Enrico Bombieri (born 26 November 1940,

Milan Milan ( , , Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4 million, while its metropolitan city ...

) 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, structure, space, models, and change. History On ...

, 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 Diri ...

, 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 Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

, and

group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...

. Bombieri is currently Professor Emeritus in the School of Mathematics at the

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

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of w ...

. Bombieri won the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

in 1974 for his contributions to large sieve mathematics, conceptualized by Linnick 1941, and its application to the distribution of prime numbers.

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 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 college at either Cambridge or Oxford. ...

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 The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...

in 1966–1974, and then at the

Scuola Normale Superiore di Pisa The Scuola Normale Superiore in Pisa (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. It was founded in 181 ...

in 1974–1977. From Pisa he emigrated in 1977 to the USA, 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 ( en, 'for the public good'), usually shortened to , is a Latin phrase for professional work undertaken voluntarily and without payment. In the United States, the term typically refers to provision of legal services by legal professionals for pe ...

'' service on behalf of the

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

profession A profession is a field of 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 accepted b ...

, 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 The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein onl ...

. It improves Dirichlet's theorem on

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 ...

s in

arithmetic progression An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common differ ...

s, 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".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.

Awards

Bombieri's research in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied ...

have earned him many international prizes — a

in 1974 and the

Balzan Prize The International Balzan Prize Foundation awards four annual monetary prizes to people or organizations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the br ...

in 1980. He was a plenary speaker at the International Congress of Mathematicians in 1974 at Vancouver. He is a member, or foreign member, of several learned academies, including the

Accademia Nazionale dei Lincei The Accademia dei Lincei (; literally the "Academy of the Lynx-Eyed", but anglicised as the Lincean Academy) is one of the oldest and most prestigious European scientific institutions, located at the Palazzo Corsini on the Via della Lungara in Rom ...

(elected 1976), the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des 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 research. It was at ...

(elected 1984), and the

United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the N ...

(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 Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

). and in 2020 he was awarded the Crafoord Prize 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 PDE theorists Scientists from Milan University of Milan alumni Members of the Royal Swedish Academy of Sciences