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Shizuo Kakutani 角谷 静夫' (Kakutani Shizuo, August 28, 1911–August 17, 2004) was a Japanese mathematician, best known for his eponymous fixed-point theorem.

Kakutani attended Tohoku University in Sendai, where his advisor was Tatsujirō Shimizu. Early in his career he spent two years at the Institute for Advanced Study in Princeton at the invitation of the German mathematician Hermann Weyl. While there, he also met John von Neumann.

Kakutani received his Ph.D. in 1941 from Osaka University[1] and taught there through World War II. He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale in 1949, where he won a students choice award for excellence in teaching[2].

Kakutani received two major awards of the Japan Academy, the Imperial Prize and the Academy Prize in 1982, for his scholarly achievements in general and his work on functional analysis in particular.

The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important use is in proving the existence of Nash equilibria in game theory.

Kakutani's other well-known mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory, and his solution of the Poisson equation using the methods of stochastic analysis.

The Collatz conjecture is also known as the Kakutani conjecture.

His daughter, Michiko Kakutani, is a Pulitzer Prize-winning literary critic for the New York Times.

See also

* Kakutani fixed point theorem
* Kakutani's theorem (geometry)

List of books available in English

* Selected papers / Shizuo Kakutani ; Robert R. Kallman, editor (1986)


1. ^ Shizuo Kakutani at the Mathematics Genealogy Project
2. ^ DeVane Medalists http://www.yale.edu/pbk/devane.html

External links

* Obituary, University of Massachusetts newsletter
* Obituary, Yale Bulletin and Calendar
* Biography, University of St. Andrews/Turnbull
* The Lost Theorems of Kakutani


Mathematics Encyclopedia

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