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:
“In some withdrawn, unpublic mead
Let me sigh upon a reed,
Or in the woods, with leafy din,
Whisper the still evening in:
Some still work give me to do,—
Only—be it near to you!
For I’d rather be thy child
And pupil, in the forest wild,
Than be the king of men elsewhere,
And most sovereign slave of care:
To have one moment of thy dawn,
Than share the city’s year forlorn.”
—Henry David Thoreau (1817–1862)
“Where the whole man is involved there is no work. Work begins with the division of labor.”
—Marshall McLuhan (1911–1980)
“An ordinary man will work every day for a year at shoveling dirt to support his body, or a family of bodies; but he is an extraordinary man who will work a whole day in a year for the support of his soul. Even the priests, men of God, so called, for the most part confess that they work for the support of the body.”
—Henry David Thoreau (1817–1862)