The Poincaré conjecture, now proved, posited that every simply connected closed three-manifold is homeomorphic to the three-sphere.

The three-sphere is the only type of bounded three-dimensional space possible that contains no holes.

Smale's second problem

formulation date | 1904 (121 years ago) formulator | Henri Poincaré status | proved proof date | 2003 (99 years later) (22 years ago) prover | Grigori Perelman

prize offered for solution | $1 million "Millennium Prize Problem" of The Clay Mathematics Institute. (Refused by solver.) prize awarded for solution | Perelman shared the 2006 Fields Medal for his proof. (Refused by solver.)

Millennium Prize problems | prize mathematics problems | proved conjectures | Smale's problems | solved mathematics problems | mathematics theorems