A Hundred Years Later, Poincaré's Conjecture...

has been proven to have been solved.

Perelman's first paper, promising "a sketch of an eclectic proof," came as a bolt from the blue when it was posted on the Internet in November 2002. "Nobody knew he was working on the Poincare conjecture," said Michael Anderson of the State University of New York in Stony Brook.

Perelman had already established himself as a master of differential geometry, the study of curves and surfaces, which is essential to, among other things, relativity and string theory. Born in St. Petersburg in 1966, he distinguished himself as a high school student by winning a gold medal with a perfect score in the International Mathematical Olympiad in 1982. After getting a doctorate from St. Petersburg State, he joined the Steklov Institute of Mathematics at St. Petersburg.

In a series of postdoctoral fellowships in the United States in the early 1990s, Perelman impressed his colleagues as "a kind of unworldly person," in the words of Greene of UCLA -- friendly but shy and not interested in material wealth.

"He looked like Rasputin, with long hair and fingernails," Greene said.

Asked about Perelman's pleasures, Anderson said that he talked a lot about hiking in the woods near St. Petersburg looking for mushrooms.

Perelman returned to those woods and the Steklov Institute in 1995, spurning offers from Stanford and Princeton, among others. In 1996 he added to his legend by turning down a prize for young mathematicians from the European Mathematics Society.

Until his papers on Poincare started appearing, some friends thought Perelman had left mathematics. Although they were so technical and abbreviated that few mathematicians could read them, they quickly attracted interest among experts. In the spring of 2003, Perelman came back to the United States to give a series of lectures at Stony Brook and the Massachusetts Institute of Technology, and also spoke at Columbia, New York University and Princeton.

But once he was back in St. Petersburg, he did not respond to further invitations. The e-mail gradually ceased.

"He came once, he explained things, and that was it," Anderson said. "Anything else was superfluous."

Recently, Perelman is said to have resigned from Steklov. E-mail messages addressed to him and to the Steklov Institute went unanswered.