Stephen Smale proves in 1961, in Annals of Mathematics, the generalized Poincaré conjecture for dimensions greater than or equal to 5: every closed n-dimensional manifold, n≥5, homotopy equivalent to the n-dimensional sphere is in fact homeomorphic to it. The result surprises the mathematical community, since it reverses the usual intuition that topological problems become harder as dimension increases; Smale develops in the same work the h-cobordism technique, fundamental to all subsequent differential topology. Smale received the Fields Medal in 1966.