John Milnor

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John Willard Milnor (b. February 20, 1931) is a mathematician known for his work in differential topology and K-theory.

As an undergraduate at Princeton University he was named a Putnam Fellow in 1949 and 1950. He continued on to graduate school at Princeton, wrote his thesis on the isotopy of links. His advisor was Ralph Fox. Upon completing his doctorate he went on to work at Princeton. He is currently working at Stony Brook University.

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 and has written several influential books, including Morse Theory, Characteristic Classes (with Stasheff), The h-Cobordism Theorem, Dynamics in One Complex Variable, Singular Points of Complex Hypersurfaces, and Topology from the Differentiable Viewpoint.

His most celebrated single result is his proof that a 7-dimensional sphere can have several (more precisely, 15) differentiable structures. A sphere with such a nonstandard differential structure is called an exotic sphere.

His notable students have included Michael Spivak, John Mather, and Tadatoshi Akiba.

Now, John Milnor is a distinguished professor in Stony Brook University, with his wife Dusa McDuff.

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