BOMBIERI, ENRICO

born Nov. 26, 1940, Milan, Italy Italian mathematician who was awarded the Fields Medal in 1974 for his work in number theory. Between 1979 and 1982 Bombieri served on the executive committee of the International Mathematical Union. Bombieri received a Ph.D. from the University of Milan in 1963. He held appointments at the University of Pisa (196673) and the Scuola Normale Superiore in Pisa (1974 ) and held the IBM von Neumann Chair at the Institute for Advanced Study, Princeton, N.J., U.S. Bombieri was awarded the Fields Medal at the International Congress of Mathematicians in Vancouver, B.C., Can., in 1974. His work leading up to the Fields Medal spanned a wide range of mathematical fields. One of his most notable achievements was his theorem on the distribution of primes in arithmetical progressions. This work has its origin in Goldbach's famous conjecture, as yet unproved, that every even integer greater than four can be written as the sum of two odd primes. In 1920 Viggo Brun introduced a sieve method to prove that every sufficiently large even integer is a sum of two integers, each of which has no more than nine prime factors. Ivan Vinogradov proved in 1937 that every sufficiently large odd integer is a sum of three primes; Yury Linnik proved in 1961 that every sufficiently large integer is the sum of a prime and two squares; and J. Chen showed in 1967 that every sufficiently large even integer is a sum of a prime and an integer with at most two prime factors. In 1950 Alfrd Rnyi proved an inequality demonstrating that every sufficiently large even integer is the sum of a prime and an integer that is the product of a bounded number of prime factors. Bombieri extended Rnyi's work, developing a density theorem that allowed him to prove his results on the primes in arithmetic progressions and to treat problems like those listed above, where earlier proofs had required the assumption of the extended Riemann hypothesis or other powerful means from analytic number theory. In addition Bombieri's interests included quasi-crystal tilings, meromorphic maps, the theory of univalent functions, the theory of partial differential equations, minimal surfaces, combinatorics, and complexity theory. Bombieri's publications include Geometric Measure Theory and Minimal Surfaces (1973), Le Grand Crible dans la thorie analytique des nombres (1974; The Large Sieve in Analytic Number Theory), Seminar on Minimal Submanifolds (1983), An Introduction to Minimal Currents and Parametric Variational Problems (1985), and Number Theory, Trace Formulas, and Discrete Groups (1989).