologize for Bruno's execution. [Sarton, p. 62. Masson, p.131. Rory Carroll; Vatican on defensive as Italian atheists honour their martyr; The Guardian (17 Feb 2000) 18.] About 1915, the 14year old Enrico FERMI bought two antique volumes of elementary physics from bookstalls in the Campo dei Fiori which made him decide to be a physicist [Gerald Holton; The miracle of the two tables; Times Literary Supplement (11 Jan 2002) 1213]. The first modern learned society was the ACCADEMIA DEI LINCEI (or Lyncei), founded in Rome by Prince Federigo Cesi in 1603. (But see under Naples, above, for a shortlived predecessor.) The word 'lincei' means 'lynxeyed', but actually derives from the Greek argonaut Linkeus, the eponym of the animal. Lynxes are on the crest of the Accademia. In 1603, GALILEO (1564-1642) visited Rome and stayed with Prince Cesi in the Palazzo Cesi, 21 Via della Maschera d'Oro, a bit NW of Piazza Navona [Masson, p. 187]. Presumably the Accademia originally met here. Della Porta was also a founder member. The Accademia still exists, but has had several hiatuses in its existence, e.g. it disbanded on Cesi's death in 1630. It is housed in the Palazzo Corsini, Via della Lungara, Trast)vere. Between the street and the Tiber is one of the art treasures of Rome the Villa Farnesina, decorated by Raphael, Peruzzi and Sodoma which is used for receptions of the Accademia I attended one in 1973. (Older guidebooks say the Accademia was housed in the Farnesina, but there were no offices in it in 1973.) [Masson, pp. 439444]. Volterra and Castelnuovo were Presidents in the 20C. There is a great stellated dodecahedron just under the cross surmounting the concave cupola of the sacristy of St. Peter's [Istvn & Magdolna Hargittai; Symmetry A Unifying Concept ; Shelter Publications, Bolinas, Calif., 1994, p.98]. GALILEO (1564-1642) visited Rome at the height of his fame in 1611 and was made the sixth member of the Accademia dei Lincei at a banquet on 14 Apr. The word 'telescopium' was first applied to his instrument at this dinner. He showed sunspots to several people. [Van Helden, pp. 112113.] In the Borghese Chapel (or Cappella Paolina) of Santa Maria Maggiore, the cupola was frescoed by Cigoli (=Ludovico Cardi (15591613)), a friend of GALILEO. Mountains are shown on the moon under the Virgin. This was denounced as heresy. [Fahie, pp. 12-13]. [J. V. Field & James, p.43] say Cigoli used Galileo's drawings. The recantation of GALILEO took place on 22 June 1633 in the Great Hall of the former monastery of Santa Maria sopra Minerva, then the headquarters of the Dominican order. This is where he supposedly said "E pur si muove" (Nevertheless, it does move). For a long time, these words were believed to be a much later invention, but they probably date back to c1643 [Fahie, pp. 72-75]. [Scandone, p. 59] is a photo of the official transcription of the abjuration. Later, a copy of Sustermans' portrait of Galileo was hung here when the Hall was used by the Council of Public Instruction [Fahie, pp. 36-37]. After (or before?) the trial, he was imprisoned in the Villa Medici, Viale Trinita dei Monti, in 1633. There is a commemorative cippo (= half column) nearby, because the owner would not allow a plaque on the villa [Fahie, pp. 151-152 & plate XLI, opp. p. 148]. Fahie shows and describes it as topped by an armillary sphere, but I don't recall this. On the other hand, [Eastman, p. 337] says Galileo stayed at the Villa Medici during his visits to Rome in 16301633, but that, contrary to the inscription and most guide books, he lived in the Palazzo Firenze, the Florentine Embassy in Piazza Firenze, Via Metastasio, during his trial. This is now houses the Dante Alighieri Society. Further, Galileo was never officially imprisoned except for the few hours between his trial and the sentencing. ([Masson, p. 180] says Galileo stayed in the Palazzo Firenze in 1633 and that it was originally bought by the Medici in 1577 [which may have caused confusion as to which Medici house he was at], but on [p. 243], she describes the column by the Villa Medici as saying Galileo was imprisoned there from 1630 to 1633.) In 1992, the Vatican officially declared that Galileo had been the victim of an error. TORRICELLI (16081647) studied under CASTELLI, a pupil of Galileo, in Rome and then went to Florence to study briefly under Galileo. In about 1652, the architect Francesco Borromini build the Palazzo Spada. This contains a splendid 'Hall of Perspectives' which is a shallow alcove that appears to be very long. Athanasius KIRCHER (16011680) was professor of physics and mathematics at the Jesuit College in Rome. He was an early writer on acoustics Acoustics, Musurgia Universalis appeared in 1650. One of the (two or four or five) extant Roman hand abacuses was in the Museo Kircheriana, now amalgamated into the Museo Nazionale delle Terme, and may have belonged to him ?? He is best known for inventing the Magic Lantern, described in his Ars Magna Lucis et Umbrae of 1645 [Dawes, p. 84]. Kircher spent much of his life in Rome and died here [BGchel & Schreiber]. Alessandro GALILEI (??1737), a descendent of the famous family, was a noted architect. He built Castletown House, Co. Kildare, Ireland (see Section 6E2) and the facade and the Corsini Chapel of San Giovanni Laterano in Rome. [ MGG .] On the Villa Albani is a 1766 marble tablet with a 9 by 9 MAGIC SQUARE devised by Caietanus Gilardonus [Lucas, pp. 224225]. DIRICHLET relates that he "established the solution of one of the most difficult problems of the theory of numbers, with which he had for a long time striven in vain, in the Sistine Chapel in Rome, while listening to the easter music." [Barlow, p. 155.] When Italy began to be formed from disparate states, a SENATE was created, similar to the French one, comprised of distinguished citizens who became Senators for life. PLANA was a member of the first Senate in 1844. When Rome fell to Italian forces in 1870, the Senate moved to Rome. VOLTERRA was a Senator from 1905 to 1940 and CASTELNUOVO in 19491952. There is a bust of Luigi CREMONA at the University of Rome [Masotti, p. 90]. Vito VOLTERRA (18601940) was professor at the University from 1900 until 1931 when he refused to take an oath to the Fascist regime. He became a Senator in 1905 and took an active part in educational legislation and in resisting Fascism. Andr) WEIL spent 19251926 studying with Volterra. President of the Accademia dei Lincei. He died in Rome. [Giacardi & Roero, pp. 153154] Guido CASTELNUOVO (18651952) did postgraduate work at the University under Cremona in 18861887 and returned as professor of analytic and projective geometry in 1891, teaching until 1935. In 19381943, he ran a 'Secret University' for those persecuted for political or racist reasons. First President of the reestablished Accademia dei Lincei in 1946. Made a Senator in 1949. [Giacardi & Roero, pp. 171173]. Gino FANO (18711952) came to Rome as assistant to Castelnuovo in 18941899 [Giacardi & Roero, pp. 173176]. When MARCONI (18741937) returned to Italy, he lived at Villa Sforza Cesarini on the Janiculum Hill, c1918. In 1927, he remarried and then lived at his inlaws, at the BezziScali Palace in Via