In March, the Clay Mathematics Institute of Cambridge, Mass., said Grigori Perelman, 43, would be awarded the prize for proving the Poincare conjecture, one of seven problems on the institute's Millennium Prize list, RIA Novosti reported Wednesday.
Perelman did not appear at a ceremony in Paris to collect the prize and did not inform CMI of his wishes regarding the money.
"Dr. Perelman has subsequently informed us that he has decided not to accept the one million dollar prize. In the fall of 2010, CMI will make an announcement of how the prize money will be used to benefit mathematics," the institute said on its Web site.
The Poincare conjecture, first proposed in 1904, says a three-sphere is the only type of bounded three-dimensional space possible that contains no holes.
Perelman presented proof of the conjecture in 2002 and 2003. It was subsequently verified by several high-profile teams of mathematicians, RIA Novosti said.
Perelman lives in a small apartment in St. Petersburg with his elderly mother. He is unemployed and neighbors say he lives in poverty.
He has rejected job offers at several top U.S. universities, RIA Novosti reported.