# Jérôme Franel

### Quick Info

Travers, Neuchâtel canton, Switzerland

Zürich, Switzerland

**Jérôme Franel**was a Swiss mathematician who specialised in analytic number theory.

### Biography

**Jérôme Franel**was born and grew up in Travers (canton Neuchâtel) with his twelve siblings. His place of origin, however, was Provence (canton Vaud). After attending the industrial school in Lausanne he studied at the Polytechnic in Zürich for four years, at the Department for Mathematics and Physics Teachers. He then continued his studies in Berlin, where his teachers included Weierstrass, Kronecker and Kummer, and in Paris, where he attended Charles Hermite's lectures in particular. He graduated with a degree in mathematics from the Paris Academy in 1883 and returned to Switzerland to teach at his old school in Lausanne for a couple of years. In 1886 he was appointed to a professorship in mathematics mathematics in French at the Federal Polytechnic in Zürich, succeeding Eduard Méquet. He held this post until his retirement in 1929. At the beginning, he was the only mathematician who lectured in French; later on a second chair for mathematics in French was created. Franel co-supervised (at least) four PhD students, three jointly with Hurwitz and one with Hermann Weyl.

Franel served as the Polytechnic's Director from 1905-1909. In this capacity he fought for more liberal study regulations and for the Polytechnic's right to award doctorates. He also succeeded Geiser as president of the Federal Matura Committee, from 1909-1915, and 'he had a fortunate influence on the development of Swiss middle schools' [3] -- however, this influence is not elaborated. On several occasions Franel acted as intermediary between the Polytechnic and secondary schools or the Gesellschaft ehemaliger Polytechniker. Furthermore, he supported the students from French-speaking Switzerland throughout his time at the Polytechnic. Together with Geiser, Herzog and Robert Gnehm he founded the Polytechnic's Civil Fund for Widows and Orphans.

In recognition of his work the University of Zürich awarded him an honorary doctorate in 1901. Four years later he was made an honorary citizen of the town Zürich; this happened on the occasion of the Polytechnic's 50th anniversary. As Director, Franel was heavily involved in organising the celebrations.

Franel was first and foremost a teacher and not a researcher. His former student and later colleague and friend Louis Kollros speaks of him very fondly, claiming that Franel 'was one of the School's most popular teachers' [3]. His colleague George Pólya commented that 'Old Franel [was] interesting. He always dressed in the manner of an earlier generation' [4]. He also said about Franel [4]:

He is not very much remembered as a mathematician, but he was an especially attractive kind of person and a very good teacher. He gave the introductory lectures on calculus in French for several decades. He had a real interest in mathematics, but he was more interested in French literature. Teaching occupied a good deal of his time but in French literature he had to read everything available. He had no time left to do mathematics. But when he retired he suddenly tackled two of the great problems: the Riemann Hypothesis and 'Fermat's last theorem'.Franel wrote a couple of papers on problems in geometry, but then turned to analysis and number theory. He published most of his papers in the 1890s, including work on Euler sums, a fundamental formula by Kronecker and the Riemann zeta function. Franel also regularly contributed to the French journal

*L'Intermédiaire des mathématiciens*. His most important paper was

*Les suites de Farey et le problème des nombres premiers*Ⓣ which was published in the Göttinger Nachrichten in 1924, a few years before his retirement. In this short paper he proved that it is possible to link the Farey sequence to the Riemann hypothesis. The German mathematician Edmund Landau, who held a professorship at the University of Göttingen at the time, then wrote a few papers on the same topic based on and expanding Franel's ideas. Guthery says of Franel's proof [2]:

That the relationship between a series of fractions so simple can be connected to a mathematical hypothesis so profound with such economy is the mark of a teacher of mathematics of the very highest order.Franel joined the organising committee of the first International Congress of Mathematicians in July 1896, where he was responsible for the French translations. Furthermore, he was on the committee for board and lodging and was asked to join the sub-committee that chose the speakers. With Geiser, Dumas and Hirsch he also edited the final congress programme. At the congress itself he acted as the general secretary for French. Franel did not give a talk himself, but he read out Poincaré's talk in the first general meeting, which he is remembered for.

On a more trivial note, he was also the first to propose a toast (to Switzerland) at the congress banquet on the Monday. Despite having been general secretary, Franel never had the chance to edit the congress proceedings in French. Originally, the organising committee had decided to publish German and French editions of the proceedings. But since the talks were to be published in the language in which they were given, the committee decided that the two editions would be identical for the most part, and that only a German edition should be published, with French translations of the most important speeches.

Franel was a member of the organising committee of the 1932 ICM in Zürich again, but did not give a talk at the congress.

Franel was married and he had two daughters, Jeanne (born 1889) and Marie-Louise (born 1893).

### References (show)

- S U Eminger, C F Geiser and F Rudio: the men behind the First International Congress of Mathematicians
*St Andrews PhD thesis*(2014) 103-106 /Publications/Eminger.pdf - S B Guthery,
*A Motif of Mathematics. History and Application of the Mediant and the Farey Sequence*, Docent Press, Boston, 2011 - L Kollros, Prof. Dr. Jérôme Franel 1859-1939,
*Verhandlungen der Schweiz. Naturforschenden Gesellschaft***120**, 1940, 439-444 - G Pólya,
*The Pólya Picture Album: Encounters of a Mathematician*, edited by G L Alexanderson, Birkhäuser, Boston, 1987

### Additional Resources (show)

Other websites about Jérôme Franel:

### Cross-references (show)

Written by Stefanie Eminger, University of St Andrews

Last Update August 2015

Last Update August 2015