Work
His most celebrated single result is his proof in 1956 of the existence of 7-dimensional spheres with nonstandard differential structure. Later with Michel Kervaire, he showed that the 7-sphere has 15 differentiable structures (28 if one considers orientation). An n-sphere 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 5-space 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.
In 1961 Milnor disproved the Hauptvermutung by exhibiting two simplicial complexes which are homeomorphic but combinatorially distinct.
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), the Leroy P Steele Prize for Mathematical Exposition (2004), and the Leroy P Steele Prize for Lifetime Achievement (2011). He was an editor of the Annals of Mathematics for a number of years after 1962. He has written a number of books which are remarkable for their easy, clear and precise style. In 1991 a symposium was held at Stony Brook University in celebration of his 60th birthday.
Milnor was awarded the 2011 Abel Prize, for his "pioneering discoveries in topology, geometry and algebra." Reacting to the award, Milnor told the New Scientist "It feels very good,", adding that, "One is always surprised by a call at 6 o'clock in the morning."
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Famous quotes containing the word work:
“Most of our platitudes notwithstanding, self-deception remains the most difficult deception. The tricks that work on others count for nothing in that very well-lit back alley where one keeps assignations with oneself: no winning smiles will do here, no prettily drawn lists of good intentions.”
—Joan Didion (b. 1934)
“Every great work of art has two faces, one toward its own time and one toward the future, toward eternity.”
—Daniel Barenboim (b. 1942)
“Poets that lasting Marble seek
Must carve in Latine or in Greek,
We write in Sand, our Language grows,
And like the Tide our work o’erflows.”
—Edmund Waller (1606–1687)