Condotti where he died. The Museum of Postal History and Telecommunications, 11 Via Andreoli, has the apparatus used in the first transatlantic transmission in 1901 cf Poldhu Point in Section 6A. [Eastman, p. 345.] Federigo ENRIQUES (18711946) was professor in 19231938. Oscar ZARISKI (18991986) came to Rome c1923 and studied under Castelnuovo and Enriques. At Enriques' suggestion, he italicised his name when they wrote their first joint paper. He left for America when the Fascists began oppressing Jews. Francesco SEVERI (18791961) became professor of algebraic analysis at the University in 1922. In 1923 he became Rector of the University, but this post was abolished in 1925. In 1939 he founded the Istituto Nazionale di Alta Matematica and presided over it until his death. (I attended a conference of the Istituto in 1973(?) and was told that a new director had not yet been appointed and the only function of the Institute was arranging two such conferences a year. The conferences certainly were firstclass though not large. At the one I attended, there were only about 40 participants and perhaps 30 were invited speakers, including many of the leading figure in the field.) Severi died in Rome. [Giacardi & Roero, pp. 168170.] Francesco TRICOMI (1897-1978) followed Severi from Padova to Rome as Professor of Analysis in 1922, staying until 1925. His 1923 paper "Sulle equazioni lineari alle derivate parziale di 2o ordine di tipo misto" studied what is known as Tricomi's equation: y uxx + uyy = 0, which Tricomi himself said was destined 'to sleep tranquilly in the large volumes of the Memorie dei Accademia dei Lincei' turned out to be the precise type of equation governing transonic aerodynamics and he became known as the father of the Sound Barrier! Tricomi said he did not realise the connection until 1952. [Giacardi & Roero, pp. 190191]. M. C. ESCHER (18981972) moved to Rome in 1923. After his marriage in 1924, they lived on the top floor of Via Alessandro Poerio 100, in the Monte Verde section of Rome, from 1925 to 1927. They then moved to a house at Via Alessandro Poerio 94 (later renumbered 122) in 1927 and stayed there until 1935. [Locher, pp. 31 & 38.] Enrico FERMI (19011954) was born in Rome. When 14, he bought two antique volumes of elementary physics from bookstalls in the Campo dei Fiori which made him decide to be a physicist. After graduating from Pisa in 1921, he returned to Rome. In 1926?, he went to see Orso Mario Corbino, head of the Physics Institute at the University of Rome and a Senator who was appointed Minister of National Economics in 1923 by Mussolini despite not being a member of the Fascist Party. Corbino immediately recognised Fermi as a representative of the new physics that he had been seeking and got him appointed to a new Chair of Theoretical Physics at the University in 1926. The Institute was at Via Panispernia 89a Corbino lived in the same building. In 1927 Fermi published the first Italian text on atomic physics. Emilio Segr/ was Fermi's first pupil, starting the 'Rome school'. In 1934, Fermi and his group began bombarding nuclei with neutrons and produced 44 new isotopes. In late 1934, they discovered that reaction rates depended on which table the experiment was carried out on. While trying to determine what was causing this effect, Fermi suddenly decided to put a block of paraffin into the neutron beam instead of the prepared lead block and discovered a great increase in activity. By the afternoon, he had an explanation the neutrons were slowed down by elastic collisions in the paraffin and hence became much more likely to strike atoms in the target. An article was published within two weeks. The slow neutrons were exploited by the group to produce several new elements. Fermi received the Nobel Prize in Physics in 1938 after the ceremony in Stockholm, he and his Jewish wife Laura went directly to America. Otto Hahn and Fritz Strassmann bombarded uranium with slow neutrons in 1938 and observed unusual results, which Lise Meitner and Otto Frisch immediately recognised as definitive evidence for nuclear fission! The Rome group later realised that they had this evidence in 1934 but hadn't recognised it, but perhaps the delay prevented German or Soviet development of atomic weapons at the time. [Gerald Holton; The miracle of the two tables; Times Literary Supplement (11Jan2002) 1213.] The VATICAN is a vast assembly of museums and has numerous examples of tessellated pavements, etc. The entrance is via a huge open doublehelical ramp by G. Momo, probably early 20C as the entrance was from near St. Peter's at the end of the 19C. CARDAN (15011576) settled as a country doctor in SACCO, Lombardia, near Pavia, in 1526-1532. Corrado SEGRE (18631924) was born in SALUZZO, Piemonte [Giacardi & Roero, pp. 156 & 165168]. SAN REMO, Liguria, has a Liceo Ginnasio named for Gian Domenico CASSINI (16251712) who was born in nearby Perinaldo. The Villa NOBEL was Alfred NOBEL's (18331896) last home from 1891 and is now a museum with his laboratory preserved. He died here, but his will was executed in Sweden which was considered his residence. [Wilhelm, pp. 1921, with photos.] SANSEPOLCRO (or Borgo Sansepolcro), Toscana, is the native city of PIERO della Francesca (1416?-1492) and his pupil Fra Luca PACIOLI (or Luca del Borgo) (c1445-1517). Piero's house is at the corner of Via Piero della Francesca and Via de gli Aggiunti (plaque). [Photo in Giusti, p. 9.] It is now the headquarters of the Fondazione Piero della Francesca. Piero is buried in the Cathedral in what is now the Baptismal Chapel. There is a statue of him. The Museo Civico has a portrait and a bust of him and the parish record of his death. c1475, Pacioli entered the Franciscan Order here. In 1493, he gave lectures on mathematics here [R.E.Taylor, p. 177]. In 1497, he contracted to have a chapel of S. Bernardino built in the Church of St. Francis here and is described as Warden of the Monastery of St. Francis [R. E. Taylor, p.292]. Another 1497 document describes him as a Professor of Holy Writ. c1510, he retired here as Commissioner (head or warden) of the Franciscan House, though he went briefly to teach in Perugia in 1510 and in Rome in 1514 [R. E. Taylor, pp. 367368, 388393]. He probably died here, but there is no gravestone or grave site. (The DSB entry says he died here.) There is a street named after him. There is a plaque with his portrait on the Palazzo delle Laudi [photos of the Palazzo and the plaque are in Giusti, pp.20-21.] A statue of Pacioli was recently erected in the park at Via Matteotti and Via de gli Aggiunta. The base uses designs from his De Divina Proportione . The leading hotel/restaurant in town is the Albergo Ristorante Fiorentino at Via Luca Pacioli 60 and the proprietor is interested in Pacioli in the restaurant is a banner from the 500th anniversary celebrations of the publication of Summa de Arithmetica, Geometria, Proportioni et Proportionalit! in 1494. [Giusti, pp. 3841. Fennell, pp. 9, 19.] Cesare ARZEL  (18471912) was born in SANTO STEFANO DI MAGRA, near La Spezia, Liguria. He attended the Gymnasium in nearby SARZANA. He died here. [Martini.] Sarzana, Liguria see under Santo