
related topics 
{work, book, publish} 
{math, number, function} 
{math, energy, light} 
{school, student, university} 
{son, year, death} 

John Willard Milnor (born 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. 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 of mathematics at Barnard College.
Contents
Life
As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950 and also proved the Fary–Milnor 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 was an editor of the Annals of Mathematics for a number of years after 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 in 1956 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. Egbert Brieskorn found simple algebraic equations for 28 complex hypersurfaces in complex 5space such that their intersection with a small sphere of dimension 9 around a singular point is diffeomorphic to these exotic spheres. Subsequently Milnor worked on the topology of isolated singular points of complex hypersurfaces in general, developing the theory of the Milnor fibration whose fibre has the homotopy type of a bouquet of μ spheres where μ is known as the Milnor number. Milnor's 1968 book on his theory inspired the growth of a huge and rich research area which continues to develop to this day.
Full article ▸


related documents 
Alain Connes 
Ralph Merkle 
Lars Ahlfors 
Laurent Lafforgue 
Alfred Aho 
Robert Simson 
Adi Shamir 
Christopher J. Date 
Jacob Bernoulli 
Peter Shor 
Wikipedia:History of computing/Permission 
GianCarlo Rota 
PR Watch 
Hartmann Schedel 
Wikipedia:WikiProject 
Roger Angell 
William Strunk, Jr. 
Amanda Hesser 
Maxim Kontsevich 
M. A. R. Barker 
Franco Modigliani 
Larry Page 
Susning.nu 
International IMPAC Dublin Literary Award 
Svante Pääbo 
Sophus Lie 
Eudora Welty 
Realencyclopädie der Classischen Altertumswissenschaft 
Richard Hamming 
Charles Hatchett 
