# Mathematician:Stephen Smale

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## 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 PoincarĂ© 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 Horseshoe
- Smale's Theorem
- Morse-Smale System (with Harold Calvin Marston Morse)
- Morse-Smale Diffeomorphism (with Harold Calvin Marston Morse)
- Palais-Smale Compactness Condition (with Richard Sheldon Palais)
- Blum-Shub-Smale Machine (with Lenore Carol Blum and Michael Ira Shub)
- Smale-Williams Attractor with Robert Fones Williams)

## Publications