Michael Hartley FreedmanBorn 21 Apr 1951.American mathematician who was awarded the Fields Medal in 1986 for his proof of the conjecture in four dimensions (1982). The Poincaré conjecture, one of the famous problems of 20th-century mathematics, asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere. The higher dimensional Poincaré conjecture claims that any closed n-manifold which is homotopy equivalent to the n-sphere must be the n-sphere. For values of n at least 5, a solution was given by Smale in 1961. Two decades later, Freedman proved the conjecture for n = 4. However, the original conjecture for n=3 the remained open. Grigori Perelman gave a complete proof in 2003.« |
