Poincaré Conjecture
A conjecture in topology concerning the characterization of the three-dimensional sphere. It was proved by Perelman in 2003 and is the only Millennium Prize Problem that has been solved.
Core Facts
Of the seven Millennium Prize Problems, only the Poincaré conjecture was proved, by Grigori Perelman in 2003, and he declined the prize money.
Of the seven Millennium Prize Problems, only the Poincaré conjecture has been proved, by Grigori Perelman in 2003, while the remaining six remain unsolved to this day.
Timeline (last 90 days)
The mathematics community spent years holding seminars and writing detailed papers before finally confirming the correctness of Perelman's proof of the Poincaré conjecture.
The Poincaré conjecture was proposed by French mathematician Henri Poincaré in 1904, asserting that any simply connected, closed three-dimensional manifold is homeomorphic to the three-dimensional sphere.
Part of the value of solving mathematical conjectures comes from the new tools, methods, and subfields born during the process; for example, the proof of Fermat's Last Theorem spawned many advances in algebraic number theory, and the solution of the Poincaré conjecture advanced the fusion of Ricci flow and geometric analysis.
To date, only Perelman solved the Poincaré Conjecture in 2003, and he himself declined the prize money.
Of the seven Millennium Prize Problems, only the Poincaré conjecture has been solved, by Grigori Perelman.
Perelman's proof of the Poincaré conjecture was first published via arXiv.
Perelman published three papers on arXiv in 2002–2003 outlining the proof of the Geometrization Conjecture using Ricci flow and surgery techniques; the verification process took about three years, and the Clay Mathematics Institute did not officially recognize the conjecture as solved until 2010.
The Poincaré conjecture was proved by Perelman in 2006.
All Facts (10)
Of the seven Millennium Prize Problems, only the Poincaré conjecture was proved, by Grigori Perelman in 2003, and he declined the prize money.
90%VerifiedOf the seven Millennium Prize Problems, only the Poincaré conjecture has been proved, by Grigori Perelman in 2003, while the remaining six remain unsolved to this day.
80%UnverifiedThe mathematics community spent years holding seminars and writing detailed papers before finally confirming the correctness of Perelman's proof of the Poincaré conjecture.
50%UnverifiedThe Poincaré conjecture was proposed by French mathematician Henri Poincaré in 1904, asserting that any simply connected, closed three-dimensional manifold is homeomorphic to the three-dimensional sphere.
50%UnverifiedPart of the value of solving mathematical conjectures comes from the new tools, methods, and subfields born during the process; for example, the proof of Fermat's Last Theorem spawned many advances in algebraic number theory, and the solution of the Poincaré conjecture advanced the fusion of Ricci flow and geometric analysis.
50%UnverifiedTo date, only Perelman solved the Poincaré Conjecture in 2003, and he himself declined the prize money.
50%UnverifiedOf the seven Millennium Prize Problems, only the Poincaré conjecture has been solved, by Grigori Perelman.
50%UnverifiedPerelman's proof of the Poincaré conjecture was first published via arXiv.
50%UnverifiedPerelman published three papers on arXiv in 2002–2003 outlining the proof of the Geometrization Conjecture using Ricci flow and surgery techniques; the verification process took about three years, and the Clay Mathematics Institute did not officially recognize the conjecture as solved until 2010.
50%UnverifiedThe Poincaré conjecture was proved by Perelman in 2006.
50%