Seven years ago, a reclusive Russian mathematician, Grigori Perelman, startled the scientific world by claiming to solve one of the most famous and intractable problems in mathematics, called the Poincaré conjecture, and then disappearing back into St. Petersburg.

Now Dr. Perelman, who did not show up to receive a prestigious Fields Medal from the International Mathematical Union in Madrid in 2006, has been named the winner of the million-dollar prize for solving the problem by the Clay Mathematics Institute in Cambridge, Mass.

The prize was announced Thursday by James Carlson, president of the institute. It is the first of the million-dollar Millennium prizes to be awarded. They were established in 2000 by the institute for the solution of seven longstanding problems.

Will Dr. Perelman accept? “He will let me know in due time,” Dr. Carlson wrote in an e-mail message, acknowledging that they had been in touch. He declined to provide more details.