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 鈥渇or 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鈥�.
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 鈥� these are known as partial differential equations (PDEs).
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Kashiwara鈥檚 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 New 杏吧原创 he was happy to win the Abel prize, but is still actively working and hopes to make further contributions.
鈥淚 am now working on the representation theory of quantum affine algebras and its related topics,鈥� he says. 鈥淭here is a nice conjecture: [the] 鈥榓ffine quiver conjecture鈥�, but I still have no clue how to solve it.鈥�
at the University of Birmingham, UK, says Kashiwara鈥檚 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. 鈥淭hat鈥檚 the level of difficulty these things are at,鈥� he says. 鈥淚t鈥檚 incredibly esoteric.鈥�
But Craven says Kashiwara has made a huge impact in his field: 鈥淭he stuff that he鈥檚 done permeates representation theory. You can鈥檛 get away from Kashiwara if you want to do geometric representation theory, it鈥檚 just everywhere.鈥�
at the University of Glasgow, UK, says 鈥渁ll the big results in the field [algebraic analysis] are due to him, more or less鈥�, and the Abel prize win for Kashiwara has been a long time coming. 鈥淚t鈥檚 given for lifetime achievement, and he鈥檚 achieved a lot of in his lifetime,鈥� he says. 鈥淗e鈥檚 still revolutionising the field even now, I would say.鈥�
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.
