was a Japanese-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 , or is a Japanese national university located in Sendai, Miyagi in the Tōhoku Region, Japan. It is informally referred to as . Established in 1907, it was the third Imperial University in Japan and among the first three Designated Nationa ...

Sendai is the capital city of Miyagi Prefecture, the largest city in the Tōhoku region. , the city had a population of 1,091,407 in 525,828 households, and is one of Japan's 20 designated cities. The city was founded in 1600 by the ''daimyō'' Date M ...

, 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), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

at the invitation of the mathematician

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

. While there, he also met

John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

. Kakutani received his Ph.D. in 1941 from

Osaka University , abbreviated as , is a public research university located in Osaka Prefecture, Japan. It is one of Japan's former Imperial Universities and a Designated National University listed as a "Top Type" university in the Top Global University Proje ...

and taught there through

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

. He returned to the Institute for Advanced Study in 1948, and was given a professorship by

Yale Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

in 1949, where he won a students' choice award for excellence in teaching. Kakutani received two awards of the

Japan Academy The Japan Academy ( Japanese: 日本学士院, ''Nihon Gakushiin'') is an honorary organisation and science academy founded in 1879 to bring together leading Japanese scholars with distinguished records of scientific achievements. The Academy is ...

, the

Imperial Prize Imperial is that which relates to an empire, emperor, or imperialism. Imperial or The Imperial may also refer to: Places United States * Imperial, California * Imperial, Missouri * Imperial, Nebraska * Imperial, Pennsylvania * Imperial, Texas ...

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 Michiko Kakutani (born January 9, 1955) 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 ...

, is a Pulitzer Prize-winning former literary critic for ''

The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...

''.

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, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equ ...

in game theory, and the Arrow–Debreu–McKenzie model of

general equilibrium theory In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an ov ...

in microeconomics. Kakutani's other mathematical contributions include Markov–Kakutani fixed-point theorem, another fixed point theorem; the

Kakutani skyscraper Kakutani is a Japanese surname. Notable people with the surname include: * Michiko Kakutani (born 1955), Japanese-American Pulitzer Prize-winning critic * Shizuo Kakutani (1911–2004), Japanese-American mathematician **Kakutani fixed-point theorem ...

, a concept in

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

(a branch of mathematics that studies

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s with an invariant measure and related problems); his solution of the

Poisson equation Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with t ...

using the methods of stochastic analysis. The

Collatz conjecture The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of intege ...

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 People from Osaka Japanese emigrants to the United States Tohoku University alumni Laureates of the Imperial Prize Osaka University alumni Osaka University faculty Yale University faculty