- André Weil
Infobox Scientist

name = André Weil

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birth_date = birth date|1906|5|6

birth_place =Nantes

death_date = death date and age|1998|8|6|1906|5|6

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field =Mathematics

work_institutions =Lehigh University Universidade de São Paulo University of Chicago Institute for Advanced Study

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known_for =letter theory ,algebraic geometry

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prizes =Lion Prize in Mathematics

footnotes =:André Weil "should not be confused with two other mathematicians with similar names:

*Hermann Weyl (1885-1955), "who made substantial contributions totheoretical physics andnumber theory . In 1944, he helped Weil obtain aGuggenheim fellowship .

*Andrew Wiles (1953-), "whose proof ofFermat's Last Theorem required that he prove a conjecture partly due to Weil and who, like Weil, has done important work inelliptic curve s;-----**André Weil**(May 6 ,1906 -August 6 ,1998 ) (pronounced|ɑ̃dʁe vɛj [*In English, "Weil" is pronEng|ˈveɪ "vay", while "*] ) was one of the greatestWeyl " is IPA|/ˈvaɪl/ "vial" and "Wiles" is IPA|/ˈwaɪlz/ "why-ulz". However, in Russian the names Weil and Weyl are pronounced in the same way (as IPA| [vʲejlʲ] "vail").mathematician s of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work innumber theory andalgebraic geometry . He was a founding member and the "de facto" early leader of the influentialBourbaki group . Thephilosopher Simone Weil was his sister.**Life**Born in

Paris to AlsatianJew ish parents who fled the annexation ofAlsace-Lorraine toGermany , Weil studied in Paris,Rome andGöttingen and received his doctorate in 1928. While in Germany, he befriendedCarl Ludwig Siegel . He spent two academic years atAligarh Muslim University from 1930.Sanskrit literature was a life-long interest. After one year inMarseille , he taught six years inStrasbourg . He married Eveline in 1937.Weil was in

Finland whenWorld War II broke out; he had been traveling in Scandinavia since April 1939. Eveline returned to France without him. The following anecdote is taken from hisautobiography : after having been arrested under suspicion ofespionage in Finland, when the USSR attacked on30 November 1939 , he was saved from being shot only by the intervention ofRolf Nevanlinna . This is the version that Nevanlinna propagated after the war. However, such a story is a bit too good to be true. In 1992, the Finnish mathematicianOsmo Pekonen went to the archives to check the facts. Based on the documents, he established that Weil was not really going to be shot, even if he was under arrest, and that Nevanlinna probably didn't do - and didn't need to do - anything to save him. Pekonen published a paper [*Osmo Pekonen: "L'affaire Weil à Helsinki en 1939", Gazette des mathématiciens 52 (avril 1992), pp. 13—20. With an afterword by André Weil.*] on this with an afterword by André Weil himself. Nevanlinna's motivation for concocting such a story of himself as the rescuer of a famous Jewish mathematician probably was the fact that he had been a Nazi sympathizer during the war. The story also appears in Nevanlinna's autobiography, published in Finnish, but the dates don't match with real events at all. It is true, however, that Nevanlinna housed Weil in the summer of 1939 at his summer residence Korkee atLohja in Finland - and offeredHitler 'sMein Kampf as bedside reading. Weil signed 'Bourbaki ' in Nevanlinna's guestbook.Weil returned to France via Sweden and the United Kingdom, and was detained at

Le Havre in January 1940. He was charged with failure to report for duty, and was imprisoned in Le Havre and thenRouen . It was in the military prison in Bonne-Nouvelle, a district of Rouen, from February to May, that he did the work that made his reputation. He was tried onMay 3 1940 . Sentenced to five years, he asked to be sent to a military unit instead, and joined a regiment in Cherbourg. After thefall of France , he met up with his family in Marseille, where he arrived by sea. He then went toClermont-Ferrand , where he managed to join Eveline, who had been in German-occupied France.In January 1941, Weil and his family sailed from

Marseille to New York. He spent the war in the United States, where he was supported by theRockefeller Foundation andGuggenheim Foundation . For two years, he unhappily taught undergraduate mathematics atLehigh University . He taught at theUniversidade de São Paulo , 1945-47, where he worked withOscar Zariski . He taught at theUniversity of Chicago from 1947 to 1958, before spending the remainder of his career at theInstitute for Advanced Study . In 1979, he shared the secondWolf Prize in Mathematics .**Work**He made substantial contributions in many areas, the most important being his discovery of profound connections between

algebraic geometry andnumber theory . This began in his doctoral work leading to theMordell-Weil theorem (1928, and shortly applied inSiegel's theorem on integral points ).Mordell's theorem had an "ad hoc" proof; Weil began the separation of theinfinite descent argument into two types of structural approach, by means ofheight function s for sizing rational points, and by means ofGalois cohomology , which was not to be clearly named as that for two more decades. Both aspects have steadily developed into substantial theories.Among his major accomplishments were the 1940 proof, while in prison, of the

