The catapult that Archimedes built, the gambling-houses that Des- cartes frequented in his dissolute youth, the field where Galois fought his duel, the bridge where Hamilton carved quaternions---not all of these monuments to mathematical history survive today, but the mathematician on vacation can still find many reminders of our subject's glorious and inglorious past: statues, plaques, graves, the cafd where the famous conjecture was made, the desk where the

Ian Stewart* famous initials are scratched, birthplaces, houses, memorials. Does your hometown have a mathematical tourist attraction? Have you encountered a mathematical sight on your travels? If so, we invite you to submit to this column a picture, a description of its mathe- matical significance, and either a map or directions so that others may follow in your tracks. Please send all submissions to the Math- ematical Tourist Editor, Ian Stewart.

The Bernoullis in Basel David Speiser

Epitaph on the tombstone of Jacob I.

* Column Editor's address: Mathematics Institute, University of Warwick, Coventry, CV4 7AL England.

The Bernoulli family arrived in Basel in 1622, coming from Antwerp by way of Frankfurt am Main. Between ca. 1680 and 1800 eight members of the family were active in the city and abroad as mathematicians and physicists.

Many buildings and monuments in Basel still testify to the Bernoullis' activities or bear witness to their lives. Among these are the houses in which some of them lived, public buildings where they taught, and their tombstones (which, however, have been moved from their original places). Local tradition had always preserved many of these testimonials; some years ago, Dr. F. Nagel (an editor of The Bernoulli Edition) started a systematic investigation of them. The Basel Tourist Office is planning a leaflet and a "Bernoulli Walk" across the city.

All we know about the house of Jacob I (who dis- covered the formula for the radius of curvature, the

Bernoulli numbers, the fundamental theorem of prob- ability theory, the elastic curve, etc.) is that it was on the Barf~isserplatz, close to the Barfiisserkirche (today the Museum of History). His tomb was in this church, but on the occasion of a restoration in 1843, Jacob's bones and the tombstone were transferred to the clois- ter next to the cathedral. The lower part of the tomb- stone shows (by mistake) an Archimedean spiral; this should have been a logarithmic spiral, which has the property of reproducing itself under many operations (e.g., it is its own evolute). For this reason, Jacob chose it as a symbol of resurrection: eadem mutata resurgo ("in the same way, I shall be resurrected after the transfor- mation") is the device he had engraved around the spiral.

Not far from the cathedral is the present Institute of Mathematics, and a bit lower on the Rheinsprung the old university, a big yellow building where many of the Bernoullis' lectures were delivered.

46 THE MATHEMATICAL INTELLIGENCER VOL. 14, NO. 4 �9 1992 Springer-Verlag New York

Imberhof. Zur Alten Treu and plaque. Grosser Engelhof.

Photos on this page by R. Speiser and B. Speiser.

Of Johann I Bernoulli (hanging chain, brachy- stochrone, rule of Bernoulli-l'Hbpital, calculus of vari- ations, hydraulics), more can still be seen: After his return from Groningen he lived in the house Zur alten Treu (To the Old Loyalty) on Nadelberg, a street still boasting many fine old houses. Johann's father had bought this house (once the home of Johannes Froben, the printer of Erasmus; and the son used it as his fam- ily home as well as for receiving his many guests, to whom he also gave private lectures there. Thus it was also the home of his three sons. About 100 meters below, on the charming Andreasplatz, lies the Imber- hof, where Nicolaus I lived for a while.

On the same level with the Alte Treu, in the direc- tion of the Peterskirche, are the Grosser Engelhof and the Kleiner Engelhof. The latter was bought by Daniel Bernoulli (hydrodynamics, theory of oscillations), who was a bachelor, and the former by Johann II Bernoulli, the father of Jakob II and Johann III. It is in this house that Johann's friend Maupertuis died in 1759, some time after his departure from Berlin. At that time, no activity of a Catholic priest was permitted in Basel, but an exception was granted, and a Capuchin monk was allowed to administer the last rites. Maupertuis was then buried, according to his last will, at Dornach, a Catholic village about 10 kilometers from Basel.

Thirty-five years ago, Clifford Truesdell wrote in the Engelhof his introduction to vol.II/ll of Euler's Opera Omnia, a history of the theory of elasticity, in which the Bernoullis played such a prominent part.

In the Peterskirche, to the left of the main entrance, are the tombstones of Johann I, Nicolaus I, Daniel, and Johann II Bernoulli. The church faces the Petersplatz where the new university (built only in 1939) is lo- cated. From the charming diaries of the counts Teleki, who came to Basel around 1740 to study with Daniel Bernoulli, we know that Daniel and his brother fre-

quently strolled there with their students. At the other end of the square is the Stachelsch~itzenhaus (House of the Crossbowmen), where Daniel Bernoulli conducted experiments. According to Whittaker, these experi- ments, as described by the Telekis and his student Abel Socin, led Bernoulli to the first conjecture (in 1760) of the 1/r 2 law of electric attraction and repulsion.

Next to the StachelschLitzenhaus is the University Library; today it houses the Basel office of the Bernoulli Edition, responsible for the edition of the complete works and correspondences of the Bernoullis and of Jacob Hermann.

Bromhfibelweg 5 CH-4144 Arlesheim Switzerland

Stachelschiitzenhaus (House of the Crossbowmen).

THE MATHEMATICAL INTELLIGENCER VOL. 14, NO. 4, 1992 47