is a Japanese mathematician and professor at the

Kyoto University , or , is a National university, national research university in Kyoto, Japan. Founded in 1897, it is one of the former Imperial Universities and the second oldest university in Japan. The university has ten undergraduate faculties, eighteen gra ...

Institute for Advanced Study (KUIAS). He is known for his contributions to algebraic analysis,

microlocal analysis In mathematical analysis, microlocal analysis comprises techniques developed from the 1950s onwards based on Fourier transforms related to the study of variable-coefficients-linear and nonlinear partial differential equations. This includes genera ...

, ''D''-module theory,

Hodge theory In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every coho ...

sheaf theory In mathematics, a sheaf (: sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the d ...

and

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

. He was awarded the Abel Prize in 2025, and is the award's first recipient from Japan.

Biography

Kashiwara was born in

Yūki, Ibaraki 270px, Yuki Information and Communication Center is a city located in Ibaraki Prefecture, Japan. , the city had an estimated population of 49,252 in 19,889 households and a population density of 749 persons per km2. The percentage of the popula ...

on January 30, 1947. One of his early mathematical fascinations was the tsurukamezan problem, which asks the number of cranes and turtles given a set number of legs and heads. Kashiwara spent his undergraduate years at the

University of Tokyo The University of Tokyo (, abbreviated as in Japanese and UTokyo in English) is a public research university in Bunkyō, Tokyo, Japan. Founded in 1877 as the nation's first modern university by the merger of several pre-westernisation era ins ...

(UTokyo), earning his bachelor's degree in mathematics in 1969. He then went on to study at the same institution for his master's degree, which he completed in 1971. At UTokyo, Kashiwara was a student of Mikio Sato. His master's thesis, written in Japanese, laid the foundations for the study of D-modules. He continued studying under Sato at

after Sato moved to the

Research Institute for Mathematical Sciences The is a research institute attached to Kyoto University, hosting researchers in the mathematical sciences from all over Japan. RIMS was founded in April 1963. List of directors * Masuo Fukuhara (1963.5.1 – 1969.3.31) * Kōsaku Yosida (1969 ...

(RIMS) there, earning his doctorate in 1974. He was a plenary speaker at International Congress of Mathematicians in 1978 and an invited speaker in 1990. He is a foreign associate of the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

and a member 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 ...

. He has been involved in

(RIMS) since 1978 as a professor and later director. Kashiwara was awarded Japan's Order of the Sacred Treasure, Gold and Silver Star in 2020. He received the Abel Prize in 2025, the first Japanese national to do so. The Chairman of the Prize Committee, Dr. Helge Holden, described Kashiwara's contributions as "very important in many different areas of mathematics,” and explained that Kashiwara "has solved some open conjectures — hard problems that have been around nd hasopened new avenues, connecting areas that were not known to be connected before.” The award ceremony is planned to be held at

Oslo Oslo ( or ; ) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of 1,064,235 in 2022 ...

, Norway on May 20, 2025.

Research

Kashiwara and Sato established the foundations of the theory of

systems of linear equations In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example, : \begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in ...

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...

with

analytic function In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex ...

coefficients, introducing the idea of applying

sheaf cohomology In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions (holes) to solving a geometric problem glob ...

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

. Kashiwara's master thesis states the foundations of ''D''-module theory. Kashiwara developed the analytic theory of ''D''-modules, while Joseph Bernstein introduced a similar approach in the algebraic case. Kashiwara's PhD thesis proves the rationality of the roots of b-functions ( Bernstein–Sato polynomials), using ''D''-module theory and

resolution of singularities In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety ''V'' has a resolution, which is a non-singular variety ''W'' with a Proper morphism, proper birational map ''W''→''V''. For varieties ov ...

. Kashiwara's 1973 paper with Sato and Takahiro Kawai on the involutivity of characteristics of microdifferential systems and classification at generic points of microdifferential systems was described by Pierre Schapira as having "an enormous influence on the analysis of partial differential equations".

Books

*''Seminar on Micro-Local Analysis'', by

Victor Guillemin Victor William Guillemin (born 1937 in Boston) is an American mathematician. He works at the Massachusetts Institute of Technology in the field of symplectic geometry, and he has also made contributions to the fields of microlocal analysis, spec ...

, Masaki Kashiwara, and Takahiro Kawai (1979), *''Systems of Microdifferential Equations'', by Masaki Kashiwara; notes and translation by Teresa Monteiro Fernandes; introduction by Jean-Luc Brylinski (1983), *''Introduction to Microlocal Analysis'', by Masaki Kashiwara (1986) *''Foundations of Algebraic Analysis'', by Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura; translated by Goro Kato (1986), *''Algebraic Analysis : Papers Dedicated to Professor Mikio Sato on the Occasion of His Sixtieth Birthday'', edited by Masaki Kashiwara, Takahiro Kawai (1988), *''Sheaves on Manifolds'' : With a Short History by Christian Houzel, by Masaki Kashiwara, Pierre Schapira (1990), *''Topological Field Theory, Primitive Forms and Related Topics'', by Masaki Kashiwara ''et al.''(1998), *''Physical Combinatorics'', Masaki Kashiwara, Tetsuji Miwa, editors (2000), *''MathPhys Odyssey 2001: Integrable Models and Beyond: In Honor of Barry M. McCoy'', Masaki Kashiwara and Tetsuji Miwa, editors (2002), *''Bases cristallines des groupes quantiques'', by Masaki Kashiwara (rédigé par Charles Cochet); Cours Spécialisés 9 (2002), viii+115 pages, *''D-Modules and Microlocal Calculus'', Masaki Kashiwara; translated by Mutsumi Saito (2003), *''Categories and Sheaves'', Masaki Kashiwara and Pierre Schapira (2006),

Notes

External links

*
Fifty years of Mathematics with Masaki Kashiwara
by Pierre Schapira
PhotoVideos of Masaki Kashiwara
in the AV-Portal of the German National Library of Science and Technology *201
Kyoto Prize in Basic Sciences
{{DEFAULTSORT:Kashiwara Masaki 1947 births Living people 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of Tokyo alumni Academic staff of Kyoto University Academic staff of Nagoya University Members of the Japan Academy Members of the French Academy of Sciences Kyoto laureates in Basic Sciences Scientists from Ibaraki Prefecture Recipients of the Order of the Sacred Treasure, 2nd class