Stefano. SELASCA, Piemonte, above the village of Intra on the west side of Lago Maggiore, is where Bernhard RIEMANN (18261866) spent his last days at the Villa Pisani, now apparently the Casa dei Tedeschi. He is buried in the cemetery below the hamlet. [Beltrami.] Selasca is now part of the town of Verbania [Renato Spigler; After 125 years, another view of Riemann's legacy; SIAM News (Jan 1992) 24]. In SIENA, Toscana, Ambrogio (or Pietro) Lorenzetti's fresco of 13371339, Allegory of Good Government, in the Palazzo Pubblico, has the earliest known depiction of an hourglass (sandglass) [F. A. B. Ward (2), pp. 78]. Siena has one of the old Italian city academies and one of the few devoted to science the Accademia dei Fisiocritici, founded in 1691 by Pirro Maria GABRIELLI, at Prato di S. Agostino 4. The Accademia's interests have been mostly in natural science, but Gabrielli laid out a meridian line in 1704. This is much more than a line it is a large double oval (an analemma) for plotting the sun's position at noon and is about 30 ft long by about 15ft broad at its broadest. It was the fourth such to be laid out the others were in Bologna, Rome and Paris. The original was destroyed in an earthquake of 1798 and a new one was laid out in the main Hall in 1845, but it is not currently being used. The Accademia also has pieces of the meteorite shower which fell at Lucignano d'Asso in 1794 and which convinced scientists that meteorites were really extraterrestrial. [Thanks to Raffaella Franci for showing me around.] The Centro Studi della Matematica Medioevale is a leading centre for the study of medieval mathematics. It was founded in 1980 at the incentive of Gino Arrighi. It is part of the Dipartimento di Matematica of the Universit! di Siena, which is housed in a medieval palace at Via del Capitano 15, perhaps the most splendid seat of a mathematics department in the world. The Biblioteca Comunale (= Biblioteca degli Intronati) di Siena contains many manuscripts, including the oldest and best version of Fibonacci's Liber Abaci (L.IV.20) and the Codex L.IV.21 which includes the Trattato di Praticha d'Arismetricha , compiled by Maestro Benedetto da Firenze in 1463, which includes material from numerous medieval mathematicians, including alKhowarizmi, Fibonacci, Maestro Biagio, Antonio de' Mazzinghi, Giovanni di Bartolo. Benedetto can hence be counted among the first historians of mathematics. [Franci & Toti Rigatelli.] ARCHIMEDES (c287/212) lived and died at SIRACUSA (SYRACUSE), Sicilia. In 1965, it was reported that his tomb was rediscovered [Anon., 'Archimedes Tomb' found] but there was no trace of the famous inscription showing a cylinder circumscribing a sphere. There is a Roman columbarium(?) often shown to tourists as the 'Tomb of Archimedes'. Cicero's rediscovery of the tomb seems worth quoting [Cicero]. "I shall call up from the dust and his measuring-rod an obscure, insignificant person belonging to the same city, who lived many years after, Archimedes. When I was quaestor [3] I tracked out his grave, which was unknown to the Syracusans (as they totally denied its existence), and found it enclosed all round and covered with brambles and thickets; for I remembered certain doggerel lines inscribed, as I had heard, upon his tomb, which stated that a sphere along with a cylinder had been set up on the top of his grave. Accordingly, after taking a good look all round (for there are a great quantity of graves at the Agrigentine Gate), I noticed a small column rising a little above the bushes, on which there was the figure of a sphere and a cylinder. And so I at once said to the Syracusans (I had their leading men with me) that I believed it was the very thing of which I was in search. Slaves were sent in with sickles who cleared the ground of obstacles, and when a passage to the place was opened we approached the pedestal fronting us; the epigram was traceable with about half the lines legible, as the latter portion was worn away. So you see, one of the most famous cities of Greece, once indeed a great school of learning as well, would have been ignorant of the tomb of its one most ingenious citizen, had not a man of Arpinum [1] pointed it out." [3] Quaestor to Sex. Peducaeus in Lilybaeum, B.C. 75. [1] Arpinum in Latium was Cicero's native town.... (Lilybaeum is now Marsala, at the western tip of Sicily.) Stephen B. Maurer of Swarthmore College has examined the book on the excavation: Salvatore Ciancio; La tomba di Archimede ; Rome, 1965; and reports on it in a message to mathhistorylist on 6 Mar 1996. Unfortunately there is no real evidence that the tomb is Archimedes'. It is of the right era and in the right area; it is elaborate, though not royal; two rings were found, but there is no indication they are Archimedes'. Only the bottom level of stones remains and there is only some indication that there was a pillar. The 1965 report cited above says there was a lead coffin with two gold seals and that the rings were gold. It also says that Ciancio originally thought the grave belonged to one the tyrants of Syracuse. Maurer gives Ciancio's 1965 directions to the site. It is near the intersection of the state road to Catania and the road to Castello Eurialo. It is just off (or in) a parking lot off the Via Necropoli Gotticelle. Also, it can be reached from the main floor of the Motel Panorama. [ MGG-Italy(1995) , p.280] says PLATO came here to study the dictatorship of Dionysius I (405/367), the ruler who had the 'sword of Damocles' suspended by a thread over the head of Damocles when he expressed jealousy of Dionysius. Dionysius was always in fear he did not appreciate Plato's interest and had him sold as a slave. The famous red chalk self-portrait of LEONARDO is in the National Library in TORINO (TURIN) , Piemonte. There are an Egyptian icosahedron (with lettered faces, hence possibly a die) and cubooctahedron in the Museo Egiziano. In this is the Turin Papyrus , of c1370, whose diagram has been identified as a road map of part of Nubia the oldest extant map [W. J. Wintle; The romance of mapmaking; The Harmsworth London Magazine 9 (1902) 270]. The Universit! di Torino was founded by Cardinal Guala Bisshieri in the first half of the 13C at nearby Vercelli, but this ceased in 1372. In the early 15C, Prince Ludovico de Savoia Acaia reestablished it in Turin and this was confirmed by a Papal bull of 1404 and an Imperial diploma of 1412. Over the next decades, it moved several times to nearby cities, sometimes to escape the plague. ERASMUS received a degree here in 1506. The University was closed for several periods afterwards due to wars. [Giacardi & Roero, pp. 117118.] Giovanni Battista BENEDETTI (15301590) came to teach at the University in 1567 and remained till his death. A disciple of Tartaglia, his De resolutione omnium Euclidis problemata ... of 1553 showed Euclidean constructions could be carried out with a ruler and a 'rusty compass', i.e. a compass with a fixed opening. This was later developed by Mascheroni. He was a founder of mechanics, asserting that the velocity of a falling body was independent of its weight. [Giacardi & Roero, p. 118.] Alexanderson mentions the Via Lagrange and Piazza Lagrange