# Andre Weil

Barnard Medal for Meritorious Service to Science (1980)

Kyoto Prize (1994)

Fellow of the Royal Society

Andre Weil was a French mathematician who laid the foundation of number theory and algebraic geometry. He was also a gifted linguist who read Sanskrit and many other languages, and was a sympathetic expert on Indian religious writings. He was a child prodigy and was drawn towards mathematics at a very young age. His interest met with full support from his family and he decided to pursue it as his profession. His mathematical genius is evident from his research on wide variety of subjects such as algebra, number theory, algebraic geometry, differential geometry, topology, Lie groups and Lie algebras. His most important achievement was the discovery of profound connections between algebraic geometry and the number theory. He was also fond of traveling and linguistics, with a deep respect for all the religions, especially Hinduism. During his stay in India, he was spiritually enlightened, an experience which stayed with him until the end. He also faced imprisonment for neglecting his duties in the French Army but was released after a while. He served as the professor of mathematics, throughout his life, in numerous universities around the world. His life was dedicated to mathematical study and he is counted among one of the most brilliant and influential mathematicians of the 20th century.

**Childhood & Early Life**

- He was born on May 6, 1906 in Paris, France, to Bernard Bernhard Weil, a medical doctor and his wife, Salomea Reinherz. He had a younger sister, Simone Adolphine Weil, who later became a famous philosopher.
- By the age of 10, he developed a keen interest in mathematics. He was also passionate about traveling and studying different languages.
- He was religious from an early age and by the age of 16, he had read the "Bhagavad Gita" in the original Sanskrit.
- In 1925–26 he studied algebraic geometry of Italian mathematicians while in Rome.
- He traveled to Germany for his fellowship at Göttingen, where he studied the number theory of German mathematicians.
- He went on to receive his D.Sc. from the University of Paris in 1928. His doctoral thesis consisted of solving a problem concerning elliptic curves that had been proposed by Henri Poincaré.
- In 1928–29, he completed his compulsory military service and left as a lieutenant in the reserves.

**Career**

- For his first job as a professor, he traveled to India and taught mathematics at the Aligarh Muslim University, Uttar Pradesh, from 1930 to 1932.
- After that, he returned to France and taught at the University of Marseille for a year. Then he was appointed at the University of Strasbourg, where he served from 1933 to 1940.
- In 1939, he was mistakenly arrested for spying in Finland, when the Second World War broke out, while he was wandering in Scandinavia.
- On his return to France in 1940, he was again arrested for failing to report on his duty in the French Army and was imprisoned in Le Havre and then Rouen.
- During his stay in prison, he completed his most celebrated work in mathematics—he proved the Riemann hypothesis for curves over finite fields.
- During his trial in May 1940, he volunteered to return to the army so as to avoid a five-year sentence in a French jail.
- In 1941, he was reunited with his wife and fled with her to United States, where they stayed till the end of the Second World War.
- In U.S., he served at the Rockefeller Foundation and at the Guggenheim Foundation. For two years, he taught undergraduate mathematics at Lehigh University.
- After the war, he was appointed at the University of São Paulo, Brazil where he worked from 1945 to 1947. He then taught at the University of Chicago, U.S. from 1947 to 1958.
- He spent his remaining career as a professor at the Institute for Advanced Study in Princeton, New Jersey, U.S.

**Major Works**

- During the 1930s, he introduced the adele ring, a topological ring in algebraic number theory and topological algebra, which is built on the field of rational numbers.
- One of 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.
- He also developed the Weil representation, an infinite-dimensional linear representation of theta functions which gave a contemporary framework for understanding the classical theory of quadratic forms.
- His work on algebraic curves has influenced a wide variety of areas such as, elementary particle physics and string theory.

**Awards & Achievements**

- In 1979, he was awarded the Wolf Prize in Mathematics for his “inspired introduction of algebraic-geometric methods to the theory of numbers”. This prize was shared with Jean Leray for his “pioneering work on the development and application of topological methods to the study of differential equations”.
- In 1980, he received the Barnard Medal for Meritorious Service to Science by the Columbia University for his "Meritorious Service to Science".
- He was honored with the distinguished Kyoto Prize in 1994 for his significant contribution to the scientific, cultural, and spiritual betterment of mankind.
- He was an honorary member or member of several associations, including the London Mathematical Society, the Royal Society of London, the French Academy of Sciences and the American National Academy of Sciences.

**Personal Life & Legacy**

- He married Eveline in 1937. The couple had two daughters, namely, Sylvie and Nicolette.
- He died on August 6, 1998, at the age of 92, in Princeton, New Jersey.

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