He then held positions at the Institute of Mathematics of the Polish Academy of Sciences until 1983 when he left Poland.

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

[5] 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 forms on GL(2) and sieve methods.

[7] In 2017, he was awarded the AMS Doob Prize (jointly with John Friedlander) for their book Opera de Cribro, which is about sieve theory.