Enrico Bombieri (born 26 November 1940) is an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, known for his work in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dir ...

, Diophantine geometry,

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

, and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

. Bombieri is currently professor emeritus in the School of Mathematics at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

Princeton, New Jersey The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Pri ...

. Bombieri won the Fields Medal in 1974 for his work on the large sieve and its application to the distribution of

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

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 Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, 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 The Scuola Normale Superiore (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. Together with the University of Pi ...

in 1974–1977. From Pisa, he emigrated in 1977 to the United States, where he became a professor at the School of Mathematics at the

. In 2011, he became professor emeritus. Bombieri is also known for his '' pro bono'' service on behalf of the

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

profession A profession is a field of Work (human activity), work that has been successfully professionalized. It can be defined as a disciplined group of individuals, professionals, who adhere to ethical standards and who hold themselves out as, and are ...

, 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 on minimal surfaces in dimensions above eight. In 1976, Bombieri developed the technique known as the "asymptotic sieve".E. Bombieri, "The asymptotic sieve", '' Mem. Acad. Naz. dei XL'', 1/2 (1976) 243–269. 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 In mathematics, the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that every List of finite simple groups, finite simple group is either cyclic group, cyclic, or alternating gro ...

Awards

Bombieri's research in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series ( ...

has earned him many international prizes — a Fields Medal in 1974 and the Balzan Prize in 1980. He was a plenary speaker at the International Congress of Mathematicians, which took place in 1974 in

Vancouver Vancouver is a major city in Western Canada, located in the Lower Mainland region of British Columbia. As the List of cities in British Columbia, most populous city in the province, the 2021 Canadian census recorded 662,248 people in the cit ...

. He is a member, or foreign member, of several learned academies, including the Accademia Nazionale dei Lincei (elected 1976), the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

(elected 1984), the

Academia Europaea The Academia Europaea is a pan-European Academy of humanities, letters, law, and sciences. The Academia was founded in 1988 as a functioning Europe-wide Academy that encompasses all fields of scholarly inquiry. It acts as co-ordinator of Europe ...

(elected 1995), and the United States National Academy of Sciences (elected 1996). In 2002 he was made ''Cavaliere di Gran Croce al Merito della Repubblica Italiana''. In 2010, he received the King Faisal International Prize (jointly with Terence Tao). and in 2020 he was awarded the

Crafoord Prize The Crafoord Prize () is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord following a donation to the Royal Swedish Academy of Sciences. It is awarded jointly by the Acade ...

in Mathematics.

Other interests

Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.Bombieri – Mathematician
retrieved 10 February 2020

Selected publications

Sole

* E. Bombieri, ''Le Grand Crible dans la Théorie Analytique des Nombres'' (Seconde Édition). Astérisque 18, Paris 1987.

Joint

* * * B. Beauzamy, E. Bombieri, P. Enflo and H. L. Montgomery. "Product of polynomials in many variables", ''Journal of Number Theory'', pages 219–245, 1990.

References

Sources

* * * E. Bombieri, ''Le Grand Crible dans la Théorie Analytique des Nombres'' (Seconde Édition). Astérisque 18, Paris 1987. * B. Beauzamy, E. Bombieri, P. Enflo and H. L. Montgomery. "Product of polynomials in many variables", ''Journal of Number Theory'', pages 219–245, 1990. * *

External links

* *
Enrico Bombieri, Institute for Advanced Study
{{DEFAULTSORT:Bombieri, Enrico 20th-century Italian mathematicians 21st-century Italian mathematicians 1940 births Fields Medalists Institute for Advanced Study faculty Living people Members of the French Academy of Sciences Members of the United States National Academy of Sciences Number theorists Partial differential equation theorists Scientists from Milan University of Milan alumni Alumni of Trinity College, Cambridge Members of the Royal Swedish Academy of Sciences Members of Academia Europaea