CAMBRIDGE, Mass., March 18 -- The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. The citation for the award reads:
The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman.
The Poincaré conjecture is one of the seven Millennium Prize Problems established by CMI in 2000. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude.
The award of the Millennium Prize to Dr. Perelman was made in accord with their governing rules: recommendation first by a Special Advisory Committee (Simon Donaldson, David Gabai, Mikhail Gromov, Terence Tao, and Andrew Wiles), then by the CMI Scientific Advisory Board (James Carlson, Simon Donaldson, Gregory Margulis, Richard Melrose, Yum-Tong Siu, and Andrew Wiles), with final decision by the Board of Directors (Landon T. Clay, Lavinia D. Clay, and Thomas M. Clay).
James Carlson, President of CMI, said today "resolution of the Poincaré conjecture by Grigoriy Perelman brings to a close the century-long quest for the solution. It is a major advance in the history of mathematics that will long be remembered."
Formulated in 1904 by the French mathematician Henri Poincaré, the conjecture is fundamental to achieving an understanding of three-dimensional shapes (compact manifolds). In the last century, there were many attempts to prove, and also to disprove, the Poincaré conjecture. Around 1982, however, a possible new line of attack was opened by Richard Hamilton using a differential equation, the Ricci flow equation. This equation is related to the one introduced by Joseph Fourier 160 years earlier to study the flow of heat. In Ricci flow, what changes is not temperature, but geometry.
At the core of Perelman's breakthrough proof of the Poincaré conjecture is the Ricci flow method. But to it he brought a set of new ideas, techniques, and results, including a complete understanding of singularity formation in Ricci flow. Singularities are to Ricci flow what black holes are to the evolution of the cosmos. Perelman also introduced a kind of geometric entropy, akin to the entropy studied in the exchange of heat, as in a turbine or motor. With these (and other) new results in hand, he was able to go where no one had gone before. Mathematics has been deeply enriched by Perelman's work.
CONTACT: James Carlson of the The Clay Mathematics Institute, jcarlson@claymath.org, +1-617-852-7490