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After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv.

The proof followed on from the program of Richard Hamilton to use the Ricci flow to attack the problem.

Perelman introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way.

Several teams of mathematicians have verified that Perelman's proof is correct.