Mathematics is the basic language of all natural sciences and all modern technology. In the twentieth century mathematics made tremendous strides both in opening new frontiers and in solving important and difficult old problems. Its influence permeates every creative scientific and technological discipline, and extends into the social science.
With the developments in computer science, information technology, and statistics in the twentieth century, the importance of mathematics to mankind will be further enhanced in the twenty-first century.
for his development of the arithmetic theory of thin groups and the affine sieve, by bringing together number theory, analysis, combinatorics, dynamics, geometry and spectral theory.
Prize in Mathematical Sciences have been awarded to one laureate only
Prize in Mathematical Sciences have been shared by two laureates
for his groundbreaking work on partial differential equations, including creating a theory of regularity for nonlinear equations such as the Monge-Ampère equation, and free-boundary problems such as the obstacle problem, work that has influenced a whole generation of researchers in the field.
for their remarkable results in many central areas of algebraic geometry, which have transformed the field and led to the solution of long-standing problems that had appeared out of reach.
for his far-reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance.
for their introduction and development of fundamental tools in number theory, allowing them as well as others to resolve some longstanding classical problems.
for his fundamental contributions to algebra, algebraic geometry, and representation theory, and for weaving these subjects together to solve old problems and reveal beautiful new connections.
for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.
