Weil, André

Weil (vā), André. 1906-1998.

French mathematician who influenced the development of modern number theory and algebraic geometry.

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▪ 1999

      French mathematician (b. May 6, 1906, Paris, France—d. Aug. 6, 1998, Princeton, N.J.), greatly influenced the course of mathematical research in the 20th century, most notably with his conjectures, in which he formulated the foundations of modern algebraic geometry. Weil developed an interest in numbers at an early age. He earned a Ph.D. (1928) from the University of Paris and accepted his first academic position as professor of mathematics (1930-32) at the Aligarh Muslim University in India. He then moved to the University of Strasbourg, France, and there (1933-40) Weil and a number of French mathematicians formed Nicolas Bourbaki, a group somewhat mischievously named after an imaginary Russian general. The Bourbaki group took on the responsibility of synthesizing the content of all major areas of mathematics, work that was published as a series of encyclopedic volumes called Éléments d'histoire des mathématiques. At the outbreak of World War II, Weil, a conscientious objector, fled to Finland to avoid the draft. He was sent back to France, however, and spent about six months in a French prison, a dangerous place for the son of Jewish parents and the brother of the mystic philosopher and French Resistance activist Simone Weil. While imprisoned, Weil formulated the Riemann hypothesis, which was named for a German mathematician and became a fundamental element of number theory. To secure his release, he joined the French army but later managed to move to the United States, where he taught at Swarthmore and Haverford colleges in Pennsylvania. In 1945 Weil accepted a position at the University of São Paulo, Brazil, and in 1947 returned to the U.S. to serve (1947-58) on the faculty at the University of Chicago. From 1958 until his retirement in 1976, Weil taught at the Institute for Advanced Study, Princeton, N.J. In 1994 he was awarded the Kyoto Prize in Basic Science from the Inamori Foundation of Kyoto, Japan, for his lifelong contribution to mathematics.

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▪ French mathematician

born May 6, 1906, Paris, France

died August 6, 1998, Princeton, New Jersey, 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.

      André was the brother of the philosopher and mystic Simone Weil (Weil, Simone). He studied at the École Normale Supérieure (now part of the Universities of Paris (Paris I–XIII, Universities of)) and at the Universities of Rome and Göttingen, 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 (1930–32), and thereafter taught at the University of Strasbourg, France (1933–40), the University of São Paulo, Brazil (1945–47), and the University of Chicago (1947–58). He joined the Institute for Advanced Study, Princeton, New Jersey, U.S., in 1958, becoming professor emeritus in 1976. He was also a gifted linguist who read Sanskrit and many other languages, and he was a sympathetic expert on Indian religious writings.

      Beginning in the mid 1930s, as one of the founding members of a group of French mathematicians writing under the collective pseudonym Nicolas Bourbaki (Bourbaki, Nicolas), Weil worked and inspired others in the effort to achieve David Hilbert's (Hilbert, David) program of unifying all of mathematics upon a rigorous axiomatic (axiomatic method) basis and directed to the solution of significant problems. Weil and Jean Dieudonné (Dieudonné, Jean) were chiefly responsible for Bourbaki's interest in the history of mathematics (mathematics), and Weil wrote on it extensively toward the end of his career.

      Weil made fundamental contributions to algebraic geometry—at that time a subject mostly contributed to by members of the “Italian school” but being reformulated along algebraic lines by Bartel van der Waerden and Oscar Zariski—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 variant of the Riemann hypothesis (Riemann zeta function) for algebraic curves while interned in Rouen, France, in 1940 for his deliberate failure, as a pacifist, 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 Weil conjectures generated many new ideas in algebraic topology. Their importance can be gauged by the fact that the Belgian mathematician Pierre Deligne (Deligne, Pierre René) was awarded a Fields Medal in 1978 in part for having proved one of the conjectures. The Weil conjectures have recently had ramifications in cryptology, computer modeling, data transmission, and other fields.

      Weil's published works include Foundations of Algebraic Geometry (1946) and his autobiography, Souvenirs d'apprentissage (1992, The Apprenticeship of a Mathematician). The three volumes of his Oeuvres scientifiques (Collected Papers) were published in 1980.

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