Riemann hypothesis forlocal zeta-function s, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). By modern standards his claim to have a proof had a very easy ride, but wartime conditions were one factor, and the fact that the German experts made little or no comment another. The so-calledWeil conjectures were hugely influential from around 1950; they were later proved byBernard Dwork ,Alexander Grothendieck ,Michael Artin , andPierre Deligne , who completed the most difficult step in 1973.He had introduced the

adele ring in the late 1930s, followingClaude Chevalley 's lead with theidele s, and given a proof of theRiemann-Roch theorem with them (a version appeared in his "Basic Number Theory" in 1967). His 'matrix divisor' (vector bundle "avant le jour") Riemann-Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. TheWeil conjecture on Tamagawa numbers proved resistant for many years. Eventually the adelic approach became basic inautomorphic representation theory. He picked up another credited "Weil conjecture", around 1970, which later under pressure fromSerge Lang became known as theTaniyama-Shimura conjecture based on the presentation of the basic ideas at the 1955 Nikkō conference. His attitude towards conjectures struck many in the field as oblique; he wrote that one should not dignify a guess as a conjecture lightly, and in the Shimura-Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.Other significant results were on

Pontryagin duality anddifferential geometry . He introduced the concept ofuniform space ingeneral topology . His work onsheaf theory hardly appears in his published papers, but correspondence withHenri Cartan in the late 1940s, and reprinted in his collected papers, proved most influential.He discovered that the so-called

Weil representation , previously introduced inquantum mechanics byIrving Segal and Shale, gave a contemporary framework for understanding the classical theory ofquadratic form s. This was also a beginning of a substantial development by others, connectingrepresentation theory andtheta-function s.**As expositor**Weil's ideas made an important contribution to the writings and seminars of

Bourbaki , before and afterWorld War II . His books had an important influence on research, and exceptional situation in mathematics. (In one famous case, the influence was possibly negative:Alexander Grothendieck is said to have complained of the 'aridity' of Weil's "Foundations of Algebraic Geometry".) The style of his books is clearly demarcated from that of his research papers.He invented the notation "Ø" for the

empty set ("q.v.").**Books***"Arithmétique et géométrie sur les variétés algébriques" (1935)

*"Sur les espaces à structure uniforme et sur la topologie générale" (1937)

*"L'intégration dans les groupes topologiques et ses applications" (1940)

*"Foundations of Algebraic Geometry" (1946)

*"Sur les courbes algébriques et les variétés qui s’en déduisent" (1948)

*"Variétés abéliennes et courbes algébriques" (1948)

*"Introduction à l'étude des variétés kählériennes" (1958)

*"Discontinuous subgroups of classical groups" (1958) Chicago lecture notes

*"Basic Number Theory" (1967)

*"Dirichlet Series and Automorphic Forms, Lezioni Fermiane" (1971) Lecture Notes in Mathematics, vol. 189,

*"Essais historiques sur la théorie des nombres" (1975)

*"Elliptic Functions According to Eisenstein and Kronecker" (1976)

*"Œuvres Scientifiques, Collected Works, three volumes" (1979)

*"Number Theory for Beginners" (1979) with Maxwell Rosenlicht

*"Adeles and Algebraic Groups" (1982)

*"Number Theory: An Approach Through History From Hammurapi to Legendre" (1984)His

autobiography :

*French: "Souvenirs d’Apprentissage" (1991) ISBN 3764325003. [*http://links.jstor.org/sici?sici=0025-5572(199307)2%3A77%3A479%3C261%3AAWSD%3E2.0.CO%3B2-B Review in English*] by J. E. Cremona.

*English translation: "The Apprenticeship of a Mathematician" (1992), ISBN 0817626506**Quotations*** "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."

* Weil's Law of university hiring: "First rate people hire other first rate people. Second rate people hire third rate people. Third rate people hire fifth rate people."**ee also**

*Weil cohomology

*Weil conjecture disambiguation page

*Weil conjectures

*Weil conjecture on Tamagawa numbers

*Weil distribution

*Weil divisor

*Siegel-Weil formula

*Weil group ,Weil-Deligne group scheme

*Weil-Châtelet group

*Chern-Weil homomorphism

*Chern-Weil theory

*Hasse-Weil L-function

*Weil pairing

*Weil reciprocity law

*Weil representation

*Borel-Weil theorem

*De Rham-Weil theorem

*Mordell-Weil theorem .**Notes****External links***

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* [*http://www.ams.org/notices/199904/index.html André Weil*] : memorial articles in the Notices of AMS byArmand Borel , Pierre Cartier,Komaravolu Chandrasekharan ,Shiing-Shen Chern , and Shokichi Iyanaga

* [*http://www.ams.org/images/weil-photo.gifImage of Weil*]

* [*http://www.ams.org/notices/200503/fea-weil.pdf A 1940 Letter of André Weil on Analogy in Mathematics*]

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