was a Japanese and American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, best known for his eponymous fixed-point theorem.

Biography

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 The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in Princeton at the invitation of the mathematician

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

. While there, he also met

John von Neumann John von Neumann ( ; ; December 28, 1903 – February 8, 1957) was a Hungarian and American mathematician, physicist, computer scientist and engineer. Von Neumann had perhaps the widest coverage of any mathematician of his time, in ...

. Kakutani received his Ph.D. in 1941 from Osaka University and taught there through

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

. 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. He was a Plenary Speaker of the ICM in 1950 in Cambridge, Massachusetts. Kakutani was married to Keiko ("Kay") Uchida, who was a sister to author Yoshiko Uchida. His daughter,

Michiko Kakutani is an American writer and retired literary critic, best known for reviewing books for ''The New York Times'' from 1983 to 2017. In that role, she won the Pulitzer Prize for Criticism in 1998. Early life and family Kakutani, a Japanese Americ ...

, is a

Pulitzer Prize The Pulitzer Prizes () are 23 annual awards given by Columbia University in New York City for achievements in the United States in "journalism, arts and letters". They were established in 1917 by the will of Joseph Pulitzer, who had made his fo ...

-winning former literary critic for ''

The New York Times ''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of ...

''.

Work

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

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, and the Arrow–Debreu–McKenzie model of general equilibrium theory in microeconomics. 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 Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

that studies dynamical systems with an invariant measure and related problems); his solution of the Poisson equation using the methods of stochastic analysis. The Collatz conjecture is also known as the Kakutani conjecture.

Selected articles

*"A generalization of Brouwer's fixed point theorem." Duke Mathematical Journal (1941): 457–459. *"Concrete representation of abstract (L)-spaces and the mean ergodic theorem." Annals of Mathematics (1941): 523–537. *"Concrete representation of abstract (M)-spaces (A characterization of the space of continuous functions)." Annals of Mathematics (1941): 994–1024. *"On equivalence of infinite product measures." Annals of Mathematics (1948): 214–224.

List of books available in English

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

References

External links

New York Times obituaryBiography, University of St. Andrews/TurnbullThe Lost Theorems of Kakutani, by prof. Stanley Eigen. (PDF)
{{DEFAULTSORT:Kakutani, Shizuo 1911 births 2004 deaths 20th-century Japanese mathematicians 21st-century Japanese mathematicians Probability theorists Scientists from Osaka Japanese emigrants to the United States Tohoku University alumni Laureates of the Imperial Prize Osaka University alumni Academic staff of Osaka University Yale University faculty