At one point he spent two years at the Institute for Advanced Study in Princeton at the invitation of the mathematician Hermann Weyl.

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.

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

Kakutani's other mathematical contributions include Markov–Kakutani fixed-point theorem, another fixed point theorem; the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems); his solution of the Poisson equation using the methods of stochastic analysis.