in Turin [Alexanderson]. There is actually a statue of Joseph Louis (= Giuseppe Luigi) LAGRANGE (1736-1813) in the Piazza, inscribed 'A Luigi Lagrange La Patria'. [I have a photo.] This is just a bit east of the large Piazza Carlo Felice in front of the main railway station. (At the time, Piedmont was dominated by French influence and Lagrange's family were of French origin, so I don't know if Lagrange's given names were in the French or the Italian form. [Giacardi & Roero, p. 124] say his father was Giuseppe Luigi, so probably he had the Italian form.) The Via Lagrange runs north from the Piazza to become the Via Accademia delle Scienze. Between the Accademia and the Piazza Lagrange, there is a plaque on no. 7 Via Lagrange, the house where he was born [Paine]. Vagliente writes that the house is currently (1996) being restored. Lagrange studied at the University from 1750, originally being enrolled in law, but soon shifted to physics and mathematics. In 1754, he published his first paper, on the analogy between powers and roots, though he soon discovered he had been anticipated by Leibniz. At age 19, in 1755, he was made substitute professor at the Royal Artillery School and continued in that post until leaving for Berlin in 1766. [Giacardi & Roero, pp. 65, 120121 & 124127.] At No. 6 Via Accademia is the Accademia delle Scienze, which was founded as a private society by Lagrange and two friends in 1757, becoming a Societ! Reale in 1759 and the Accademia Reale in 1783. In 1805, it became the Accademia Imperiale with Napol)on as perpetual president! In the arcade of the courtyard is a plaque and bust of Angelo GENOCCHI (1817-1889), of Genocchi numbers, who was a President of the Accademia and professor at the University. There is also a monument to Giovanni PLANA (17811864), who organized BABBAGE's famous lecture on the Analytical Engine here in Sep 1840 at the second Congress of Italian Scientists. This lecture was written up in 1842 by Captain Luigi F. MENABREA (later Prime Minister of Italy) and later translated and annotated by Ada LOVELACE in 1846 [Babbage]. The Accademia began publishing a Miscellanea in 1759, but it has changed name many times as well as changing languages from Latin to French to Italian. The first volume included two papers by Lagrange; the first, on maxima and minima of functions of several variables, was a foundation of the calculus of variations. He also developed the method of Lagrange multipliers and a solution of Pell's equation in this period. [Giacardi & Roero, pp. 65, 120121, 124-127 & 137138.] Amedeo AVOGADRO, Conte di Quaregna e Ceretto (17761856), was born and died in Turin, was a student at the University (initially in law), professor of physics at the Royal College at Vercelli from 1809 and first professor of Fisica Sublime, i.e. Mathematical Physics, at the University from 1820 but this post was suppressed in 1822 as a result of the risings of 1821 and he became professor emeritus. The chair was reestablished for Cauchy in 1832, and when he left in 1833, Avogadro was reappointed to it, continuing until 1850. He stated his Law and distinguished between atoms and molecules in 1811, but it was not until Cannizzaro exposited the ideas at the Karlsruhe congress of 1860 that they became known. Avogadro coined the word 'molecule'. Amp/re developed some of the same ideas in 1814. In 1911, a plaque was erected at the Accademia "Fu il primo a scrivere: Acqua = H2O". [Jaffee, pp. 121, 122, 128. Giacardi & Roero, pp. 135136.] Giovanni PLANA (17811864) studied at the (cole Polytechnique in Paris in 18001803 and brought the ideas back to Italy. Professor of astronomy at the University in 1811, then of calculus from 1814. Director of the observatory from 1813. Made a baron in 1844 and a member of the first Senate in 1844. President of the Accademia from 1851 until his death. [Giacardi & Roero, pp. 131132.] In 1832, CAUCHY was appointed professor of Fisica Sublime, i.e. mathematical physics, reviving Avogadro's position, but he left in 1833. It was here that he developed the theory of convergence of Taylor series and much of the theory of analytic functions. He published his R)sum)s Analytiques here in 1833. [Giacardi & Roero, pp. 121 & 132134.] Luigi Federico MENABREA (18091896) was a student at the University, graduating in 1831 and then teaching applied descriptive geometry at the Military Academy. In 1842, he published his report on Babbage's lecture see above. In 18461859, he was professor of construction science at the University. He made a notable contribution to the theory of elasticity, formulating a least work principle in 1858. [Giacardi & Roero, pp.140-141.] There is a Via MENABREA. Angelo GENOCCHI (18171889) was born, studied and taught Roman law at Piacenza, but fled from the Austrians to Turin, where he was able to indulge his mathematical inclinations. Professor of various topics from 1859. He lived in a room on the forth floor in Via Alfieri. President of the Accademia from 1885. [Giacardi & Roero, pp. 142144.] Francesco FA  DI BRUNO (18251888) was a student at the Military Academy and became a lieutenant on his graduation in 1846. After a few years service, he was sent to Paris for further studies in 18491851. In 1855, he left the army and returned to Paris for his doctorate, returning to Turin in 1857?. From 1857, he taught at the University, becoming Professor of Higher Analysis in 1876. He spent much of his life in religious activities, becoming an abbot and the founder of the Conservatorio di Nostra Signora del Suffragio. He died in Turin. [Giacardi & Roero, pp. 144146.] He also devised a writing apparatus for the blind. Giuseppe PEANO (18581932) came to Turin at age 12 and was a student at the Cavour School, then at the University in 18761880, where he was a student and then assistant of Genocchi. He then taught at the University until his death, becoming Professor of analysis in 1890. He is only commemorated by the departmental library and a short Via Peano near the Polytechnic. He also taught at the Royal Military Academy. [Giacardi & Roero, pp. 149150.] He died suddenly, having lectured in the morning. Vito VOLTERRA (18601940) came to Turin as professor of higher mechanics at the University in 1893-1900. He was involved in the restructuring of the Polytechnic. [Giacardi & Roero, pp. 153154.] Cesare BURALI FORTI (18611931) came to Turin as professor at the Artillery and Engineering (i.e. the Royal Military) Academy, where he became friends with Peano. Peano invited him to lecture on logic at the University in 18931894 and then to be his assistant in 18941896. However, Burali Forti failed the examination to qualify as a university teacher and I am not sure what he did after this time. He published his famous paradox of the largest ordinal in 1897. He died in Turin. [Giacardi & Roero, pp. 180181]. Gino LORIA (18621954) was a student at the University, becoming an assistant in 18641866 [Giacardi & Roero, pp. 177178]. Near Via Peano is Via C. SEGRE, named for the geometer Corrado Segre (18631924), a relative of the better known B. Segre. Corrado Segre was a student at the University, then an assistant, becoming professor of higher geometry in 