The Edmondson Blog

So Now You Know

In 2000 the Clay Mathematics Institute stated seven Millennium Prize Problems, for which they offered a $1,000,000 prize for the first correct solution to each.

One of the problems was the Poincaré Conjecture, a theorem about the characterization of the three-dimensional sphere among three-dimensional manifolds. Originally posed by Henri Poincaré, the claim concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary. The Poincaré Conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is just a three-dimensional sphere.

After nearly a century of effort by mathematicians, in 2002 and 2003, the Russian Grigori Perelman sketched a proof of the conjecture. His work survived review and was confirmed in 2006. On 18th March 2010 Perelman was awarded the $1,000,000 Millennium Prize. The Poincaré Conjecture remains the only solved Millennium problem.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré Conjecture as the scientific Breakthrough of the Year, the first time this had been bestowed in the area of mathematics.

Perelman was offered a Fields Medal, the top international award for mathemetics and equal in status to a Nobel Prize, for his proof, but he declined, saying, "... [the prize] was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed."

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