Vitali Milman

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Vitali Milman
Vitali Milman.jpg
Born (1939-08-23) 23 August 1939 (age 77)
Soviet Union
Nationality Israeli
Fields Mathematics
Institutions Tel Aviv University
Alma mater Kharkiv State University
Doctoral advisor Boris Levin
Doctoral students Semyon Alesker
Shiri Artstein-Avidan
Bo'az Klartag
Leonid Polterovich

Vitali Davidovich Milman (Hebrew: ויטלי מילמן‎‎; Russian: Виталий Давидович Мильман) (born 23 August 1939) is a mathematician specializing in analysis. He is a professor at the Tel-Aviv University. In the past he was a President of the Israel Mathematical Union and a member of the “Aliyah” committee of Tel-Aviv University.[1]


Milman received his Ph.D. at Kharkiv State University in 1965 under the direction of Boris Levin.

In a 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 arbitrarily close to being isometric 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.


He holds several positions including being the advisor to the Israel Ministry of Science on the immigration of scientists, and being a member of the European Mathematical Union.

He is on the editorial boards of several journals, including Geometric and Functional Analysis. He has published over 150 scientific publications, a monograph and eleven edited books. He has delivered lectures at Universities such as MIT, IAS Princeton, Berkeley, IHES Paris, Cambridge.

Awards and honors[edit]

Milman received the Landau Prize in Mathematics in 2002 and the EMET Prize in mathematics in 2007.[1]

In 2012 he became a fellow of the American Mathematical Society.[2]


Mathematics runs in the Milman family. His father is the mathematician David Milman, who devised the Krein–Milman theorem.[3] His brother is the mathematician Pierre Milman and his son is the young mathematician Emanuel Milman.[4]

Selected Works[edit]

  • Asymptotic Geometric Analysis, Part I. American Mathematical Society. 2015. ISBN 978-1-4704-2193-9. .


  1. ^ a b EMET prize announcement
  2. ^ List of Fellows of the American Mathematical Society, retrieved 2013-02-04.
  3. ^ I. Gohberg; M. S. Livšic; I. Piatetski-Shapiro (January 1986). "David Milman (1912–1982)". Integral Equations and Operator Theory. Birkhäuser Basel. 9 (1): ii. doi:10.1007/BF01257057. 
  4. ^ "Emanuel Milman's homepage". 

External links[edit]