The Shaw Prize in Mathematical Sciences 2015 is awarded to Gerd Faltings, Managing Director at Max Planck Institute for Mathematics in Bonn, Germany, and Henryk Iwaniec, New Jersey Professor of Mathematics at Rutgers University, USA, for their introduction and development of fundamental tools in number theory, allowing them as well as others to resolve some longstanding classical problems.
Number theory concerns whole numbers, prime numbers, and polynomial equations involving them. The central problems are often easy to state but extraordinarily difficult to resolve. Success, when it is achieved, relies on tools from many fields of mathematics. This is no coincidence since some of these fields were introduced in attempts to resolve classical problems in number theory. Faltings and Iwaniec have developed many of the most powerful modern tools in algebra, analysis, algebraic and arithmetic geometry, automorphic forms, and the theory of zeta functions. They and others have used these tools to resolve longstanding problems in number theory.