Henryk Iwaniec (born October 9, 1947) is a

Polish-American Polish Americans () are Americans who either have total or partial Polish ancestry, or are citizens of the Republic of Poland. There are an estimated 8.81 million self-identified Polish Americans, representing about 2.67% of the U.S. population, ...

mathematician, and since 1987 a professor at

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

. He is a member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

and

Polish Academy of Sciences The Polish Academy of Sciences (, 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 distinguished scholars a ...

. He has made important contributions to analytic and

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

as well as

harmonic analysis Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency. The frequency representation is found by using the Fourier transform for functions on unbounded do ...

. He is the recipient of

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-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 numbe ...

(2002), Steele Prize (2011), and Shaw Prize (2015).

Background and education

Iwaniec studied at the

University of Warsaw The University of Warsaw (, ) is a public university, public research university in Warsaw, Poland. Established on November 19, 1816, it is the largest institution of higher learning in the country, offering 37 different fields of study as well ...

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

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

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

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

, and

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

before being appointed Professor of Mathematics at

. He is a citizen of both Poland and the United States. He and mathematician Tadeusz Iwaniec are twin brothers.

Work

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

. In 1997, Iwaniec and John Friedlander 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 (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 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. He also showed that there are infinitely many numbers of the form

n^2+1

with at most two prime factors. In 2001, Iwaniec was awarded the seventh Ostrowski Prize."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 Dir ...

, mainly in

modular form In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modul ...

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 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 limi ...

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