In August 2006, Perelman was offered the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow", but he declined to accept the award, stating: "I'm not interested in money or fame; I don't want to be on display like an animal in a zoo."

On 22 December 2006, the scientific journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.

On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considered the decision of the board of CMI and the award very unfair and that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow with the aim of attacking the conjecture. He also turned down the prestigious prize of the European Mathematical Society.