Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan, and winner of the Fields Medal in 1966. He made his reputation by a proof of the Poincare conjecture for all dimensions greater than 4; he later generalized the ideas in the proof to establish the h-cobordism theorem. Stephen Smale is also famous for the proof of sphere eversion. That is, turning a sphere inside out without creating any crease.
After having made great strides in topology, he then turned to the study of dynamical systems, where he made significant advances as well as outlining a research program carried out by many others. The Smale horseshoe is an important example that jumpstarted significant research. Smale is also known for work in mathematical economics, as well as recent explorations of various theories of computation.
In 1998 he constructed a list of 18 problems in mathematics to be solved in the 21st century. This list was compiled in the spirit of Hilbert's famous list of problems produced in 1900. In fact, Smale's list includes some of the original Hilbert problems. Smale's problems include the Jacobian conjecture and the Riemann hypothesis, both of which are still unsolved.
Earlier in his career, he was involved in controversy over remarks he made regarding his work habits while proving the higher dimensional Poincare conjecture. This led to the withholding of his grant money from the NSF.
Smale has been politically active in various movements in the past, such as the Free Speech movement. At one time he was subpoenaed by the House Un-American Activities Committee.
Smale was also not a good student, earning B's and C's in many of his mathematics and physics courses while at the University of Michigan.
- Stephen Smale's homepage at the City University of Hong Kong
- Biography in the MacTutor History of Mathematics archive
- Stephen Smale's faculty listing at TTI