Mathematician:Stephen Smale

Mathematician

American mathematician working in topology, dynamical systems and mathematical economics.

Fields Medal

Stephen Smale was awarded a Fields Medal in $\text {1966}$ at the International Congress of Mathematicians in Moscow, Russia:

Worked in differential topology where he proved the generalized Poincaré conjecture in dimension $n \ge 5$: Every closed, $n$-dimensional manifold homotopy-equivalent to the $n$-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems.

Wolf Prize

Stephen Smale was awarded a Wolf Prize for Mathematics in $\text {2006/07}$:

For his groundbreaking contributions that have played a fundamental role in shaping differential topology, dynamical systems, mathematical economics, and other subjects in mathematics.

Nationality

American

History

• Born: July 15, 1930 in Flint, Michigan

Theorems and Definitions

• Smale's Theorem

• Palais-Smale Compactness Condition (with Richard Sheldon Palais)

• Smale's Horseshoe
• Smale's Problems

• Blum-Shub-Smale Machine (with Lenore Carol Blum and Michael Ira Shub)
• Morse-Smale Diffeomorphism (with Harold Calvin Marston Morse)
• Morse-Smale System (with Harold Calvin Marston Morse)
• Smale-Williams Attractor with Robert Fones Williams)

Publications

• 1974: Differential Equations, Dynamical Systems and Linear Algebra (with Morris W. Hirsch)

Sources

• John J. O'Connor and Edmund F. Robertson: "Stephen Smale": MacTutor History of Mathematics archive