organization of annual meetings and the publication of a sci- entific journal. (Local societies were already in existence.) At math.ch/100 the beginning of the twentieth century, specialized scientific societies were organized as subsections of the SNG: the Swiss Schweizerische Mathematische Chemistry Society in 1901, the Swiss Physics Society in 1908 and, last but not least, the Swiss Mathematical Society (SMS) in Gesellschaft Socie´te´ 1910. The SMS founders were Rudolf Fueter, Hans Fehr, and Mathe´matique Suisse Marcel Grossmann. Fueter, of Basel origin, left Swizerland in 1899 to study under David Hilbert. After earning his doctorate, Swiss Mathematical Society he spent time in various European mathematical institutes before returning to Basel as a professor in 1908. He soon 1910–2010 realized how fragmented the mathematical community was in edited by Bruno Colbois, Christine Riedtmann, Switzerland. Mathematicians from different Swiss universities and Viktor Schroeder had no contact with each other whereas mathematicians of German origin were rather looking across the Rhine. One ZURICH: EUROPEAN MATHEMATICAL SOCIETY, 2010, 526 PP., reason Fueter created the SMS was certainly to prevent local HARDCOVER, 68.00 EURO, ISBN 978-3-03719-089-0 and international isolation. Fueter was a recognized number-theorist. His book on REVIEWED BY MAX-ALBERT KNUS ‘‘Synthetische Zahlentheorie’’, published in 1917 soon after he moved to the University of Zurich, was very successful; a third edition appeared in 1950. Fueter was also involved in many his unusual book was published in 2010 by the Swiss activities outside of mathematics. It is thanks to him and his Mathematical Society (SMS) to celebrate its 100th anni- colleague, the group-theorist Andreas Speiser, that the Swiss TT versary, and a copy was presented to every member. It House in the Cite´ universitaire of Paris was built by the famous consists of 23 contributions covering many aspects of a architect Le Corbusier in 1930. Less known is his activity century of mathematics in Switzerland. The authors evoke during the first year of World War II as a colonel of the Swiss prominent personalities as well as institutes and institutions— army. Responsible for press censorship, Fueter fought cou- even personal memories and student life find a place. There is rageously for the democratic rights of the Swiss press in 1940. great diversity in the contributions: French, German, and Some of the influential newspapers were openly critical of the English are used, and nearly half of the articles are reprinted Nazi regime. This was viewed as a provocation by Germany, from older publications. Authors were encouraged to write and quite a broad part of official Switzerland supported the what they liked as they liked. Many contributions are full of German accusations. life, whereas others reflect some academic dryness. Authors Fehr began his career as a mathematics teacher in Geneva also freely chose their illustrations, with the result that many and became professor at the University of Geneva in 1900. photographs emerged from little-known private albums. Para- One of his major contributions was the journal L’Enseigne- phrasing the title of one of the essays, I would describe the ment Mathe´matique, which he founded in 1899, together volume primarily as a collection of glimpses. It is not (and with his friend Charles-Ange Laisant, as the first international was not intended to be) an encyclopædia giving a systematic journal emphasizing mathematics teaching. and detailed account of mathematics in Switzerland, but it is Grossmann was a fellow student and friend of Albert an exciting source of information. The steering committee of Einstein. In 1907 he became professor of descriptive geom- the SMS, Bruno Colbois, Christine Riedtmann, and Viktor etry at ETH. After Einstein came back to ETH as a professor of Schroeder, edited the work carefully. The result is an anni- theoretical physics in 1912, Grossmann pointed out to him versary gift with a special touch. the relevance of the tensor calculus to general relativity. Their The first contribution is a memorial essay on the history of collaboration led to the first paper on the general theory mathematics in Switzerland, written by Michel Plancherel on of relativity in 1913. During World War I, Grossmann was the occasion of the 50th anniversary of the SMS. The second is very active in improving relations between the French- and a history of the SMS commissioned by our centenarian soci- German-speaking parts of Switzerland. ety. The science historian Erwin Neuenschwander has written The first meeting of the SMS was held in Basel, September a well-documented report on the origin and activities of the 4–10, 1910, with Fueter as president. Fehr succeeded him, society during its first hundred years, including a useful and Grossmann was the third president. During its first year, chronicle of year-to-year events. The remaining pieces in the more than one hundred people joined the