Shizuo Kakutani

Who was Shizuo Kakutani?

Shizuo Kakutani was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.

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

Kakutani received his Ph.D. in 1941 from Osaka University 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.

Kakutani received two 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.