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 pioneering work on symplectic geometry, especially for envisioning the existence of a category — nowadays called the Fukaya category — consisting of Lagrangians on a symplectic manifold, for leading the monumental task of constructing it, and for his subsequent ground-breaking and impactful contributions to symplectic topology, mirror symmetry, and gauge theory.
Prize in Mathematical Sciences have been awarded to one laureate only
Prize in Mathematical Sciences have been shared by two laureates
for his work on concentration inequalities, on suprema of stochastic processes and on rigorous results for spin glasses.
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.
