Grigori Perelman
Grigori 'Grisha' Perelman is a Russian mathematician who is an expert on Ricci flow. It is thought that he has proven Poincare conjecture, a major open problem in mathematics.In the late 80s and early 90s, Perelman worked at various universities in United States. He returned to Russia in 1995 or 1996. Since then, has been quietly working at the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, Russia. Until the fall of 2002, Perelman was best known for his work in comparison geometry, proving several notable results, such as Cheeger and Gromoll's Soul Conjecture.
In November 2002, he e-published on the arXiv the first of a series of papers purporting to prove Thurston's Geometrization Conjecture, a result that includes the Poincaré conjecture as a particular case. The Poincaré conjecture, proposed by French mathematician Henri Poincaré in 1904, is considered to be very difficult by itself. Loosely speaking, it says that if a "three-dimensional object" has a set of sphere-like properties (most notably that all loops in it can be shrunken to points), then it is really just a "deformed version" of a sphere. Many mathematicians have unsuccessfully tried to prove it and Clay Mathematics Institute has announced $1 million dollar reward for its proof.
Perelman's plan of attack lies in modifying Richard Hamilton 's program for geometrization through Ricci flow. Compared to the more direct, topological programs (notably the differing approaches of W.P. Thurston, J.W. Cannon, and D. Gabai), this Ricci flow approach appears particularly promising at this stage.
Perelman's work is still under review by the mathematical community, as of May 2004. He has given a sequence of lectures at leading universities and parts of the proof have been e-published on the arXiv. The known parts are considered to be very plausible but not all details have been verified yet.
There is speculation whether he will receive the $1 million prize if the proof continues unchallenged. He turned down a prize from the European Mathematical Society in the early 1990s, is said to be "very unmaterialistic", and has not shown interest in publication of the proof in a peer-reviewed mathematics journal, as the current rules for the prize require. On the other hand, the scrutiny the on-line publication has already elicited is said to be well beyond that of pre-publication peer review, and the grantor has explicitly stated that its board may change the requirements.
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