Person: Dvoretzky, Aryeh
Aryeh Dvoretzky was a Ukrainian-born Israeli mathematician who worked in functional analysis, statistics and probability.
Mathematical Profile (Excerpt):
- The principal of the school was Dr Arthur Biram who developed the school greatly during the years that Dvoretzky was a pupil.
- After graduating from the Hebrew Reali School, Dvoretzky entered the Hebrew University of Jerusalem.
- This university, which opened in 1925, had only awarded its first degrees a few years before Dvoretzky began his studies there.
- Dvoretzky was awarded his Master's Degree by the Hebrew University in 1937 and continued to undertake research there for his doctorate advised by Fekete.
- After the award of his doctorate in 1941, Dvoretzky was appointed to the teaching staff of the Hebrew University of Jerusalem.
- Dvoretzky made many research visits abroad, mainly to the United States but also to the Collège de France.
- Let us now look briefly at Dvoretzky's mathematical contributions.
- His best known fundamental result in this field is the Dvoretzky theorem, which was related by Vitali Milman to Paul Lévy's measure concentration phenomena and served as a starting point to modern Banach space theory.
- At the same time, Dvoretzky was producing work on probability.
- Throughout the years, Dvoretzky cooperated with Erdős, Jacob Wolfowitz, Abraham Wald, Herbert Robbins and Y S Chow in producing elegant and fundamental work in probability theory.
- We should say a little more about the Dvoretzky theorem.
- In 1950 Dvoretzky published a joint paper with Ambrose Rogers entitled Absolute and Unconditional Convergence in Normed Linear Spaces.
- One such proof appeared in Grothendieck's 1956 paper Sur certaines classes de suites dans les espaces de Banach et le théorème de Dvoretzky-Rogers Ⓣ(On certain classes of sequences in Banach spaces and the Dvoretzky-Rogers theorem) which also contained a number of important conjectures.
- In 1959 Dvoretzky proved the conjecture by Grothendieck which today is known as Dvoretzky's theorem.
- Dvoretzky's theorem initiated an avalanche of work on finite-dimensional normed spaces, guided by the heuristic principle: "All convex bodies behave like ellipsoids, and ever more so as the dimension increases." This principle runs completely counter to one's initial experience.
- Later Dvoretzky wrote a number of single-author papers on Brownian motion including On the oscillation of the Brownian motion process (1963) and Polygons on two-dimensional Brownian paths (1986).
- Dvoretzky received many honours for his contributions.
- In 2009, the Einstein Institute of Mathematics at the Hebrew University established an annual lecture series in memory of Dvoretzky.
Born 3 May 1916, Khorol, Ukraine. Died 8 May 2008, Jerusalem, Israel.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive