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Bourgain and Tao Awarded 2012

Jean Bourgain of the Institute for Advanced guarantee that the solutions to these equations Study, Princeton and of the Univer- evolve in a unique way, no matter how irregular the sity of California, Los Angeles have been awarded initial state of the system might be. He has made the 2012 Crafoord Prize in of the contributions in many areas, such as his 2010 Royal Swedish Academy of Sciences “for their result in Apollonian gaskets—infinite collections brilliant and groundbreaking work in harmonic of circles that just touch without overlapping. In analysis, partial differential equations, ergodic these arrangements, the radius of each bubble is theory, number theory, combinator- 1 divided by an integer. Together with Elena Fuchs, ics, and theoretical Bourgain showed that, if you pick any integer n, computer science.” there is a nonzero probability that some bubble The prize citation reads in part: in the Apollonian foam has radius equal to 1/n. “This year’s Crafoord Prize Laureates Bourgain was awarded the in 1994 have solved an impressive number of and has also been awarded the (1983), important problems in mathematics. the Damry-Deleeuw-Bourlart Prize (Belgian Science Their deep mathematical erudition and Prize, 1985), the Langevin (1985) and Cartan (1990) exceptional problem-solving ability Prizes of the French Academy, the Ostrowski Prize have enabled them to discover many (1991), and the (2010). new and fruitful connections and to Tao is a world-renowned work- make fundamental contributions to ing in a number of branches of mathematics, current research in several branches of including harmonic analysis, partial differential mathematics. On their own and jointly equations, , number theory, and sig- with others, Jean Bourgain and Terence nal processing. He is known for his highly original Tao have made important contribu- solutions of very difficult and important problems tions to many fields of mathematics— and for his technical brilliance in the use of the from number theory to the theory of necessary mathematical machinery. He and Ben nonlinear waves. The majority of their Green proved that there are arbitrarily long arith- most fundamental results are in the metic progressions of prime numbers—a result field of . They now known as the Green–Tao theorem—which had have developed and used the toolbox been a major unsolved problem in number theory of analysis in groundbreaking and sur- for centuries. He is also known for such practical prising ways. Their ability to change work as his invention, with Emmanuel Candes, of

Photo by Reed Hutchinson/UCLA. perspective and view problems from compressed sensing. His areas of research include Terence Tao new angles has led to many remark- harmonic analysis, partial differential equations, able insights, attracting a great deal of combinatorics, and number theory. He received the attention among researchers worldwide.” Fields Medal in 2006 for his contributions in these Bourgain has proved several groundbreaking fields. He has held Sloan Foundation (1999–2001), results on well-posedness of nonlinear differential Packard (1999–2006), and MacArthur (2007) fel- equations, such as the Schrödinger equation of lowships. He has also received the Salem Prize quantum mechanics and the Korteweg–de Vries (2000), the Bôcher Prize (2002), the SASTRA Ra- equation of wave propagation. These theorems manujan Prize (2006), the Ostrowski Prize (2007), the Waterman Award (2008), and the King Faisal Elaine Kehoe is contributing writer for the Notices. Her Prize (2010). email address is [email protected] “Bourgain and Tao have similar and very unique DOI: http://dx.doi.org/10.1090/noti840 strengths,” says Peter Sarnak of the Institute for

676 NOTICES OF THE AMS VOLUME 59, NUMBER 5 Advanced Study. “Their ability to see through technical difficulties that prevent almost anyone else to move forward has allowed them to resolve long-standing problems in an amazingly diverse set of areas.” They will share the monetary award of four mil- lion Swedish kronor, approximately US$580,000. The Anna-Greta and Holger Crafoord Fund Moving? was established in 1980, and the first prize was awarded in 1982. The prize is intended to promote international basic research in the disciplines of astronomy, mathematics, the geosciences, the biosciences (with particular emphasis on ecology), and polyarthritis (rheumatoid arthritis). Previous recipients of the Crafoord Prize in Mathematics are and Ed- ward Witten (2008), (2001), and Shing-Tung Yau (1994), Pierre Please make sure that the Deligne and (1988), and V. I. Arnold and (1982). AMS Notices and Bulletin

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