1888 until his death in Turin. In 19091918 he was president of the Faculty of Science. [Giacardi & Roero, pp. 156 & 165168.] Guido CASTELNUOVO (18651952) came to Turin in 18871891 as an assistant. He had long discussion with C. Segre about algebraic curves during their long walks under the porticoes of Via Po. [Giacardi & Roero, pp. 171173.] Gino FANO (18711952) entered the University in 1888 to study engineering, but changed to mathematics, studying with C. Segre and meeting Castelnuovo. As a student, he translated Klein's Erlanger Program into Italian. He was an assistant in 18921893 and returned as professor of projective and descriptive geometry in 1901, sometimes teaching in the School of Engineering. He was active in teaching women. In 1935, racial persecution caused him to flee to Switzerland. He returned as professor emeritus in 1945, but took little part in academic work and died in Verona. [Giacardi & Roero, pp. 173176.] Francesco SEVERI (18791961) entered the University to study engineering in 1896, but was converted to mathematics and graduated in 1900 doing his thesis with C. Segre. After some years as an assistant, he went to Bologna. [Giacardi & Roero, pp. 168170.] Guido FUBINI (18791943) came as professor of higher analysis at the University and mathematical analysis at the Polytechnic in 1908. Fubini's Theorem in measure theory appeared in 1907 he considered this a minor work and was later surprised to find it the best known of his results. Royal Prize of the Accademia dei Lincei in 1920. He was forced out in 1939 and emigrated to the USA. In 19211922, bECH studied with him and they coauthored Geometria Proiettiva Differenziale of 1926. [Koutn1k. Giacardi & Roero, pp. 185186.] Francesco TRICOMI (18971978) came from Florence as a professor in 1928 and remained until his death here. He spent 19481950 at CalTech on the Bateman Manuscript Project. [Giacardi & Roero, pp. 190191.] In the Chapter House of the Seminary of S. Niccolo, TREVISO, Veneto, are a series of superb frescoes of Franciscans at their desks by Tomaso da Modena, 1352. One of the monks is using a magnifying glass which exhibits the Aristotelian conception that rays emanated from the eye. (I have seen a statement that the earliest known depiction of a magnifying glass is by George Hofnagel in 1592.) The first printed mathematics book was produced in Treviso in 1478, but the author is unknown and there is no title. In English, it has been called The Treviso Arithmetic , but a modern facsimile has taken the end of the opening sentence as the title: Larte de Labbacho . (This facsimile was produced by the Libreria Canova, Calmaggiore 31, Treviso. No date is given for the facsimile, but it cites a 1976 work.) [HM 25:1 (1998) 100] reports that Jacopo and Vincenzo Riccati are buried in the Cathedral of Treviso. When I was in Treviso for an afternoon in early 1998, the guide book said there wasn't anything to see in the Cathedral and I didn't look into it! BOLTZMANN committed suicide somewhere near TRIESTE, FriuliVenezia Giulia. Salvatore PINCHERLE (18531936) was born in Trieste. In 1964, Abdus SALAM (19261996) established the International Centre for Theoretical Physics here, supported by the International Atomic Energy Agency, to train physicists from developing countries. He remained Director until 1995. Federico COMMANDINO (15091575) was born and died in URBINO, Marche. After study at Padua, he returned to Urbino in 1544, married and had three children. After the death of his wife and son, he turned to a life of scholarship, becoming physician and tutor to the Duke of Urbino, then to the Duke's brotherinlaw, who was a Cardinal at Rome, but who later served in Venice and Bologna. He was a key figure in the 16C mathematical renaissance, translating and commenting on works of Archimedes, Apollonius, Aristarchus, Hero, Pappus, Ptolemy and especially a translation of Euclid into Latin in 1572, of which he supervised a translation into Italian in 1575. In 1565, his patron died and he returned to Urbino. After some recuperation of his health, he returned to work after a visit from John DEE! [ BDM .] VELIA, Campania, 30km SSE of Paestum, is the ruins of the ancient city of ELEA, home of the Elastic school of philosophy. The best known members were Parmenides (c539/ ) and his pupil ZENO (c500/ ) of the paradoxes (c450). Statues of these were found in the ruins and are in the Museum. [ MGG .] The house of MARCO POLO (12541324) was in Corte Seconda del Milion, VENEZIA (VENICE) , Veneto, and the site is marked with a plaque. The two arches at No. 5858, the Teatro Malibran, may be part of Marco's house. He was buried in the church of San Lorenzo, but the coffin was lost during rebuilding in 1592. The airport of Venice is named for Marco Polo. [Eastman, p. 355. Blue Guide . Buckley & Robinson, p. 152.] The clock on San Giacomo di Rialto dates from 1410 [ Blue Guide ]. [Buckley & Robinson, p. 110] assert that its inaccuracy has been notorious since its installation. In the Basilica of San Marco, there is a mosaic panel, c14251430, on the floor at the door of San Pietro (this is not labelled on the maps that I have seen it is the inner doorway corresponding to the outer doorway second from the left, i.e. between Porta di Sant'Alipio and Porta di San Clemente, which are often labelled), which seems to show the small stellated dodecahedron {5/2, 5}. This mosaic has recently (1955 & 1957) been attributed to Paolo Uccello (13971475), so it can only be found in more recent books on him. See, e.g., Ennio Flaiano & Lucia Tongiorgi Tomase; L'Opera Completa di Paolo Uccello ; Rizzoli, Milan, 1971 (and several translations). The mosaic is item 5.A: Rombo con elementi geometrici in the Catalogo delle Opere, with description and a small B&W picture on p. 85. Coxeter [Elem. der Math. 44 (1989) 25-36] says it "is evidently intended to be a picture of this star polyhedron." However, J. V. Field says the shape is not truly the small stellated dodecahedron, but just a 'spiky' dodecahedron. She, and now I, have examined the mosaic and the 'lines' of the pentagrams are clearly not all quite straight, though some seem to be dead straight, so I am inclined to agree with Coxeter and I would attribute the unstraightnesses to poor execution. [The above cited photo is too small to confirm this. I have better photos.] J. V. Field says it appears to be a direct copy of a drawing in Daniele Barbaro; La Practica della Perspectiva ; Venice, 1569, ??NYS, and is most unlikely to be by Uccello. I have recently seen a poster which shows a different object, where the lines of the pentagrams are distinctly not straight. The poster simply says it is a mosaic in Venice. Could there be two versions at San Marco? The explorers John CABOT (Giovanni Caboto, c14501498) and Sebastian CABOT (14771537) were natives of Venice (actually John came from nearby Chioggia, though another source claims he came from Genova and another source opines that Sebastian was born in Bristol). They lived at the first house on the south side of the west end of Via Garibaldi (plaque) [ Blue Guide ; Buckley & Robinson, p. 182]. Alvise Da Mosto (14321488), discoverer of the Cape Verde Islands, was