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Four Fields Medals were awarded on August 22, the opening day of the 2006 International Congress of Mathematicians. The winners are Andrei Okounkov, Grigori Perelman, Terence Tao, and Wendelin Werner. The Nevanlinna Prize for contributions to mathematical information theory was awarded to Jon Kleinberg. A new prize for contributions to applied mathematics, named for Gauss, went to Kiyoshi Itô.

Andrei Okounkov received the Fields Medal "for his contributions bridging probability, representation theory and algebraic geometry."
Okounkov is known for using notions of randomness and of classical ideas from representation theory to attack problems from algebraic geometry and statistical mechanics, among others. Born in Moscow in 1969, Okounkov received his doctorate from the University of Moscow in 1995. After holding positions at many prestigious institutions, he is now professor of mathematics at Princeton.


Grigori Perelman received the Fields Medal "for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow."
Perelman's work provides a way of proving two of the most famous conjectures in geometry and topology: Thurston's Geometrization Conjecture and the Poincaré Conjecture. (See our report from the AugustSeptember 2006 issue of FOCUS for more details.) Perelman was born in 1966 in what was then the Soviet Union. He received his doctorate from St. Petersburg State University. After spending some time in the United States in the 1990s, he was a researcher in the St. Petersburg Department of the Steklov Institute of Mathematics. John Ball, president of the IMU, announced at the awards ceremony that Perelman has refused the award.


Terence Tao received the Fields Medal "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory."
Terence Tao is a talented problemsolver whose spectacular work has had an impact across several mathematical areas, including harmonic analysis, nonlinear partial differential equations, and combinatorics. Tao was born in Adelaide, Australia, in 1975 and received his PhD from Princeton in 1996. He is now professor of mathematics at the University of California, Los Angeles.


Wendelin Werner received the Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of twodimensional Brownian motion, and conformal field theory".
Werner's work deals with some of the most important points of contact between mathematics and physics. He has developed a framework, combining geometric insights and ideas from probability theory and classical complex analysis, for understanding critical phenomena in physics. Born in 1968 in Germany, Werner is of French nationality. He received his PhD at the University of Paris VI in 1993 and has been professor of mathematics at the University of ParisSud in Orsay since 1997.

The Nevanlinna Prize is awarded every four years at the ICM for work in the "mathematics of information theory", i.e., theoretical computer science. This year's prize went to Jon Kleinberg, whose work "has brought theoretical insights to bear on important practical questions that have become central to understanding and managing our increasingly networked world." His work has dealt with many areas, including network analysis and routing, data mining, comparative genomics and protein structure analysis.
Kleinberg was born in 1971 in Boston, Massachusetts, USA. He received his Ph.D. in 1996 from the Massachusetts Institute of Technology and is now professor of computer science at Cornell University.

Kiyoshi Itô is the first winner of the Gauss Prize for applications of mathematics. The new prize is named for Carl Friedrich Gauss, one of the greatest mathematicians of all time, whose work demonstrated the ability to apply mathematics to many sorts of problems in physics, astronomy and engineering. The prize is awarded jointly by the Deutsche MathematikerVereinigung (DMV = German Mathematical Union) and the International Mathematical Union (IMU), and administered by the DMV. It consists of a medal and a monetary award (currently valued at 10,000 Euros).
Kiyoshi Itô, aged 90, received the prize for his work on stochastic analysis, allowing the study of stochastic processes by means of what are now known as "stochastic differential equations." These have found applications all over science, and also, perhaps most famously, in mathematical finance via the BlackScholes equations. Though Itô first developed these ideas in the 1940s, it took quite a while for mathematicians to understand and appreciate his results. Only after 1954, when Itô visited the Institute of Advanced Studies, did his ideas begin to have their true impact. Today, stochastic analysis is a basic tool in the study of stochastic processes and plays a crucial role in many branches of applied mathematics. 
More information, including descriptions of the winners' work, photographs, and interviews, can be found at ICM press site and at the site describing the awards to be given at ICM.