ポアンカレ予想
On March 18, 2010, it was announced that Perelman had met the criteria to receive the first Clay Millennium Prize for his proof of the Poincaré conjecture, first published in 2003. On July 1, 2010, Perelman subsequently turned down the award and the associated prize money as he had done with the Fields Medal, saying that he believed his contribution in proving the Poincaré conjecture was no greater than that of Hamilton, who first suggested a program for the solution. However while Perelman's solution was indeed based on Richard Hamilton's theory of Ricci flow, it included major advancements by Perelman and made use of results on spaces of metrics due to Cheeger, Gromov, and Perelman himself. Perelman also proved William Thurston's Geometrization Conjecture, a special case of which is the Poincaré conjecture, without which the Poincaré conjecture proof wouldn't have been possible; its review was completed in August 2006.