born in the Ca' da Mosto [ Blue Guide ; Buckley & Robinson, pp. 153 & 191]. In 1461, Nicolas Jensen came from Mainz to Venice and set up the first Italian printing press. By 1500, there were 268 printers in Venice and they had produced over 2,000,000 books, several times the total produced in Rome, Florence and Milan. Aldus Manutius (Aldo Manuzio) (14501516), the inventor of italic type, the first to produce pocket editions of the classics and one of the first great printers, came to Venice in 1490 and began publishing in 1494. The traditional site of his press is No. 2311 in Rio Terr! S. Antonio (or Rio Terr! Seconda), north of Campo San Polo, but late in his life he moved to Campo Manin on the Grand Canal. [ Blue Guide . Buckley & Robinson, p. 119.] Luca PACIOLI (c14451517) spent some time in Venice, c14661470, teaching in the house of Antonio de Rompiasi in the Giudecca, near Sant' Eufemia, and attended lectures of Domenico Bragadino at the Scuola di Rialto. He later came here to publish his Summa de Arithmetica in 1494. As a Franciscan, he stayed at the Ospite del Convento dell'Ordine al Ca'Grande. DFRER came to Venice during his Wanderjahre in 1493, and knew Jacopo de Barbari, painter of the famous portrait of Pacioli, now in Naples (qv above). Pacioli later taught here. In 1508-1509, Pacioli returned to publish his De Divina Proportione and gave a lecture on the Fifth Book of Euclid at the Church of St. Bartholomew. The famous portrait of Pacioli by de Barbari is thought to have been painted in Venice at this time [Fennell, p. 10]. It is conjectured that Pacioli may have met DGrer who was in Venice in 15051507 and painted an altarpiece Madonna del Rosario for Christopher Fugger, for the German colony's church of S. Bartolomeo in 1506 or 1505 (this is now in Prague) [Headlam(2), p. 193; Buckley & Robinson, p. 77]. [Eastman, p. 390] lists DGrer as staying at Pander's Inn, near S. Bartolomeo, at this time. [R. E. Taylor, pp. 299300] cites an author who suggests that DGrer studied under Pacioli in Bologna in 1506, apparently based on a comment of DGrer in 1506 that he was going to Bologna to see the leading authority on perspective. Pacioli was in Florence at this period, but they could have both gone to Bologna. DGrer certainly studied with de Barbari [Fennell, p.10]. Despite entreaties by the Doge, DGrer returned to NGrnberg. ERASMUS was also in Venice at the time and may have attended Pacioli's lecture he certainly satirizes Pacioli and his works in In Praise of Folly . [R. E. Taylor, p. 27] says Pacioli refers to San Rocco as 'our monastery in Venice' and feels that Pacioli probably stayed there, but this may just mean that it was a Franciscan monastery. [Mackinnon (3). Giusti, pp. 39-40. Fennell, pp.7-8, 11, 1618.] [Fennell] and [R. E. Taylor, p. 44] say Pacioli was first in Venice c14641471.] In 1446, Venice founded public schools for the teaching of humanities. In 1449, public lectures in philosophy, geometry and arithmetic were being given by Paolo della Pergola. [R. E. Taylor, pp. 5354.] The University of Venice was founded in 1490, but it was subsidiary to Padua [Foligno, p. 150]. The 'Mori', which strike the hours at the top of the Torre dell' Orologio on the Piazza San Marco were cast at the Arsenal in 1497. The tower was built in 14961506. The clock was made by Paolo and Carlo Rainieri in three years. Popular legend says they were subsequently blinded to prevent their making clocks for others, but in fact they were well honoured and given a generous pension. (See Olomouc and Prague, Czechoslovakia in Section 10 for similar legends.) The staircase to the roof, which passed by the clock mechanism, was closed in the mid 1980s and is unlikely to reopen, In 1998, the whole tower was being renovated and is behind scaffolding and a huge sheet on which the tower is so well depicted that one doesn't immediately realise one is being tricked. [ Blue Guide . Buckley & Robinson, p. 67.] TARTAGLIA (1499?1557) moved to Venice in 1534 or 1535 and stayed there the rest of his life except for a year and a half teaching in Brescia in 15481549. He taught at S. Zanipolo among other places and published his books here. He lived in Calle del Sturion (= Storione) and it was probably there that he solved the cubic equations with no x2 term during 12/13 Feb 1535, but there is no monument. He died in Venice, presumably at his house in Calle del Sturion where he had made his will three days earlier. He was buried in S. Silvestro but Masotti says there is no monument. His will is preserved in the state Archives. [Masotti (2), pp. 1718; plates 31-33 show Tartaglia's will.] In 1592, Giordano BRUNO was a guest at Palazzo Mocenigo Vecchio, the westernmost of the Palazzi Mocenigi on the Grand Canal, when his host, Giovanni Mocenigo, betrayed him to the Inquisition. Bruno's ghost is said to haunt the building. Cf under Rome, above. [ Blue Guide . Buckley & Robinson, p. 193.] Venice controlled Padua, so GALILEO (1564-1642) was really employed by the Venetians when he taught at Padua. When news of his telescope reached Venice in August 1609, Galileo was summoned from Padua to demonstrate it. On 23 Aug, he set it up on top of the Campanile in the Piazza San Marco and many senators and nobles went up and saw arriving ships two hours before they were seen without the telescope. On 24 Aug, Galileo presented this telescope to the Doge in the Presence Chamber of the Doge's Palace and was confirmed in the professorship for life with his salary doubled! [Letter of 29 Aug 1609 from Galileo to his brother-in-law in Florence, quoted in Fahie, pp. 82-83.] '... an object which is at a distance of nine miles will appear as if it were only one mile away, ... one can detect ships and sails of the enemy at sea ... we can see him two or more hours earlier than he can possibly see us, ....' [Galileo's letter to the Doge on 24 Aug 1609, quoted in Scandone, pp.12-14 & in Van Helden, pp. 78]. Sadly, this telescope has long been lost. There is a bust of Galileo with inscription in the inner balcony of the Doge's Palace [Fahie, p. 161]. I have been told by a Venetian scholar, Tudy Sammartini, that Galileo lived a good part of this period in the vanished Palazzo Sagredo near S. Francesco della Vigna (not the extant Palazzo Sagredo on the Grand Canal) she discovered this from a document complaining about a fire in Galileo's laboratory. However, Velucchi writes that the Domus Galilaeana in Pisa has no record of a Galileo house in Venice, so he may have just been staying with a friend. Both Bruno and Galileo stayed with the Morosinis when they owned Casa CornerMartinengoRav!, now the Azienda Autonoma del Turismo [ Blue Guide ]. The Arsenal of Venice was their ship building yard and the greatest industrial site in Europe for centuries. They once built a fully equipped ship in a day. Galileo, with his interest in practical techniques, spent some time there and said he learned much from the artisans there. Incidentally, the general word 'arsenal' derives from this one, which is named for its location. Elena Lucrezia Cornaro (or Corner) Piscopia, the first woman to receive a university degree (in philosophy, from Padua, in 1678), lived in