Masaki Kashiwara—Abel Prize Laureate 2025. Peter Badge/Typos1/The Abel Prize
Topics: Abel Prize, Mathematics, Modern Physics, Research
Masaki Kashiwara, this year’s Abel Prize winner, co-founded a new field of mathematics called algebraic analysis.
One of the landmarks of Kyoto, the home of mathematician Masaki Kashiwara, is the Kamo River. At certain points, there are stepping stones that allow residents to cross the river away from the bridges. If you take a closer look at these stones, you can see how the water forms swirls and small eddies around them. Describing this flow of a liquid is not easy. You have to solve complicated equations that have been known for centuries but still pose many mysteries today: Do the equations always have a solution? How can they be calculated? And what properties do they have? It seems that mathematicians have reached a limit with the tools of their trade. To make progress, a new toolbox is needed. The Japanese mathematician Masaki Kashiwara developed such a toolbox for similarly difficult questions in the 1970s.
Kashiwara introduced proven methods from algebra into analysis—the theory underlying calculus that explores functions, limits, and other concepts—and, together with his colleagues, founded an entirely new branch of mathematics: algebraic analysis. This led to significant advances in various fields. For example, Kashiwara succeeded in solving one of the problems posed by mathematician David Hilbert in the early 20th century and developed new techniques that are now used in modern physics.
Kashiwara “has proved astonishing theorems with methods no one had imagined. He has been a true mathematical visionary,” read a recent press release from the Norwegian Academy of Sciences and Letters, which honored him with this year’s Abel Prize—one of the highest honors in mathematics.
Kashiwara was born near Tokyo in 1947. He discovered his passion for mathematics at an early age through traditional Japanese puzzles known as tsurukamezan. These puzzles involve correctly calculating the number of cranes and turtles: Suppose x heads and y legs are visible. How many cranes and turtles are there? Kashiwara’s parents didn’t have much exposure to the abstract subject, but the young Masaki enjoyed solving this problem using algebraic methods.
Abel Prize Goes to Pioneer Whose ‘Math Toolbox’ Can Be Used to Describe the Natural World, Manon Bischoff, Gary Stix (Editor), Scientific American
