Shizuo Kakutani
Encyclopedia
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese-born American mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, best known for his eponymous fixed-point theorem.
Kakutani attended Tohoku University
Tohoku University
, abbreviated to , located in the city of Sendai, Miyagi Prefecture in the Tōhoku Region, Japan, is a Japanese national university. It is the third oldest Imperial University in Japan and is a member of the National Seven Universities...
in Sendai
Sendai, Miyagi
is the capital city of Miyagi Prefecture, Japan, and the largest city in the Tōhoku Region. In 2005, the city had a population of one million, and was one of Japan's 19 designated cities...
, where his advisor was Tatsujirō Shimizu. Early in his career he spent two years at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
in Princeton
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
at the invitation of the German mathematician Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...
. While there, he also met John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
.
Kakutani received his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in 1941 from Osaka University
Osaka University
, or , is a major national university located in Osaka, Japan. It is the sixth oldest university in Japan as the Osaka Prefectural Medical College, and formerly one of the Imperial Universities of Japan...
and taught there through World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. He returned to the Institute for Advanced Study in 1948, and was given a professorship by Yale
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
in 1949, where he won a students choice award for excellence in teaching.
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
Correspondence (mathematics)
In mathematics and mathematical economics, correspondence is a term with several related but not identical meanings.* In general mathematics, correspondence is an alternative term for a relation between two sets...
instead of function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
s. Its most important use is in proving the existence of Nash equilibria in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
.
Kakutani's other well-known mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
, and his solution of the Poisson equation using the methods of stochastic analysis
Stochastic processes and boundary value problems
In mathematics, some boundary value problems can be solved using the methods of stochastic analysis. Perhaps the most celebrated example is Shizuo Kakutani's 1944 solution of the Dirichlet problem for the Laplace operator using Brownian motion...
.
The Collatz conjecture
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture , Kakutani's problem , the Thwaites conjecture , Hasse's algorithm The Collatz conjecture is a...
is also known as the Kakutani conjecture.
His daughter, Michiko Kakutani
Michiko Kakutani
is an American Pulitzer Prize-winning critic for The New York Times and is considered by many to be a leading literary critic in the United States.-Life and career:...
, is a Pulitzer Prize
Pulitzer Prize
The Pulitzer Prize is a U.S. award for achievements in newspaper and online journalism, literature and musical composition. It was established by American publisher Joseph Pulitzer and is administered by Columbia University in New York City...
-winning literary critic for the New York Times.
List of books available in English
- Selected papers / Shizuo Kakutani ; Robert R. Kallman, editor (1986)