2010年邵逸夫数学科学奖授予普林斯顿高等研究所Jean Bourgain教授


Jean Bourgain

邵逸夫基金2010527在香港举行新闻发布会,公布2010 年度邵逸夫数学科学奖颁予辛康‧布尔甘Jean Bourgain以表彰他在数学分析方面的工作及其在多项科学上的应用:偏微分方程、数学物理、组合学、数论、遍历理论与理论计算机科学。



辛康布爾甘(Jean Bourgain) 1954年出生比利時布魯塞爾,1994年至今在美普林斯頓高等研究院任教授。1977年獲比利時布魯塞爾自由大學博士學位。他曾普魯塞爾自由大學(1981 – 1985)、 美伊利諾州大學巴納-香檳分校(1985 – 2006)和法高等科學研究院 (1985 – 1995)等大學任學教授,是法、波蘭及瑞典皇家科學院外籍院士。




辛康布爾甘(Jean Bourgain)當代最卓越的分析學家之一。在以上提到的每個領域他都解決了中心地位的和長期存在的難題。他此引入的許多基本技術已成這些領域的標準工具。他的工作和思想已極大地促使不同的領域相互吸取精華,開花結果。


更讓人驚奇的是,布爾甘所用的技術與精微何的Kakeya問題,有密切的關連。在Kakeya問題中,是以非常大的N輛小車(理想化為一個小線段)進行 N點轉向,使小車在任意小的區域裡倒向。





The Shaw Prize in Mathematical Sciences 2010 is awarded to 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.


Biographical Notes

Jean Bourgain, born 1954 in Brussels, 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.


Press Release

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.

Jean Bourgain is one of the most brilliant analysts of our times. He has resolved central and long-standing problems in each of the above fields. In doing so he has introduced fundamental techniques many of which have become standard tools in these areas. His work and ideas have greatly enhanced the very fruitful cross fertilizations between all these disciplines.

A prime example of his work is his development of the sum product phenomenon. This is a fundamental combinatorial property which quantifies the relation between the two most basic operations of addition and multiplication. He has used this sum-product theory to resolve problems connected with distribution and counting of symmetries, combinatorics, number theory and solutions of algebraic equations.

More surprisingly, these techniques of Jean Bourgain are intimately related to the very subtle geometry of the Kakeya problem, where a car (idealized as a line segment) is to be reversed in an arbitrarily small area, using an N-point turn with very large N.

In many areas of mathematics and science, random numbers play a key role, but they are in fact hard to produce: tossing a coin is not a practical solution and the coin may be biased. Bourgain has applied his techniques to provide explicit structures that exhibit randomness, and these have important applications in theoretical computer science.