Work
Milman received his Ph.D. at Kharkov State University in 1965 under the direction of Boris Levin.
In a famous 1971 paper, Milman gave a new proof of Dvoretzky's theorem, stating that every convex body in dimension N has a section of dimension d(N), with d(N) tending to infinity with N, that is isomorphic to an ellipsoid. Milman's proof gives the optimal bound d(N) ≥ const log N. In this proof, Milman put forth the concentration of measure phenomenon which has since found numerous applications.
Milman made important contributions to the study of Banach spaces of large (finite) dimension, which led to the development of asymptotic geometric analysis. His results in this field include Milman's reverse Brunn–Minkowski inequality and the quotient of subspace theorem.
Read more about this topic: Vitali Milman
Famous quotes containing the word work:
“I must work, so as not to be a fool, to get on, to become a journalist, because that’s what I want!... I can’t imagine that I would have to lead the same sort of life as Mummy ... and all the women who do their work and are then forgotten. I must have something besides a husband and children, something that I can devote myself to!”
—Anne Frank (1929–1945)
“We have not the motive to prepare ourselves for a “life-work” of teaching, of social work—we know that we would lay it down with hallelujah in the height of our success, to make a home for the right man. And all the time in the background of our consciousness rings the warning that perhaps the right man will never come. A great love is given to very few. Perhaps this make-shift time filler of a job is our life work after all.”
—Ruth Benedict (1887–1948)
“The best work of artists in any age is the work of innocence liberated by technical knowledge. The laboratory experiments that led to the theory of pure color equipped the impressionists to paint nature as if it had only just been created.”
—Nancy Hale (b. 1908)