society; today the volume appear in alphabetic order (based on the authors’ SMS has around five hundred members. names). I will not review the essays individually nor follow Besides national solidarity, mathematicians in Switzerland their order, but try instead to provide a personal synthesis of united to edit the complete works of Leonhard Euler. The the book along a historical thread. far-seeing decision to publish the ‘‘Leonhardi Euleri Opera The first countrywide scientific organization in Switzerland omnia’’ was taken in 1909 by the SNG. Publication is still was the Swiss Society for Natural Sciences (Schweizerische under way; it will extend to around one hundred volumes naturforschende Gesellschaft, SNG), established in 1815 to when complete. Many mathematicians in Switzerland con- encourage natural sciences in Switzerland through the tributed to the edition. Ó 2011 Springer Science+Business Media, LLC DOI 10.1007/s00283-011-9265-9 As with most scientific societies, meetings and journals are Many of the new professors came from Germany. A essential activities of the SMS. There are two meetings every number of young, highly talented German mathematicians year, the Fall meeting or general assembly, and the Spring took the opportunity in Zurich to start successful careers, meeting, which is dedicated to specialized topics. The SMS among them Richard Dedekind, Elwin Bruno Christoffel, owns two journals. ‘‘Commentarii Helvetici Mathematicae’’ Hermann Amandus Schwarz, Heinrich Weber, and Ferdi- was founded in 1928 to make the research of mathematicians nand Georg Frobenius. Ever since, it has been a tradition in in Switzerland better known internationally. Today it is rec- Swiss universities to invite people without regard to national ognized worldwide. Here too Fueter played a decisive role as borders. Later examples are Ludwig Bieberbach and Erich its main editor until his death. The second journal, ‘‘Elemente Hecke in Basel, Matyas Lerch in Fribourg, Hermann Min- der Mathematik’’, was established in 1946 by Louis Locher- kowski, Adolph Hurwitz, Hermann Weyl at ETH, and Ernst Ernst to convey the relevance of today’s mathematics to a Zermelo at the University of Zurich. Other more recent cases large circle of readers. Since 2005, both journals have been are described in the volume. Some mathematicians remained published by the European Mathematical Society Publishing in Switzerland for their entire careers, but many stayed for House in Zurich, founded in 2001 at the initiative of Rolf only a short time. Jeltsch (ETH Zurich). The decision to leave the previous Weyl was active in Zurich from 1913 until 1930 and then publisher, Birkha¨user Verlag, was taken after a lively dis- moved for three years to Go¨ttingen, where he assumed the cussion in an extraordinary general assembly of the SMS. chair of his former teacher David Hilbert. In 1933, he accepted One historical duty of the SMS is to represent the Swiss a call to the Institute for Advanced Study in Princeton, but he mathematical community in international organizations. As an never lost his contacts with Zurich, in part for family reasons. example, Fueter met with J. C. Fields in the summer of 1931 As Weyl once said, his seventeen years in Switzerland were and the SMS approved the idea of the Fields medal in the the most fruitful of his life: seven books and nearly seventy following general assembly. In the last century, the small Swiss papers appeared in that period. It was therefore not easy for mathematical community has clearly been overrepresented ETH to cope with the loss of Weyl. After both Emil Artin and internationally. The first International Congress of Mathema- Rolf Nevanlinna declined the ETH position, its board fol- ticians was held in 1897 in Zurich, as were two later ICMs (1932 lowed the advice of Issai Schur and offered it to Heinz Hopf. and 1994). After the rebirth of the International Mathematical (Nevanlinna later accepted a position at the University of Union in 1952, five IMU presidents were active in Switzerland: Zurich). Heinz Hopf, Rolf Nevanlinna, Georges de Rham, Komaravolu Born near Breslau, Hopf wrote his thesis in 1925 in Berlin Chandrasekharan, and Ju¨rgen Moser. More recently Jeltsch under Bieberbach. He spent the year after his doctorate at was president of the European Mathematical Society. Go¨ttingen where he met Paul Alexandrov and began a life- Today, some nontraditional activities, such as developing long friendship. He then stayed for the academic year 1927 to links with high-schools, are emerging. However, the SMS is a 1928 with Alexandrov at Princeton University, on a Rocke- small society with a very small administration. Its success feller fellowship. Solomon Lefschetz, Oswald Veblen, and depends largely on the personal commitment of its members. James W. Alexander were all at Princeton at the time. Back in The golden age of Swiss mathematics, with the Bernoullis Berlin, Hopf began working with Alexandrov, at the sug- and Euler, was the eighteenth century.