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."
Read more about this topic: John Milnor
Famous quotes containing the word work:
“A poet’s work is to name the unnameable, to point at frauds, to take sides, start arguments, shape the world, and stop it going to sleep.”
—Salman Rushdie (b. 1947)
“In most modern instances, interpretation amounts to the philistine refusal to leave the work of art alone. Real art has the capacity to make us nervous. By reducing the work of art to its content and then interpreting that, one tames the work of art. Interpretation makes art manageable, conformable.”
—Susan Sontag (b. 1933)
“Sleep, beloved, such a sleep
As did that wild Tristram know
When, the potion’s work being done,
Roe could run or doe could leap
Under oak and beechen bough,
Roe could leap or doe could run....”
—William Butler Yeats (1865–1939)