what is now the Palazzo Loredan on the Grand Canal [ Blue Guide ; Buckley & Robinson, p. 192]. The fact that she was a descendent of Doges of Venice may well have had something to do with the award the next woman to get a degree was over fifty years later at Bologna. I recently came across a plaque on Ponte S. Severo in Salizzada Zorzi, commemorating Marino Sanuto TORSELLO da S. Severo, a historian whose description of the conquest of Egypt is considered an early use of statistics. I could not find out anything about him, but Luciano Paiusco has found that Mario Sanuto (or Sanudo), called Torsello, lived in the 14C. His narrative was titled Liber Secretorum Fidelium Crucis super Terrae Sanctae Recuperatione et Conservatione and a facsimile or reprint was produced by Toronto Univ. Press in 1972. This Sanuto may be a confusion with, or a relative of, Marino Sanudo (or Sanuto) (14661536), Venetian historian and diarist. His diary runs from 1496 to 1533 and was printed in 58 volumes. A Marco Sanuto of the same family was a professor of mathematics at Venice in the 1490s as well as Governor of Bergamo and advanced the funds to print Pacioli's Summa in 1494. Pacioli thanks him on f. 1v of the book. [R. E. Taylor, pp.187188 & 198.] The MUSEO QUERINI STAMPALIA has a miscellaneous collection which includes early 17C globes by Willem Blaeu, globes from the 18C and an armillary sphere from 18/19C. James STIRLING (1692-1770) spent 1715-1725 in Venice, leading to his being called 'the Venetian' when he returned to the UK. DOPPLER retired to Venice in 1852 and died there in 1853 [Hughes]. Guido CASTELNUOVO (18651952) was born in Venice [Giacardi & Roero, pp. 171173.] Guido FUBINI (18791943) was born in Venice [Giacardi & Roero, pp. 185186]. There are tide and barometric pressure recorders at the base of the Campanile [ Blue Guide ]. Across the Piazzetta from the Doge's Palace is the Libreria Sansoviniana which contains the OLD LIBRARY (or Biblioteca Nazionale Marciana) which contains the world map of Fra Mauro (1459), Hadji Mehemed's map of c1560 and Marco Polo's will. Fra Mauro (14331459) was a monk in the Camoldolensian monastery on the Isola San Michele and drew his map there. This material is sometimes on display in the adjacent Salone Sansovino whose ceiling has paintings of many philosophers and of Matematiche, Geometria, Astrologia, Aritmetica, etc. The room also has two pairs of celestial and terrestrial globes, one set by Blaeu, c1630, and the other from Paris, 1688. The Istituto Veneto is in the Palazzo Loredan on Campo Santo Stefano [ Blue Guide ]. The Museo Storico Navale, near S. Biagio, contains various navigational instruments [ Blue Guide ]. In VERONA, Veneto, the Museo Civico di Storia Naturale, Palazzo Pompei, Largo Porta Vittoria 9, contains perhaps the oldest known reasonably regular DODECAHEDRON [Herz-Fischler, p. 61], which is in the central case of Sala XIX. I have now been to see this. It was discovered in 1886 at Monte Loffa, NE of Verona and has been dated as far back as 10C, but is currently considered to be 3C or 2C [Herz-Fischler, p. 61]. The Director of the Museum told me the site was inhabited by tribes who had retreated into the mountains when the Romans came to the area, c3C. These tribes were friendly with the Romans and were assimilated over a few centuries, so it is not possible to know if this object belongs to the preRoman culture or was due to Roman influence. She dates it as 4C/1C. It is clearly not perfectly regular some of the face angles appear to be 90o and some edges are clearly much shorter than others. But it also seems clear that it is an attempt at a regular dodecahedron the faces are quite flat. Its faces are marked with holes and lines, but their meaning and the function of the object are unknown. (I wonder if there are ancient Greek models of the regular polyhedra?) But see also the carved stone balls in the National Museum in Edinburgh (Section 6-C-1). The Director, Dr. Alessandra Aspes has kindly sent me a slide and a photocopy of an article on it [Stefano de'Stefani; Intorno un dodecaedro quasi regolare di pietra a facce pentagonali scolpite con cifre scoperto nelle antichissime capanne di pietra del Monte Loffa; Atti del Reale Istituto Veneto di Scienze e Lettere, (Ser. 6) 4 (1885) 14371459 + plate 18. Separately reprinted by G. Antonelli, Venezia, 1886, which has pp. 125 and Tavola 18.] The ARCO DI GAVI, beside the Castelvecchio, was built by VITRUVIUS in 1C, though it has been moved from its original site nearby (I don't know if any of his other works survive). The CASTELVECCHIO Museum was redesigned by Carlo Scarpa in 19571964 and is one of the seminal examples of modern museum design. In Room 19 are several paintings by Nicola Giolfino (14761555) including La Matematica, L'Astronomia and La Geografia. TARTAGLIA (1499?1557) came to Verona in c1517 and stayed until c1535. He lived in Contrada di S. Maria Antica and held a school in Palazzo di Mazzanti. [Masotti (2), pp. 1718.] In the PIAZZA DELLE ERBE are several structures. The second from the SE end is a small templelike structure which has standards of volume cut into the step and standards of length marked on the southern column. One can see the vertical grooves and some of the metal ends for several distances of about a meter or yard, but none of these are very clear. A local guide book calls this structure the 'berlina', but it then erroneously says the standards are on the column at the end of the Piazza, which it calls the market column, so I am not sure which name is correct. Gino FANO (18711952) died in Verona [Giacardi & Roero, pp. 173176]. M. C. ESCHER married Jetta Umiker at the Town Hall of VIAREGGIO, Toscana, on 12 Jun 1924, with a second ceremony at a catholic school on 16 Jun [Locher, p. 30]. In VICENZA, Veneto, the Torre di Piazza was started in the 12C and raised several times, ending in 1444. Its clock is claimed to be the first public clock in Italy, but the source gives no date for the clock. [Buckley & Robinson, p.307. Antonio PIGAFETTA, Magellan's deputy (or navigator) who completed the first circumnavigation in 1522, was a native of Vicenza and there is a commemorative plaque on the house at 1113 Contra Antonio Pigafetta, where he was born and lived. Cf SanlCcar de Barrameda, Spain, in Section 10 for more on the voyage. [Buckley & Robinson, pp. 307308. DBS.] Another source says the ship was captained by Juan Sebastin Elcano cf Getaria, Spain. In Vicenza, the Museo Civico has globes by Hondius, c1640, and by Coronelli, 1688 [DBS]. Olinto de PRETTO, an industrialist and amateur scientist from Vicenza, published a paper containing the relation E=mc2 in 1903, but he did not have any theory of relativity related to it. Einstein is believed to have seen de Pretto's paper, but did not cite it and it is unlikely that it influenced Einstein. [Rory Carroll; Einstein's E = mc2 'was Italian's idea'; The Guardian (11 Nov 1999) 18.] The TEATRO OLIMPICO of 15791585 by Palladio and his pupil Scamozzi was the first indoor theatre in Europe and features a remarkable perspective scene at the back of the stage, certainly one of the most extraordinary examples of trompe l'oeil [DBS; Buckley & Robinson, p. 306]. LEONARDO DA VINCI (1452-1519) was born in VINCI, Toscana, a small village about 25 miles west of Florence (or perhaps in the next village or suburb of Anchiano) and lived here until 1467. There is no record of the site, but a house called Anchiano is claimed to be the site. In 1952, there was an attempt to restore the interior, but it had been changed so often that the 'original' form could not be identified. Part of Vinci Castle (=Palazzo Pretorio) has been made into a Museo Vinciano, with models of his mechanical devices made by IBM. [Anon., Vinci. Eastman, p. 343.] The 13C commentator on Euclid, CAMPANUS Novariensis (c12151296), spent the last years of his life at the Augustinian convent in VITERBO, Lazio. His will provided for a chapel to St. Anne in the Church of the Holy Trinity at Viterbo. [ BDM .] Giovanni PLANA (17811864) was born in VOGHERA, Lombardia, [Giacardi & Roero, p. 131]. In VOLTERRA, Tuscany, there is a fine example of a wooden inlay labyrinth on the cathedral lectern, now removed to the diocesan museum. It is dated to about 1400. [Manuela Mastrigli; The Volterra lectern labyrinth; Caerdroia 30 (1999) 69.]  10.MONUMENTS IN OTHER COUNTRIES.  First, a general topic. BABBAGE Island is a small island near Carnarvon, Western Australia. Mt. BABBAGE is in the north west of New South Wales. Mt. BABBAGE in north west South Australia and BABBAGE Peninsula in Lake Eyre, South Australia, are named after Babbage's eldest son Benjamin Herschel Babbage, who was Surveyor-General of South Australia. His children moved to New Zealand and a portion of the Difference Engine assembled by H. P. Babbage in 1879 is preserved by descendants in AUCKLAND [Photo in [Tee (2)]]. Other pieces are in the MacLeay Museum of the University of SYDNEY. There are a BABBAGE River and a HERSCHEL Island in arctic CANADA, near the Alaska border [Tee(2)]. There are certainly many other geographic sites named for mathematicians, etc., but these don't have the same associations with the individuals as the majority of the items considered here. I will continue in alphabetic order of country, then location. AFGHANISTAN Aurel STEIN, the explorer of Central Asia see under Dunhuang, China, below is buried in the Gora Kabar (White Graveyard) in KABUL. A 2002 report says the grave has survived the recent fighting and has been restored. ALGERIA BUGIA (now Bougie) is where Leonardo FIBONACCI's father was a scribe or customs official for the Pisan merchant colony and the young Leonardo learned Arabic numerals and computation with them, c1190. ARGENTINA Alberto CALDERON (1922?1998) was born in MENDOZA. Educated in Switzerland, then did a degree in civil engineering at the University of BUENOS AIRES. In 1948, he met Antoni Zygmund there and was invited to the University of Chicago. AUSTRALIA Horace LAMB was professor at the University of ADELAIDE, 1875-1885. W. L. BRAGG (18901971) was born in Adelaide while his father W. H. BRAGG (18621942) was teaching here in 18851909. When Bragg was appointed Professor of Mathematics and Physics, he had read no physics and had to learn it. He did not start to do research until his 42nd year, in 1904, but his initial work on  rays was recognised as important by Rutherford and soon earned an FRS. Mark OLIPHANT (19012000) was born in Adelaide and studied at the University. He then went to Cambridge, where he was the first person to describe nuclear fusion and became Assistant Director of the Cavendish Laboratory. In 1937, he became Professor at Birmingham and was instrumental in bringing Frisch and Peierls results on the feasibility of an atomic bomb to the attention of the British and then the American establishments. He headed the group which developed the cavity magnetron and then joined the Manhattan project. After the War, he was the first scientific adviser to the UN Atomic Energy Commission and a founder of the Pugwash conferences. He was on the council which set up the Australian National University and returned to Australia to head up its physical sciences research group in 19501970 (my source doesn't say where this was). He promoted the creation of the Australian Academy of Sciences. In 19711975, he was Governor of South Australia. [Anthony Tucker; [Obituary] Sir Mark Oliphant; The Guardian (18 Jul 2000) 20.] R. A. FISHER went to the CSIRO Division of Mathematical Statistics at the University of Adelaide in 1959 and died there in 1962 [Goodhart; Gower]. There is a monument to him in the Cathedral and there is a Fisher Building at the University [Arthur Lucas; Letter; IN: The great scientific memorial search; History of Australian Science Newsletter 33 (1994) 16.] Aleksandr Mikhailovich PROKHOROV (19162002) was born in ATHERTON, Australia of )migr) parents, but the family returned to the USSR in 1923. Shared the Nobel Prize in Physics in 1964 for the development of the maser and laser. On the NULLARBOR PLAIN is the world's longest stretch of straight railway, 297 miles long. [Philip S. Watson; The Giant's Causeway ; HMSO, Belfast, 1992, p. 1] says there is a columnar basalt formation similar to Giant's Causeway (cf Section 6D) at POONINGBAH in New South Wales, but I haven't yet located this. James COCKLE (18191895) was the first Chief Justice of QUEENSLAND in 18631879. He was a noted mathematician of his time cf in Section 3. The largest Australian observatory is at SIDING SPRING, near Coonabarabran, New South Wales. This has the AngloAustralian Telescope, a 153 inch reflector, and the United Kingdom Schmidt, with a 48inch mirror. This and the Schmidt at Palomar Mountain, California, are producing an atlas of the entire sky. The site is not very high (c4000 ft), but has adequate viewing. [P. Moore (4), pp.72-74. On p. 74, he says the Schmidt is 49-inch, but he also says it is a twin of the Palomar 48inch and his table on p. 113 lists both as 48inch. There is a statue of Captain COOK in Hyde Park, SYDNEY, New South Wales. William Stanley JEVONS (18351882) worked at the mint in Sydney in 18541859 [Gardner, p.91]. Horatio Scott CARSLAW (18701954) was Professor at the University of Sydney. In 1979, a large sculpture by John Robinson, 'Bonds of Friendship', was erected at Sydney Cove to commemorate the disembarkation of the First Fleet of settlers from England in 1787. The sculpture consists of two interlocked tori, each just fitting through the opening of the other. An identical sculpture, with a different finish, is at the point of embarkation at Portsmouth, England. AUSTRIA In 1949, the centre of Austria was determined to be at BAD AUSSEE and there is a commemorative monument there [information from Al Posamentier]. BRFNN is now BRNO in the Czech Republic, qv below. From 1843 MENDEL (18221884) was at the Augustinian Abbey of St. Thomas, known as K?nigskloster, in BRFNN, except for a two year course in Vienna in 18511853. [Klotz, p. 29, calls it Altbrunn; Hayman, p.132, calls it Star) Brno which means old BrGnn.] He adopted the name Gregor when he entered the monastery. He failed the state examination to become a schoolteacher in 1850 (as did Einstein fifty years later) but was sent to graduate school anyway. He taught physics and natural history from 1853 to 186