For 10 points, name this Millenium Problem, a conjecture named for a French mathematician, whose solution led to the declining of the 2006 Fields Medal by Grigory Perelman.
The Rego-Rourke and Rubenstein-Thompson algorithms attempted to disprove it, and John Stallings once wrote a paper on "How Not to Solve" this problem. The method eventually used to solve it was introduced by Richard Hamilton in 1982, but it was not until a series of papers written in 2002 and 2003 applied Ricci Flow with "surgery" that it was considered provable to say that the namesake relationship existed between a simply close connected 3-manifold and the three-sphere. For 10 points, name this Millenium Problem, a conjecture named for a French mathematician, whose solution led to the declining of the 2006 Fields Medal by Grigory Perelman.
The Rego-Rourke and Rubenstein-Thompson algorithms attempted to disprove it, and John Stallings once wrote a paper on "How Not to Solve" this problem.
The {Poincaré} Conjecture