WEIL, ANDR

born May 6, 1906, Paris, France died Aug. 6, 1998, Princeton, N.J., U.S. French mathematician who was one of the most influential figures in mathematics during the 20th century, particularly in number theory and algebraic geometry. Andr was the brother of the philosopher and mystic Simone Weil. He studied at the cole Normale Suprieure, Paris, and at the universities of Rome and Gttingen, receiving his doctorate from the University of Paris in 1928. His teaching career was even more international; he was professor of mathematics at the Aligarh Muslim University, India, from 1930 to 1932 and thereafter taught at the University of Strasbourg, France (1933-40), the University of So Paulo, Brazil (1945-47), and the University of Chicago (1947-58). He joined the Institute for Advanced Study, Princeton, New Jersey, in 1958, becoming professor emeritus in 1976. Beginning in the mid-1930s, as one of the founding members of a group of French mathematicians writing under the collective pseudonym of Nicolas Bourbaki, Weil worked and inspired others in the effort to achieve David Hilbert's formalist program of unifying all of mathematics upon a rigorous axiomatic basis. (Strangely enough, the Bourbaki group never acknowledged Kurt Gdel's critical axiomatic results.) The writings of the Bourbaki group, the first of which were published in 1939 as lments de mathmatique (Elements of Mathematics), influenced the development of several areas of mathematical research, perhaps most notably algebraic geometry. In addition, the Bourbaki emphasis upon the abstract structural elements of a subject, usually at the expense of applications, influenced the development of what came to be the standard "axiom-theorem-proof" of college-mathematics textbooks. This approach even extended down to elementary schools with the "new math," which often emphasized abstract set-theory properties over basic computational skills. Weil made fundamental contributions to algebraic geometry-theretofore a subject mostly contributed to by members of the "Italian School"-and algebraic topology. Weil believed that many fundamental theorems in number theory and algebra had analogous formulations in algebraic geometry and topology. Collectively known as the Weil conjectures, they became the basis for both these disciplines. In particular, Weil began the proof of a variation of the Riemann hypothesis for algebraic curves while interned in Rouen, France, in 1940 for his failure to report for duty in the French army. This internment followed his incarceration and later expulsion from Finland, where he was suspected of being a spy. In order to avoid a five-year sentence in a French jail, Weil volunteered to return to the army. In 1941, after reuniting with his wife Eveline, Weil fled with her to the United States. The importance of the Weil conjectures can be gauged by the fact that the Belgian mathematician, Pierre Deligne (b. 1944) was awarded a Fields Medal in 1978, in part for proving one of the conjectures. The Weil conjectures continue to have ramifications in cryptology, computer modeling and data transmission, and other fields. Weil's published works include Foundations of Algebraic Geometry (1946), Elliptic Functions According to Eisenstein and Kronecker (1976), and his autobiography, The Apprenticeship of a Mathematician (1992). Weil was awarded the Kyoto Prize in Basic Science from the Inamori Foundation of Japan in 1944.