Masaki Kashiwara’s work is seen as highly abstract but vital Peter Bagde / Typos1 / The Abel Prize
has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis.
Kashiwara, a professor at , Japan, received the award “for his fundamental contributions to algebraic analysis and representation theory, in particular the development of the theory of D-modules and the discovery of crystal bases”.
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His work involves the use of algebra to investigate geometry and symmetry, and has focused on using those ideas to find solutions for differential equations, which involve relationships between mathematical functions and their rates of change. Finding solutions to such equations can be particularly tricky, especially in the case of functions that have several variables and therefore several rates of change – these are known as partial differential equations (PDEs).
Kashiwara’s vital work on D-modules, a highly specific area of algebraic analysis involving linear PDEs, was done surprisingly early in his career, during his PhD thesis. He has worked with over 70 collaborators. Kashiwara told Â鶹´«Ã½ he was happy to win the Abel prize, but is still actively working and hopes to make further contributions.
“I am now working on the representation theory of quantum affine algebras and its related topics,” he says. “There is a nice conjecture: [the] ‘affine quiver conjecture’, but I still have no clue how to solve it.”
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at the University of Birmingham, UK, says Kashiwara’s work is extremely abstract, far from direct real-world applications, and understanding even a basic summary would require a mathematics PhD as a bare minimum. “That’s the level of difficulty these things are at,” he says. “It’s incredibly esoteric.”
But Craven says Kashiwara has made a huge impact in his field: “The stuff that he’s done permeates representation theory. You can’t get away from Kashiwara if you want to do geometric representation theory, it’s just everywhere.”
at the University of Glasgow, UK, says “all the big results in the field [algebraic analysis] are due to him, more or less”, and the Abel prize win for Kashiwara has been a long time coming. “It’s given for lifetime achievement, and he’s achieved a lot of in his lifetime,” he says. “He’s still revolutionising the field even now, I would say.”
The Abel prize, named after Norwegian mathematician Niels Henrik Abel, is awarded each year by the King of Norway. Last year, it was won by Michel Talagrand for his research into probability theory and the extremes of randomness.
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