Henryk Iwaniec
Encyclopedia
Henryk Iwaniec is a Polish American
mathematician
, and since 1987 a professor at Rutgers University
. He was awarded the fourteenth Frank Nelson Cole Prize in Number Theory
in 2002. He received the Leroy P. Steele Prize for Mathematical Exposition in 2011.
, where he got his Ph.D.
in 1972 under Andrzej Schinzel
. He then held positions at the Institute of Mathematics of the Polish Academy of Sciences
until 1983 when he left Poland. He held visiting positions at the Institute for Advanced Study
, University of Michigan
, and University of Colorado at Boulder
before being appointed Professor of Mathematics at Rutgers University
. He is a citizen of both Poland and the United States.
In 1997, Iwaniec and John Friedlander
proved that there are infinitely many prime number
s of the form
. Results of this strength had previously been seen as completely out of reach: sieve theory—used by Iwaniec and Friedlander in combination with other techniques—cannot usually distinguish between primes and products of two primes, say.
In 2001 Iwaniec was awarded the seventh Ostrowski Prize
. The prize citation read, in part, "Iwaniec's work is characterized by depth, profound understanding of the difficulties of a problem, and unsurpassed technique. He has made deep contributions to the field of analytic number theory
, mainly in modular form
s on GL(2) and sieve methods
."
Polish American
A Polish American , is a citizen of the United States of Polish descent. There are an estimated 10 million Polish Americans, representing about 3.2% of the population of the United States...
mathematician
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....
, and since 1987 a professor at Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
. He was awarded the fourteenth Frank Nelson Cole Prize in Number Theory
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
in 2002. He received the Leroy P. Steele Prize for Mathematical Exposition in 2011.
Background and education
Iwaniec studied at the University of WarsawUniversity of Warsaw
The University of Warsaw is the largest university in Poland and one of the most prestigious, ranked as best Polish university in 2010 and 2011...
, where he got his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1972 under Andrzej Schinzel
Andrzej Schinzel
Andrzej Bobola Maria Schinzel is a Polish mathematician, studying mainly number theory.- Biography :Schinzel received his Ph.D...
. He then held positions at the Institute of Mathematics of the Polish Academy of Sciences
Polish Academy of Sciences
The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...
until 1983 when he left Poland. He held visiting positions 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...
, University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, and University of Colorado at Boulder
University of Colorado at Boulder
The University of Colorado Boulder is a public research university located in Boulder, Colorado...
before being appointed Professor of Mathematics at Rutgers University
Rutgers University
Rutgers, The State University of New Jersey , is the largest institution for higher education in New Jersey, United States. It was originally chartered as Queen's College in 1766. It is the eighth-oldest college in the United States and one of the nine Colonial colleges founded before the American...
. He is a citizen of both Poland and the United States.
Work
Iwaniec is well-known for his proficiency in both sieve methods and deep complex-analytic techniques, with a particular emphasis on the theory of automorphic forms and harmonic analysis.In 1997, Iwaniec and John Friedlander
John Friedlander
John Benjamin Friedlander is a Canadian mathematician specializing in analytic number theory. He received his B.Sc. from the University of Toronto in 1965, an M.A. from the University of Waterloo in 1966, and a Ph.D. from Pennsylvania State University in 1972. He was a lecturer at M.I.T...
proved that there are infinitely many 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 of the form
. Results of this strength had previously been seen as completely out of reach: sieve theory—used by Iwaniec and Friedlander in combination with other techniques—cannot usually distinguish between primes and products of two primes, say.In 2001 Iwaniec was awarded the seventh Ostrowski Prize
Ostrowski Prize
The Ostrowski Prize is a mathematics award given every other year by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands...
. The prize citation read, in part, "Iwaniec's work is characterized by depth, profound understanding of the difficulties of a problem, and unsurpassed technique. He has made deep contributions to the field of analytic number theory
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 Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
, mainly in modular form
Modular form
In mathematics, a modular form is a analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections...
s on GL(2) and sieve methods
Sieve theory
Sieve theory is a set of general techniques in number theory, designed to count, or more realistically to estimate the size of, sifted sets of integers. The primordial example of a sifted set is the set of prime numbers up to some prescribed limit X. Correspondingly, the primordial example of a...
."