Smale, Stephen

Smale, Stephen

▪ American mathematician
born July 15, 1930, Flint, Mich., U.S.

      American mathematician, who was awarded the Fields Medal in 1966 for his work on topology in higher dimensions.

      Smale grew up in a rural area near Flint. From 1948 to 1956 he attended the University of Michigan (Michigan, University of), obtaining B.S., M.S., and Ph.D. degrees in mathematics. As an instructor at the University of Chicago (Chicago, University of) from 1956 to 1958, Smale achieved notoriety by proving that there exists an eversion of the sphere (meaning, in a precise theoretical sense, that it is possible to turn a sphere inside out).

      In 1960 Smale obtained his two most famous mathematical results. First he constructed a function, now known as the horseshoe, that serves as a paradigm for chaos (chaos theory). Next Smale proved the generalized Poincaré conjecture (topology) for all dimensions greater than or equal to five. (The classical conjecture states that a simply connected closed three-dimensional manifold is a three-dimensional sphere, a set of points in four-dimensional space at the same distance from the origin.) The two-dimensional version of this theorem (the two-dimensional sphere is the surface of a common sphere in three-dimensional space) was established in the 19th century, and the three-dimensional version was established at the start of the 21st century. Smale's work was remarkable in that he bypassed dimensions three and four to resolve the problem for all higher dimensions. In 1961 he followed up with the h-cobordism theorem, which became the fundamental tool for classifying different manifolds in higher-dimensional topology.

      In 1965 Smale took a six-month hiatus from mathematical research to join radical activist Jerry Rubin in establishing the first campaign of nonviolent civil disobedience directed at ending U.S. involvement in the Vietnam War. Smale's mathematical and political lives collided the following year at the International Congress of Mathematicians in Moscow, where he received the Fields Medal. There Smale held a controversial press conference in which he criticized the actions of both the U.S. and Soviet governments.

      Smale's mathematical work is notable for both its breadth and depth, reaching the areas of topology, dynamical systems, economics, nonlinear analysis, mechanics, and computation. In 1994 Smale retired from the University of California at Berkeley and then joined the faculty of the City University of Hong Kong.

      Smale's publications include Differential Equations, Dynamical Systems, and Linear Algebra (1974; with Morris W. Hirsch), The Mathematics of Time: Essays on Dynamical Systems, Economic Processes, and Related Topics (1980), and The Collected Papers of Stephen Smale (2000).

Steven Lee Batterson

Additional Reading
Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier (2000), is directed at a general scientific audience.

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Universalium. 2010.

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  • SMALE (S.) — SMALE STEPHEN (1930 ) Mathématicien américain né à Flint (Michigan). Après des études à l’université du Michigan (où il passa son doctorat en 1956), Stephen Smale enseigna à l’université Columbia (1961 1964), puis à Berkeley à partir de 1964. En… …   Encyclopédie Universelle

  • Smale's paradox — In differential topology, Smale s paradox states that it is possible to turn a sphere inside out in 3 space with possible self intersections but without creating any crease, a process often called sphere eversion ( eversion means to turn inside… …   Wikipedia

  • Stephen Smale — (* 15. Juli 1930 in Flint, Michigan, USA) ist ein US amerikanischer Mathematiker, der hauptsächlich durch seinen Beweis der Poincaré Vermutung für den Fall n > 4 bekannt wurde. Smale begann sein Studium an der Universität von Michigan 1948,… …   Deutsch Wikipedia

  • Stephen Smale — (né le 15 juillet 1930 à Flint dans le Michigan) est un mathématicien américain, lauréat de la médaille Fields en 1966, récompensé pour ses remarquables travaux en topologie différentielle. Sa réputation est due à une démonstration de la… …   Wikipédia en Français

  • Stephen Smale — (Flint, Michigan, 15 de julio de 1930) es un matemático estadounidense, conocido por sus contribuciones en Topología y Geometría diferencial. Se doctoró en 1957, en la Universidad de Míchigan, bajo la supervisión de Raoul Bott. En ese momento… …   Wikipedia Español

  • Smale — ist der Familienname folgender Personen: John Smale (1927–2011), US amerikanischer Manager Stephen Smale (* 1930), US amerikanischer Mathematiker Diese Seite ist eine Begriffsklärung zur Unterscheidung mehrerer mit demselben Wort bezeichneter Beg …   Deutsch Wikipedia

  • Smale —   [smeɪl], Stephen, amerikanischer Mathematiker, * Flint (Michigan) 15. 7. 1930; 1961 Professor an der Columbia University, New York, seit 1964 an der University of California, Berkeley. Smale beschäftigte sich zuerst mit Problemen der… …   Universal-Lexikon

  • Stephen Smale — Infobox Scientist image width = 200px name = Stephen Smale caption = birth date = birth date and age|1930|07|15 birth place = death date = death place = residence = citizenship = nationality = ethnicity = field = Mathematics work institution =… …   Wikipedia

  • Steve Smale — Stephen Smale in Berkeley, 1988 Stephen Smale (* 15. Juli 1930 in Flint, Michigan, USA) ist ein US amerikanischer Mathematiker, der hauptsächlich durch seinen Beweis der Poincaré Vermutung für den Fall n > 4 bekannt wurde …   Deutsch Wikipedia

  • Morse–Smale system — In dynamical systems theory, an area of applied mathematics, a Morse–Smale system is a smooth dynamical system whose non wandering set consists of finitely many hyperbolic equilibrium points and hyperbolic periodic orbits and satisfying a… …   Wikipedia