Masaki Kashiwara becomes the first Japanese scholar to win the Abel Prize, recognized globally as the “Nobel of Mathematics,” for groundbreaking work in D-module theory.
Japanese mathematician Masaki Kashiwara has been awarded the 2025 Abel Prize, one of the highest distinctions in mathematics, honoring his pioneering contributions to the field of algebraic analysis and his foundational work in D-module theory.
With this recognition, Kashiwara becomes the first scholar from Japan — and only the second from Asia — to receive the award in its 22-year history.
The Norwegian Academy of Science and Letters highlighted Kashiwara’s central role in creating and developing the analytical theory of D-modules, a mathematical framework that has reshaped multiple research fields, from number theory to quantum physics. Experts emphasize that his work has enabled profound advances in understanding complex differential equations and their geometric structure.
Oscar García Prada, professor at the Institute of Mathematical Sciences (ICMAT) in Spain, noted that Kashiwara is widely regarded as the founder of the modern D-module analytic theory. “It is a key tool in many branches of mathematics, from algebraic geometry to mathematical physics,” he said.
D-module theory originated within the broader framework of algebraic analysis, a field initiated in the 1950s by Mikio Sato, who later supervised Kashiwara’s graduate work. The central idea was to study differential equations through geometric methods, including sheaf cohomology, which was considered groundbreaking at the time.
A D-module is an algebraic structure that encodes systems of partial differential equations. Kashiwara, together with mathematicians such as Takahiro Kawai and Henri Stapp, applied this framework to Feynman integrals — essential components of quantum field theory — providing new insights into their analytic behavior.
Beyond D-modules, Kashiwara made significant contributions to representation theory, helping express symmetry in algebraic terms. He also resolved the Kazhdan-Lusztig conjecture for infinite-dimensional representations in collaboration with Jean-Luc Brylinski, a landmark achievement that continues to influence the study of deformation theory.
Colleagues describe him not only as a brilliant researcher but also as an intellectual catalyst. His informal talks, often presenting ideas not yet published, have been cited as “deeply influential” across the global mathematical community.
Kashiwara’s fascination with mathematics began in childhood, when he was assigned a classical arithmetic puzzle involving cranes and turtles: using the total number of heads and legs to determine the number of each animal. He not only solved the exercise but generalized the method, planting the seeds of what would become his life’s work.
Years later at the University of Tokyo, he revisited the problem in his master’s thesis under Sato’s guidance. At age 23, he established the mathematical foundations of D-module theory — a milestone that propelled him to international recognition.
His academic career took him from Nagoya University to the Massachusetts Institute of Technology (MIT) in 1978, and later to Kyoto, where he conducted influential research at the Research Institute for Mathematical Sciences (RIMS) and the Kyoto University Institute for Advanced Study. His previous honors include the Asahi Prize for Science, the Japanese Academy Prize, and the Fujihara Award.
With the Abel Prize — considered the closest equivalent to a “Nobel Prize” in mathematics — Kashiwara’s legacy is now cemented among the most influential mathematicians of the modern era. His work continues to shape global research in algebra, geometry, and theoretical physics.
