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==Proof of the conjecture==
==Proof of the conjecture==
The original statement of the conjecture went unproved until Gregori Perelman, a relatively unknown Russian mathematician, completed the proof which had eluded a century of expert mathematicians by demonstrating that no "cigar singularities" form in the Ricci flow on manifolds satisfying the conditions of the conjecture.
The original statement of the conjecture went unproved until Gregori Perelman, a relatively unknown Russian mathematician, completed the proof which had eluded a century of expert mathematicians by demonstrating that no "cigar singularities" form in the Ricci flow [See [[Gregorio Ricci-Curbastro]]] on manifolds satisfying the conditions of the conjecture.
===Easy cases===
===Easy cases===