In the early 1990s, working in the United States, Perelman had emerged as a major player in Riemannian geometry, which studies subjects such as curvature. "In that domain he was considered a phenomenon at that time, incredibly brilliant," recalls Cheeger.

Then abruptly, Perelman all but vanished from the mathematical scene. In 1995, he turned down job offers from several top universities and returned to Russia. When U.S. mathematicians asked Perelman's colleagues at the Steklov Institute what he was working on, they generally replied that they had no clue.

Some mathematicians speculated that Perelman had quit mathematics. Every now and then, however, one or another mathematician would receive an e-mail from Perelman with probing, insightful questions. "All of a sudden, there would be concrete evidence that he was following certain developments," Cheeger says.

Once Perelman's first paper on the Ricci flow appeared on the Internet in November 2002, rumors started flying that he had proven the Poincar? conjecture and Thurston's geometrization conjecture. On March 10, Perelman posted a second paper that developed the ideas in his first paper and explicitly claimed a proof of the two conjectures. He has promised a third paper with a few remaining details.