Andrei Okounkov: “for his contributions bridging probability, representation theory and algebraic geometry”
Grigori Perelman: “for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow”
Terence Tao: “for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory”.
Wendelin Werner: “for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory”.
Most significantly, his results provide a way of resolving two outstanding problems in topology: the Poincare Conjecture and the Thurston Geometrization Conjecture. As of the summer of 2006, the mathematical community is still in the process of checking his work to ensure that it is entirely correct and that the conjectures have been proved. After more than three years of intense scrutiny, top experts have encountered no serious problems in the work (Further information at www.icm2006.org)