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Steve Smale

Stephen Smale
Stephen Smale2.jpg
Born (1930-07-15) July 15, 1930 (age 86)
Flint, Michigan
Nationality United States
Fields Mathematics
Institutions Toyota Technological Institute at Chicago
City University of Hong Kong
University of Chicago
Columbia University
University of California, Berkeley
Alma mater University of Michigan
Doctoral advisor Raoul Bott
Doctoral students Rufus Bowen
César Camacho
Robert L. Devaney
John Moore Franks
John Guckenheimer
Morris Hirsch
Nancy Kopell
Gregorio Malajovich
Jacob Palis

J. Maurice Rojas
Siavash Shahshahani
Mike Shub
Per Tomter
Known for Generalized Poincaré conjecture
Handle decomposition
Homoclinic orbit
Smale's horseshoe
Smale's theorem
Morse–Smale system
Morse–Smale diffeomorphism
Palais–Smale compactness condition
Blum–Shub–Smale machine
Smale–Williams attractor
Morse–Palais lemma
Regular homotopy
Sard's theorem
Sphere eversion
Structural stability
Whitehead torsion
Diffeomorphism
Notable awards Wolf Prize (2007)
National Medal of Science (1996)
Chauvenet Prize (1988)
Fields Medal (1966)
Oswald Veblen Prize in Geometry (1966)
Sloan Fellowship (1960)

Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan. His research concerns topology, dynamical systems and mathematical economics. He was awarded the Fields Medal in 1966 and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960–1961 and 1964–1995).

Smale entered the University of Michigan in 1948. Initially, he was a good student, placing into an honors calculus sequence taught by Bob Thrall and earning himself A's. However, his sophomore and junior years were marred with mediocre grades, mostly Bs, Cs and even an F in nuclear physics. However, with some luck, Smale was accepted as a graduate student at the University of Michigan's mathematics department. Yet again, Smale performed poorly in his first years, earning a C average as a graduate student. It was only when the department chair, Hildebrandt, threatened to kick Smale out that he began to work hard. Smale finally earned his Ph.D. in 1957, under Raoul Bott.

Smale began his career as an instructor at the college at the University of Chicago. In 1958, he astounded the mathematical world with a proof of a sphere eversion. He then cemented his reputation with a proof of the Poincaré conjecture for all dimensions greater than or equal to 5, published in 1961; in 1962 he generalized the ideas in a 107-page paper that established the h-cobordism theorem.

After having made great strides in topology, he then turned to the study of dynamical systems, where he made significant advances as well. His first contribution is the Smale horseshoe that started significant research in dynamical systems. He also outlined a research program carried out by many others. Smale is also known for injecting Morse theory into mathematical economics, as well as recent explorations of various theories of computation.


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