Enrico Bombieri, Fields Medal 1974

Enrico Bombieri (born 26 November 1940 in Milan) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. He won a Fields Medal in 1974. Bombieri is currently Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.

Career

Bombieri published his first mathematical paper in 1957 when he was 16 years old. In 1963 at age 22 he earned his first degree (Laurea) in mathematics from the Università degli Studi di Milano under the supervision of Giovanni Ricci and then studied at Trinity College, Cambridge with Harold Davenport.

Bombieri was an assistant professor (1963–1965) and then a full professor (1965–1966) at the Università di Cagliari, at the Università di Pisa in 1966–1974, and then at the Scuola Normale Superiore di Pisa in 1974–1977. From Pisa he emigrated in 1977 to the USA, where he became a professor at the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey. In 2011 he became professor emeritus.

Bombieri is also known for his pro bono service on behalf of the mathematics profession, e.g. for serving on external review boards and for peer-reviewing extraordinarily complicated manuscripts (like the paper of Per Enflo on the invariant subspace problem).

Research

The Bombieri–Vinogradov theorem is one of the major applications of the large sieve method. It improves Dirichlet's theorem on prime numbers in arithmetic progressions, by showing that by averaging over the modulus over a range, the mean error is much less than can be proved in a given case. This result can sometimes substitute for the still-unproved generalized Riemann hypothesis.

In 1969 Bombieri, De Giorgi, and Giusti solved Bernstein's problem.

In 1976, Bombieri developed the technique known as the "asymptotic sieve". In 1980 he supplied the completion of the proof of the uniqueness of finite groups of Ree type in characteristic 3; at the time of its publication it was one of the missing steps in the classification of finite simple groups.

Awards

• 1966, Caccioppoli Prize
• 1974, Fields Medal
• 1976, Feltrinelli Prize
• 1980, Balzan Prize
• 2006, Pythagoras Prize
• 2008, Joseph L. Doob Prize
• 2010, King Faisal International Prize
• 2020, Crafoord Prize