He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang (resp. Eventually the adelic approach became basic in automorphic representation theory. The Weil conjecture on Tamagawa numbers proved resistant for many years. His 'matrix divisor' ( vector bundle avant la lettre) Riemann–Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. Weil introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and gave a proof of the Riemann–Roch theorem with them (a version appeared in his Basic Number Theory in 1967). The so-called Weil conjectures were hugely influential from around 1950 these statements were later proved by Bernard Dwork, Alexander Grothendieck, Michael Artin, and finally by Pierre Deligne, who completed the most difficult step in 1973. Both aspects of Weil's work have steadily developed into substantial theories.Īmong his major accomplishments were the 1940s proof of the Riemann hypothesis for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). Mordell's theorem had an ad hoc proof Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which would not be categorized as such for another two decades. This began in his doctoral work leading to the Mordell–Weil theorem (1928, and shortly applied in Siegel's theorem on integral points). Weil made substantial contributions in a number of areas, the most important being his discovery of profound connections between algebraic geometry and number theory. In 1979, he shared the second Wolf Prize in Mathematics with Jean Leray. Weil was elected Foreign Member of the Royal Society in 1966. He was a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts, in 1954 in Amsterdam, and in 1978 in Helsinki. He then returned to the United States and taught at the University of Chicago from 1947 to 1958, before moving to the Institute for Advanced Study, where he would spend the remainder of his career. Weil and his wife had two daughters, Sylvie (born in 1942) and Nicolette (born in 1946). He quit the job at Lehigh and moved to Brazil, where he taught at the Universidade de São Paulo from 1945 to 1947, working with Oscar Zariski. For two years, he taught undergraduate mathematics at Lehigh University, where he was unappreciated, overworked and poorly paid, although he did not have to worry about being drafted, unlike his American students. He spent the remainder of the war in the United States, where he was supported by the Rockefeller Foundation and the Guggenheim Foundation. In January 1941, Weil and his family sailed from Marseille to New York. He then went to Clermont-Ferrand, where he managed to join his wife Éveline, who had been living in German-occupied France. After the fall of France in June 1940, he met up with his family in Marseille, where he arrived by sea. Sentenced to five years, he requested to be attached to a military unit instead, and was given the chance to join a regiment in Cherbourg. It was in the military prison in Bonne-Nouvelle, a district of Rouen, from February to May, that Weil completed the work that made his reputation.
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He was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen. Weil returned to France via Sweden and the United Kingdom, and was detained at Le Havre in January 1940. Weil was mistakenly arrested in Finland at the outbreak of the Winter War on suspicion of spying however, accounts of his life having been in danger were shown to be exaggerated.
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His wife Éveline returned to France without him. Weil was in Finland when World War II broke out he had been traveling in Scandinavia since April 1939. He married Éveline de Possel (née Éveline Gillet) in 1937. After teaching for one year at Aix-Marseille University, he taught for six years at University of Strasbourg. Aside from mathematics, Weil held lifelong interests in classical Greek and Latin literature, in Hinduism and Sanskrit literature: he had taught himself Sanskrit in 1920. Starting in 1930, he spent two academic years at Aligarh Muslim University in India. While in Germany, Weil befriended Carl Ludwig Siegel. He studied in Paris, Rome and Göttingen and received his doctorate in 1928. Simone Weil, who would later become a famous philosopher, was Weil's younger sister and only sibling.
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André Weil was born in Paris to agnostic Alsatian Jewish parents who fled the annexation of Alsace-Lorraine by the German Empire after the Franco-Prussian War in 1870–71.