William Thurston develops, starting from a 1976 preprint from the Princeton mathematics department, directly motivated by the Poincaré conjecture, the program that would culminate in 1982 in the complete formulation of the geometrization conjecture: every closed three-dimensional manifold can be canonically decomposed into pieces, each of which admits one of eight possible geometric structures (the so-called "Thurston geometries"). In the same year he proves his hyperbolization theorem, which confirms the conjecture for the broad class of Haken manifolds, a result for which he receives the Fields Medal in 1982. The geometrization conjecture implies, as a special case, the Poincaré conjecture itself, and its formulation would directly inspire Richard Hamilton to develop, also in 1982, the Ricci flow program with which he would pursue completing the general proof over the following two decades — a program Grigori Perelman would finally complete in 2002-03, thereby proving both the full geometrization conjecture and, with it, the Poincaré conjecture.