Stephen Smale


Stephen Smale

Infobox Scientist


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name = Stephen Smale
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birth_date = birth date and age|1930|07|15
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field = Mathematics
work_institution = University of Chicago, Columbia University and University of California, Berkeley
alma_mater = University of Michigan
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prizes = Fields Medal and Wolf Prize
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Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan. He was awarded the Fields Medal in 1966, and spent more than three decades on the mathematics faculty of the University of California, Berkeley (1960-61 and 1964-1995). He entered the University of Michigan in 1948. Initially, Smale 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 his first years, earning a C average as a graduate student. It was only when the department chair, Hildebrant, threatened to kick out Smale, 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; he later 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 jumpstarted 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.

In 1998 he compiled a list of 18 problems in mathematics to be solved in the 21st century, known as Smale's problems. This list was compiled in the spirit of Hilbert's famous list of problems produced in 1900. In fact, Smale's list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilbert's sixteenth problem, both of which are still unsolved. Other famous problems on his list include the Poincaré conjecture, the P = NP problem, and the Navier-Stokes equations, all of which have been designated Millennium Prize Problems by the Clay Mathematics Institute.

Earlier in his career, Smale was involved in controversy over remarks he made regarding his work habits while proving the higher dimensional Poincaré conjecture. He said that his best work had been done "on the beaches of Rio". This led to the withholding of his grant money from the NSF. He has been politically active in various movements in the past, such as the Free Speech movement. At one time he was subpoenaed by the House Un-American Activities Committee.

In 1960 Smale was appointed an associate professor of mathematics at the University of California, Berkeley, moving to a professorship at Columbia University the following year. In 1964 he returned to a professorship at UC Berkeley where he has spent the main part of his career. He retired from UC Berkeley in 1995 and took up a post as professor at the City University of Hong Kong. He also amassed over the years one of the finest private mineral collections in existence. Many of Smale's mineral specimens can be seen in the book - "The Smale Collection: Beauty in Natural Crystals" [http://www.lithographie.org/bookshop/the_smale_collection.htm] .

Smale is currently a professor at the Toyota Technological Institute at Chicago, a research institute closely affiliated with the University of Chicago.

In 2007, Smale was awarded the Wolf Prize in mathematics. [ [http://www.huji.ac.il/cgi-bin/dovrut/dovrut_search_eng_dev.pl?mesge116895485932688760 Press release] ] He is the last of only eight Fields Medallists to win both prizes.

Important publications

* S. Smale, "Generalized Poincaré's conjecture in dimensions greater than four" , Annals of Mathematics, 2nd Ser., 74 (1961), no. 2, 391 – 406. ( [http://links.jstor.org/sici?sici=0003-486X%28196109%292%3A74%3A2%3C391%3AGPCIDG%3E2.0.CO%3B2-B via JSTOR] )
* S. Smale, "Differentiable dynamical systems", Bulletin of the American Mathematical Society, 73 (1967), 747 – 817. ( [http://www.ams.org/bull/1967-73-06/S0002-9904-1967-11797-X/home.html] )

References

External links

*
* [http://www6.cityu.edu.hk/ma/people/smale%20main.htm Stephen Smale's homepage] at the City University of Hong Kong
*
* [http://www.tti-c.org/smale.html Stephen Smale's faculty listing at TTI]
*
* Robion Kirby, " [http://www.ams.org/notices/200011/rev-kirby.pdf Stephen Smale: The Mathematician Who Broke the Dimension Barrier] ", a book review of a biography in the Notices of the AMS.


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  • 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 (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 — 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, 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… …   Universalium

  • 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

  • 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

  • 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


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