American William Thurston completes the Geometrization Conjecture: in 3-dimensional space, there are only 8 different geometries, instead of the 3 found in 2-dimensional space. The Geometrization Conjecture implies the Poincaré Conjecture. Most 3-manifolds in 3-space have a hyperbolic structure. The same is true in 2-space: with the exception of the sphere and the torus, all others are hyperbolic.
