Bourgain Receives 2010 Shaw Prize

On May 27, 2010, the Shaw Foundation announced fact hard to produce: tossing a coin that it would award its annual Shaw Prize in is not a practical solution, and the Mathematical Sciences to Jean Bourgain “for his coin may be biased. Bourgain has profound work in mathematical analysis and its applied his techniques to provide application to partial differential equations, math- explicit structures that exhibit ran- ematical physics, combinatorics, number theory, domness, and these have important ergodic theory, and theoretical computer science.” applications in theoretical com- The prize carries a cash award of US$1 million. puter science.” The Shaw Prize in Mathematical Sciences com- Jean Bourgain, born in 1954 in mittee made the following statement: Brussels, Belgium, has been a pro- “Mathematical analysis deals with limiting pro- fessor at the Institute for Advanced cesses such as the approximation of a circle by Study in Princeton since 1994. He inscribed regular polygons with increasing num- obtained his Ph.D. from the Free bers of sides (a method used by Archimedes) or the University of Brussels in 1977. He Jean Bourgain notion of instantaneous velocity used in dynamics. served as professor of mathemat- The calculus of Newton and Leibniz provided the ics at the Free University of Brussels from 1981 machinery for its successful application, from the to 1985, at the University of Illinois at Urbana- orbits of planets to flight of aeroplanes and the Champaign from 1985 to 2006, and at the Institut devastation of a tsunami. Underpinning this limit- des Hautes Études Scientifiques, Paris, from 1985 ing process is a variety of inequalities, often of a to 1995. He is a foreign member of the Academies combinatorial nature, whose precise formulation of Science of France, Poland, and Sweden. and proof require great insight and ingenuity. The The Shaw Prize is an international award es- tools and language of analysis form the founda- tablished to honor individuals who are currently tion for vast areas of mathematics, ranging from active in their respective fields and who have probability theory and statistical physics to partial achieved distinguished and significant advances, differential equations, dynamical systems, combi- who have made outstanding contributions in natorics, and number theory. culture and the arts, or who have achieved excel- “Jean Bourgain is one of the most brilliant lence in other domains. The award is dedicated to analysts of our times. He has resolved central and furthering societal progress, enhancing quality of long-standing problems in each of the above fields. life, and enriching humanity’s spiritual civilization. In doing so he has introduced fundamental tech- Preference is given to individuals whose significant niques, many of which have become standard tools work was recently achieved. in these areas. His work and ideas have greatly The Shaw Prize consists of three annual awards: enhanced the very fruitful cross-fertilizations the Prize in Astronomy, the Prize in Life Science between all these disciplines. and Medicine, and the Prize in Mathematical Sci- “A prime example of his work is his develop- ences. Established under the auspices of Run Run ment of the sum-product phenomenon. This is Shaw in November 2002, the prize is managed and a fundamental combinatorial property which administered by the Shaw Prize Foundation based quantifies the relation between the two most basic in Hong Kong. operations of addition and multiplication. He has Previous recipients of the Shaw Prize in Math- used this sum-product theory to resolve problems ematical Sciences are Simon K. Donaldson and connected with distribution and counting of sym- Clifford H. Taubes (2009), Vladimir Arnold and metries, combinatorics, number theory, and solu- Ludwig Faddeev (2008), Robert Langlands and tions of algebraic equations. Richard Taylor (2007), David Mumford and Wen- “More surprisingly, these techniques of Bour- Tsun Wu (2006), Andrew Wiles (2005), and Shiing- gain are intimately related to the very subtle geom- Shen Chern (2004). etry of the Kakeya problem, where a car (idealized as a line segment) is to be reversed in an arbitrarily —From Shaw Foundation announcements 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

SEPTEMBER 2010 NOTICES OF THE AMS 987