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

邵逸夫奖基金会于2010年5月27日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。

「邵逸夫奖」设有三个奖项，分別为天文学、生命科学与医学、数学科学。每年颁奖一次，每项奖金一百万美元。今年为第七届颁发，颁奖典礼定于2010年9月28日举行。

得獎人簡介

辛康‧布爾甘(Jean Bourgain) 1954年出生於比利時布魯塞爾，1994年至今在美國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。他曾於普魯塞爾自由大學（1981 – 1985）、美國伊利諾州大學厄巴納－香檳分校(1985 – 2006）和法國高等科學研究院（1985 – 1995）等大學任數學教授，是法國、波蘭及瑞典皇家科學院外籍院士。

新聞稿

數學分析論述極限過程，例如圓圈可以用內接正多邊形近似，隨邊數增加而任意逼近（阿基米德使用的方法），又或動力學中瞬時速度的概念等，牛頓和萊布尼茨的微積分便提供了一個數學分析工具，成功地應用於行星軌道，航空飛行和海嘯波浪等問題上。

為這些極限過程確證的多是各種組合數學的不等式。如要精確地立出和證明這些不等式，需要高度的洞察力和心智創造力。分析學的工具和語言是眾多數學領域的基礎，從概率論、統計物理以至偏微分方程、動力系統、組合數學和數論。

辛康‧布爾甘(Jean Bourgain)是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佔中心地位的和長期存在的難題。他為此引入的許多基本技術已成為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。

一個典型例子是關於他的“和積現象”的工作。這一基本組合性現象定量闡明了加法和乘法這兩種基本運算的關係。他用和積理論成功地解決了一系列難題，包括對稱的分佈和計數、組合學、數論和代數方程解等。

更讓人驚奇的是，布爾甘所採用的技術與精微幾何的Kakeya問題，有密切的關連。在Kakeya問題中，是以非常大的數N讓一輛小車（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。

在數學和許多其他科學領域，隨機數起著關鍵作用。但是實際上很難製造一個隨機數。抛擲硬幣並不是辦法，何況硬幣的重心可能有偏倚。布爾甘應用他的技術提供了精確的隨機性結構，此技術已在理論計算機科學中獲得了重要應用。

英文原文

Announcement

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.