John Willard Milnor (b. February 20, 1931 in Orange, New Jersey) is an American mathematician known for his work in differential topology, Ktheory, and dynamical systems, and for his influential books, which are widely considered to be examples of fine mathematical writing. He won the Fields Medal in 1962 and Wolf Prize in 1989. As of 2005, Milnor is a distinguished professor at the State University of New York at Stony Brook. His wife, Dusa McDuff, is a professor at Barnard College.
Life
As an undergraduate at
Princeton University he was named a
Putnam Fellow in 1949 and 1950 and also proved the
FaryMilnor theorem. He continued on to graduate school at Princeton and wrote his thesis, entitled
isotopy of links, which concerned link groups (a generalization of the classical knot group) and their associated link structure. His advisor was
Ralph Fox. Upon completing his doctorate he went on to work at Princeton.
In 1962 Milnor was awarded the Fields Medal for his work in differential topology. He later went on to win the National Medal of Science (1967), the Leroy P Steele Prize for Seminal Contribution to Research (1982), the Wolf Prize in Mathematics (1989), and the Leroy P Steele Prize for Mathematical Exposition (2004). He has been editor of the Annals of Mathematics since 1962.
His students have included Tadatoshi Akiba, Jon Folkman, John Mather, Laurent C. Siebenmann, Jonathan Sondow, and Michael Spivak.
Work
His most celebrated single result is his proof of the existence of 7dimensional spheres with nonstandard differential structure. Later with
Michel Kervaire, he showed that the 7sphere has 15
differentiable structures (28 if you consider orientation). An
nsphere with nonstandard differential structure is called an
exotic sphere, a term coined by Milnor.
See also
References
Articles

Books
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* Milnor, John W. (1965). Lectures on the hcobordism theorem, notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, NJ.
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External links
 Home page at SUNYSB
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