Enrico Bombieri
Encyclopedia
Enrico Bombieri is a mathematician
who has been working at the Institute for Advanced Study
in Princeton, New Jersey
. Bombieri's research in number theory
, algebraic geometry
, and mathematical analysis
have earned him many international prizes --- a Fields Medal
in 1974 and the Balzan Prize
in 1980. In 2010 he received the King Faisal International Prize (jointly with Terence Tao
).
The Bombieri–Vinogradov theorem
is one of the major applications of the large sieve method. It improves Dirichlet's theorem
on prime number
s in arithmetic progression
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 1976, he developed the technique known as the "asymptotic sieve".
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 papers of John Nash on embedding Riemannian manifolds
and of Per Enflo
on the invariant subspace problem).
Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who has been working at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
. Bombieri's research in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, and mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
have earned him many international prizes --- a Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1974 and the Balzan Prize
Balzan Prize
The International Balzan Prize Foundation awards four annual monetary prizes to people or organisations who have made outstanding achievements in the fields of humanities, natural sciences, culture, as well as for endeavours for peace and the brotherhood of man.-Rewards and assets:Each year the...
in 1980. In 2010 he received the King Faisal International Prize (jointly with Terence Tao
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
).
The Bombieri–Vinogradov theorem
Bombieri–Vinogradov theorem
In mathematics, the Bombieri–Vinogradov theorem is a major result of analytic number theory, obtained in the mid-1960s. The first result of this kind was obtained by Barban in 1961 and the Bombieri–Vinogradov theorem is a refinement of Barban's result. The Bombieri-Vinogradov theorem is named...
is one of the major applications of the large sieve method. It improves Dirichlet's theorem
Dirichlet's theorem on arithmetic progressions
In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n ≥ 0. In other words, there are infinitely many primes which are...
on prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s in arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
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
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, which are formally similar to the Riemann zeta-function...
.
In 1976, he developed the technique known as the "asymptotic sieve".
Bombieri is also known for his pro bono
Pro bono
Pro bono publico is a Latin phrase generally used to describe professional work undertaken voluntarily and without payment or at a reduced fee as a public service. It is common in the legal profession and is increasingly seen in marketing, technology, and strategy consulting firms...
service on behalf of the mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
profession
Profession
A profession is a vocation founded upon specialized educational training, the purpose of which is to supply disinterested counsel and service to others, for a direct and definite compensation, wholly apart from expectation of other business gain....
, e.g. for serving on external review boards and for peer-reviewing
Peer review
Peer review is a process of self-regulation by a profession or a process of evaluation involving qualified individuals within the relevant field. Peer review methods are employed to maintain standards, improve performance and provide credibility...
extraordinarily complicated manuscripts (like the papers of John Nash on embedding Riemannian manifolds
Nash embedding theorem
The Nash embedding theorems , named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path...
and of Per Enflo
Per Enflo
Per H. Enflo is a mathematician who has solved fundamental problems in functional analysis. Three of these problems had been open for more than forty years:* The basis problem and the approximation problem and later...
on the invariant subspace problem).
Bombieri, accomplished also in the arts, explored for wild orchids and other plants as a hobby in the Alps when a young man.
See also
- Bombieri normBombieri normIn mathematics, the Bombieri norm, named after Enrico Bombieri, is a norm on homogeneous polynomials with coefficient in \mathbb R or \mathbb C...
- Bombieri-Lang conjecture
- Bombieri–Vinogradov theoremBombieri–Vinogradov theoremIn mathematics, the Bombieri–Vinogradov theorem is a major result of analytic number theory, obtained in the mid-1960s. The first result of this kind was obtained by Barban in 1961 and the Bombieri–Vinogradov theorem is a refinement of Barban's result. The Bombieri-Vinogradov theorem is named...