Michael Freedman proves in 1981-1982 the topological Poincaré conjecture for dimension 4: every closed, simply connected topological 4-manifold is homeomorphic to the 4-dimensional sphere. The result, published in the Journal of Differential Geometry, completes — together with Smale's work for dimension 5 or higher (1961) and Perelman's later proof for dimension 3 (2002-03) — the topological classification of the Poincaré conjecture in every dimension, leaving dimension 4 as the only one in which the analogous smooth differentiable problem (the "smooth Poincaré conjecture") remains open. Freedman received the Fields Medal in 1986.