Russian mathematician Grigori “Grisha” Perelman submitted a paper to www.arXiv.org presenting a proof of the Poincaré Conjecture, formulated in 1904: every compact, simply connected three-manifold (i.e., one on which every closed path can be reduced to a point) is homeomorphic (i.e., topologically identical) to the three-sphere. Perelman stated: “I have already proved almost everything Richard Hamilton conjectured about the Ricci Flow [Editor’s note: a mathematical construct named after the Ricci tensor that controls the radius of curvature in smooth manifolds, one of the few objects independent of the choice of coordinates]. Oh, by the way, this means I have proved the geometrization conjecture and, hence, the Poincaré Conjecture.”
