Stephen Smale (born July 15, 1930) is an American mathematician from Flint, Michigan, and winner of the Fields Medal in 1966. 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. July 15 is the 196th day (197th in leap years) of the year in the Gregorian Calendar, with 169 days remaining. ... Year 1930 (MCMXXX) was a common year starting on Wednesday (link is to a full 1930 calendar). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Nickname: The Vehicle City, Buick City, Flint Town, Bedrock, The 810 Location of Flint within Genesee County, Michigan. ... The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. ... 1966 (MCMLXVI) was a common year starting on Saturday (the link is to a full 1966 calendar). ... The University of Michigan, Ann Arbor (UM or U of M) is a coeducational public research university in the U.S. state of Michigan. ... Calculus is the name given to a group of systematic methods of calculation, computation, and analysis in mathematics which use a common and specialized algebraic notation. ... Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... Doctor of Philosophy (Ph. ... Raoul Bott (Harvard University News Office) Raoul Bott, FRS (born September 24, 1923, died December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense. ...

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. The University of Chicago is a private co-educational university located in Chicago, Illinois. ... In differential topology, Smales 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. ... In mathematics, the Poincaré conjecture (IPA: [])[1] is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. ... A cobordism W between M and N is an h-cobordism if the inclusion maps M → W and N → W are homotopy equivalences. ...

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. A Möbius strip, a surface with only one side and one edge; such shapes are an object of study in topology. ... In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... In the mathematics of chaos theory, a horseshoe map is any member of a class of chaotic maps of the square into itself. ... A Morse function is also an expression for an anharmonic oscillator In differential topology, the techniques of Morse theory give a very direct way of analyzing the topology of a manifold by studying differentiable functions on that manifold. ... This article or section does not cite its references or sources. ... Look up computation in Wiktionary, the free dictionary. ...

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 versus NP problem, and the Navier-Stokes equations, all of which have been designated Millennium Prize problems by the Clay Mathematics Institute. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... David Hilbert (January 23, 1862, Königsberg, East Prussia – February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. ... Unsolved problems in mathematics: Is the real part of a non-trivial zero of the Riemann zeta function always ½? In mathematics, the Riemann hypothesis (also called the Riemann zeta-hypothesis), first formulated by Bernhard Riemann in 1859, is one of the most famous unsolved problems. ... Hilberts sixteenth problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, together with the other 22 problems. ... In mathematics, the Poincaré conjecture (IPA: [])[1] is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. ... This article or section is in need of attention from an expert on the subject. ... The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts. ... The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Cambridge, Massachusetts. ...

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. NSF is an abbreviation. ... The Free Speech Movement was a student protest which began in 1964 - 1965 on the campus of the University of California, Berkeley under the informal leadership of student Mario Savio and others. ... A subpoena is a writ commanding a person to appear under penalty (from Latin). ... HUAC hearings House Committee on Un-American Activities (HUAC or HCUA) (1938–1975) was an investigative committee of the United States House of Representatives. ...

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. The University of California, Berkeley (also known as UC Berkeley, Berkeley, Cal, and by other names, see below) is the oldest and flagship campus of the ten-campus University of California system. ... Columbia University is a private research university whose main campus lies in the Morningside Heights neighborhood of the Borough of Manhattan in New York City. ... The City University of Hong Kong (CityU) (Traditional Chinese: 香港城市大學) is one of the universities in Hong Kong. ...

Smale is currently a professor at the Toyota Technological Institute at Chicago, a research institute closely affiliated with the University of Chicago. In 2003 Toyota opened the Toyota Technological Institute at Chicago, jointly with the University of Chicago. ... The University of Chicago is a private university located principally in the Hyde Park neighborhood of Chicago. ...

In 2007, Smale was awarded the Wolf Prize in mathematics^[1]. The Wolf Prize has been awarded annually since 1978 to living scientists and artists for achievements in the interest of mankind and friendly relations among peoples . ...

References

1. ^ Press release.[1]

Important publications

• S. Smale, Generalized Poincaré's conjecture in dimensions greater than four (via JSTOR), Annals of Mathematics, 2nd Ser., 74 (1961), no. 2, 391 – 406
• S. Smale, Differentiable dynamical systems, Bulletin of the American Mathematical Society, 73 (1967), 747 – 817

The Annals of Mathematics (ISSN 0003-486X), often just called Annals, is a bimonthly mathematics research journal published by Princeton University and the Institute for Advanced Study. ... The American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...

External links

• Stephen Smale at the Mathematics Genealogy Project
• Stephen Smale's homepage at the City University of Hong Kong
• O'Connor, John J., and Edmund F. Robertson. "Stephen Smale". MacTutor History of Mathematics archive.
• Stephen Smale's faculty listing at TTI
• Smale's problems on MathWorld
• Robion Kirby, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, a book review of a biography in the Notices of the AMS.

The Mathematics Genealogy Project is a web-based database that gives an academic genealogy based on dissertation supervision relations. ... Robion Kirby is a professor of mathematics at the University of California at Berkeley who works in low-dimensional topology. ... AMS, a three-letter abbreviation, may refer to: Accelerator mass spectrometry Acute mountain sickness, the commonest type of altitude illness. ...