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poincare-conjecture
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Higher dimensions fell first: Smale in dimension 5 and up in 1961, Freedman in dimension 4 in 1982. Perelman finished dimension 3 by running Hamilton's Ricci flow, cutting out singularities as they formed, and proving Thurston's geometrization along the way. He declined both the Fields Medal and the Millennium Prize. The smooth four-dimensional version is still open.
Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.
Posed 1904, Henri Poincaré. Closed 2003, Grigori Perelman.
Prize
Clay Millennium Prize awarded 2010, declined
Related problems
- The original curation links this problem to Smooth 4-dimensional Poincaré conjecture; the argument for the link has not been written yet.