He credited his acumen to his family goddess, Namagiri Thayar (Goddess Mahalakshmi) of Namakkal. He looked to her for inspiration in his work[111] and said he dreamed of blood drops that symbolised her consort, Narasimha. Later he had visions of scrolls of complex mathematical content unfolding before his eyes.

"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing"

In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field.

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 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 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 rejected the prize of one million dollars, saying that he considered the decision of the board of the Clay Institute to be unfair, in that his contribution to solving the Poincaré conjecture was no greater than that of Richard S. Hamilton, the mathematician who pioneered the Ricci flow partly with the aim of attacking the conjecture. He had previously rejected the prestigious prize of the European Mathematical Society in 1996.

In September 2011, an anonymous poster on the Science & Math ("/sci/") board of 4chan proved that the smallest superpermutation on n symbols (n ≥ 2) has at least length n! + (n−1)! + (n−2)! + n − 3. In reference to the Japanese anime series The Melancholy of Haruhi Suzumiya, particularly the fact that it was originally broadcast as a nonlinear narrative, the problem was presented on the imageboard as "The Haruhi Problem": if you wanted to watch the 14 episodes of the first season of the series in every possible order, what would be the shortest string of episodes you would need to watch?

On 25 October 2018, Robin Houston, Jay Pantone, and Vince Vatter posted a refined version of this proof in the On-Line Encyclopedia of Integer Sequences (OEIS). A published version of this proof, credited to "Anonymous 4chan poster", appears in Engen and Vatter (2021).