Henryk Iwaniec (born October 9, 1947) is a

Polish-American Polish Americans ( pl, Polonia amerykańska) are Americans who either have total or partial Poles, Polish ancestry, or are citizens of the Republic of Poland. There are an estimated 9.15 million self-identified Polish Americans, representing abou ...

mathematician, and since 1987 a professor at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...

Background and education

Iwaniec studied at the

University of Warsaw The University of Warsaw ( pl, Uniwersytet Warszawski, la, Universitas Varsoviensis) is a public university in Warsaw, Poland. Established in 1816, it is the largest institution of higher learning in the country offering 37 different fields of ...

, where he got his PhD in 1972 under Andrzej Schinzel. He then held positions at the Institute of Mathematics of the

Polish Academy of Sciences The Polish Academy of Sciences ( pl, Polska Akademia Nauk, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of ...

until 1983 when he left Poland. He held visiting positions 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 ...

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

, and

University of Colorado Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University of Colorado syst ...

before being appointed Professor of Mathematics at

. He is a citizen of both Poland and the United States. He and mathematician

Tadeusz Iwaniec Tadeusz Iwaniec (born October 9, 1947 in Elbląg) is a Polish-American mathematician, and since 1996 John Raymond French Distinguished Professor of Mathematics at Syracuse University.

are twin brothers.

Work

Iwaniec studies both sieve methods and deep complex-analytic techniques, with an emphasis on the theory of

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of ...

s and

harmonic analysis Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fo ...

. In 1997, Iwaniec and

John Friedlander John 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 i ...

proved that there are infinitely many

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 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 Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Alexan ...

."Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize"
/ref> 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 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 ...

, mainly in

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

s on and sieve methods."

Awards and honors

He became a fellow of the American Academy of Arts and Sciences in 1995. He was awarded the fourteenth Frank Nelson Cole Prize in Number Theory in 2002. In 2006, he became a member of the National Academy of Science. He received the

Leroy P. Steele Prize The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories. The prizes have b ...

for Mathematical Exposition in 2011. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. In 2015 he was awarded the Shaw Prize in Mathematics. In 2017 he was awarded the AMS Doob Prize (jointly with John Friedlander) for their book ''Opera de Cribro'', which is about

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 prototypical example of a sifted set is the set of prime numbers up to some prescribed lim ...

Publications

* * * * * *

References

External links

* * {{DEFAULTSORT:Iwaniec, Henryk People from Elbląg 20th-century Polish mathematicians 21st-century Polish mathematicians Number theorists Institute for Advanced Study visiting scholars Rutgers University faculty Living people 1947 births Members of the United States National Academy of Sciences Fellows of the American Mathematical Society International Mathematical Olympiad participants University of Michigan people Recipients of the State Award Badge (Poland) Polish twins