Stephen Smale
fl. 1930, Flint, Michigan, United States
TopologyAnalysisDifferential equations and dynamical systemsFields Medal 1966
American mathematician who founded modern dynamical-systems theory and proved the higher-dimensional h-cobordism theorem.
Stephen Smale transformed topology and dynamical systems. His horseshoe construction showed how deterministic systems can exhibit chaotic behavior, while his work in topology led to the proof of the generalized Poincare conjecture in dimensions at least five. He received the 1966 Fields Medal.
Workplaces: University of California, Berkeley
United States
Award-winning work
Fields Medal 1966The 1966 Fields Medal honored Smale's work in differential topology, which revolutionized the study of manifolds in high dimensions. He proved the generalized Poincaré conjecture in dimensions five and higher: every closed manifold homotopy-equivalent to a sphere is homeomorphic to it, using handlebody decompositions and his h-cobordism theorem to bypass the low-dimensional obstructions. He also proved that the standard sphere can be turned inside out through immersions — the sphere eversion — using general position arguments. His techniques opened the era of classification of high-dimensional manifolds and shaped the subsequent development of dynamical systems.