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 h ...

) 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 Diric ...

Diophantine geometry In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study ...

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 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), 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 scholar ...

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 whi ...

. 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 ho ...

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 The University of Milan ( it, Università degli Studi di Milano; la, Universitas Studiorum Mediolanensis), known colloquially as UniMi or Statale, is a public research university in Milan, Italy. It is one of the largest universities in Europe ...

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 Henry VIII, King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge ...

with

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar Scho ...

. 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 1810 wi ...

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 by ...

, e.g. for serving on external review boards and for peer-reviewing extraordinarily complicated manuscripts (like the paper of

Per Enflo Per H. Enflo (; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved mathematical problems, problems that had been considered fundamental. Three of these problems had been open problem, ...

on the

invariant subspace problem In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some non-trivial closed subspace to itself. Many vari ...

Research

The

Bombieri–Vinogradov theorem In mathematics, the Bombieri–Vinogradov theorem (sometimes simply called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averaged over a ...

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 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 because the only ways ...

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 The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global ''L''-functions, whic ...

. In 1969 Bombieri, De Giorgi, and Giusti solved

Bernstein's problem In differential geometry, Bernstein's problem is as follows: if the graph of a function on R''n''−1 is a minimal surface in R''n'', does this imply that the function is linear? This is true in dimensions ''n'' at most 8, but false in dimens ...

. 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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

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, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

have earned him many international prizes — a

in 1974 and the Balzan Prize 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 of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

(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 Nati ...

(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 The King Faisal Prize ( ar, جائزة الملك فيصل, formerly King Faisal International Prize), is an annual award sponsored by King Faisal Foundation presented to "dedicated men and women whose contributions make a positive difference". T ...

(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 The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...

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