Image Credit

Jean Bourgain

for his profound work in mathematical analysis and its application to partial differential equations, mathematical physics, combinatorics, number theory, ergodic theory and theoretical computer science.


Mathematical analysis deals with limiting processes such as the approximation of a circle by inscribed regular polygons with increasing numbers of sides (a method used by Archimedes), or the notion of instantaneous velocity used in dynamics. The calculus of Newton and Leibniz provided the machinery for its successful application, from the orbits of planets, to flight of aeroplanes and the devastation of a tsunami.

Underpinning this limiting process is a variety of inequalities, often of a combinatorial nature, whose precise formulation and proof require great insight and ingenuity. The tools and language of analysis form the foundation for vast areas of mathematics, ranging from probability theory and statistical physics to partial differential equations, dynamical systems, combinatorics and number theory.

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An Essay on the Prize

Mathematical analysis is concerned with the study of infinite processes, and the differential calculus of Newton and Leibniz lies at its heart.  It provided the foundation and the language for Newtonian mechanics and the whole of mathematical physics.  Over the past three centuries it has permeated much of mathematics and science.

Associated with the limiting process there are many technically difficult “estimates” or inequalities, of a combinatorial or algebraic nature, which prepare the ground and justify passing to the limit.  Such estimates are often extremely hard since they address some subtle and important aspect of the problem at hand.  Establishing this becomes a key step, opening the door to a wide variety of applications.

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About the Laureates
Jean Bourgain (1954-2018)

Jean Bourgain, born 1954 in Ostende, Belgium, has been a Professor at the Institute for Advanced Study, Princeton, USA since 1994. He obtained his PhD from the Free University of Brussels, Belgium in 1977. He was a Professor of Mathematics at the Free University of Brussel, Belgium from 1981 to 1985, the University of Illinois at Urbana-Champagne, USA from 1985 to 2006 and at the Institut des Hautes Études Scientifiques, Paris, France from 1985 to 1995. He is a Foreign Member of the Academics of Science of France, Poland and Sweden

Feature Story
The Shaw Prize Lecture in Mathematical Sciences 2010