A Russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics.

The mathematician, Dr. Grigori Perelman of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, is describing his work in a series of papers, not yet completed.

It will be months before the proof can be thoroughly checked. But if true, it will verify a statement about three-dimensional objects that has haunted mathematicians for nearly a century, and its consequences will reverberate through geometry and physics.

If his proof is accepted for publication in a refereed research journal and survives two years of scrutiny, Dr. Perelman could be eligible for a $1 million prize sponsored by the Clay Mathematics Institute in Cambridge, Mass., for solving what the institute identifies as one of the seven most important unsolved mathematics problems of the millennium.