When I was little, to Masaki Kashiwara They put a problem in school: the tsurukamezan. If the number of heads is x and the number of legs is y, how many cranes and turtles are there? A simple example: if there are two heads and six legs, there must be a crane and a turtle. The Kashiwara boy not only solved the specific problem, but enjoyed finding a method to always solve it, whatever the number of legs and heads. Thus began his passion for arithmetic, which would accompany him a lifetime and that this Wednesday, at 78, he has been especially recognized. The Norwegian Academy of Sciences and Letters has awarded the Japanese mathematician, a specialist in algebraic analysis, with the prestigious ABEL Awardknown as the ‘Nobel’ of Mathematics and endowed with 660,000 euros.
According to the Norway Academy, Masaki Kashiwara, a professor at the University of Kyoto, is a “bridge builder” between different fields of mathematics, bridges comparable to “unite Norway with South America or Japan with Antarctica.” Kashiwara connected “the continents mathematics of algebra and analysis, and then the third mathematical continent of geometry, with their original thinking.” In the institution’s opinion, “his ideas are not only beautiful and brilliant in themselves, but they open paths so that many other mathematicians explore new territories and solve new problems.”
At the University of Tokyo, along with his supervisor and mentor, Mikio Sato, Kashiwara was a pioneer in algebraic analysis, applying algebra methods to analysis problems: mathematics that explain how things change. His master’s thesis, written when he was only 23 years old, laid the foundations for the Module D theory, as a way to algebraically analyze systems of linear partial differential equations. For the next 25 years, this thesis remained available only in Japanese, but its impact and influence were so great that it finally translated into English.
With his master’s thesis as a starting point, Kashiwara continued his mathematical career with innovative discoveries and solutions. His numerous achievements have exerted a great influence in various fields of mathematics and have contributed significantly to their development. Over the years, many mathematicians have inspired Kashiwara’s ideas.
How things change
Differential equations describe how things change, as in school problems that ask questions of the type ‘at what speed does this car move at a certain point?’ ‘Is it accelerating or slowing down?’ Mathematicians such as Kashiwara work with systems of linear partial differential equations. They are less interested in solving equations and more discover the properties that a solution will have, if it exists.
Using his module theory, Kashiwara was able to demonstrate that, in any dimension, there will always be a unique differential equation that meets the planned requirements.
Being a postgraduate student, Kashiwara traveled to France with Sato and his mathematical colleague Takahiro Kawai, where he met his life collaborator, Pierre Schapira and developed his work on Haz, a bridge towards another mathematical area: the theory of representation. The representation theory uses algebra to study symmetry. After completing his doctorate at the University of Kyoto in 1974, Kashiwara was appointed associated professor at the University of Nagoya. In 1977, he moved as a researcher to MIT, before returning to Japan in 1978, where he has since remained at the Mathematical Science Research Institute (Rims).
«For more than half a century in mathematics, Masaki Kashiwara has opened the doors to a new field. It has tended bridges and created tools. It has demonstrated amazing theorems with unimaginable methods. He has been a true mathematical visionary, ”said the academy. His work “continues to be at the forefront of contemporary mathematics and inspiring generations of researchers,” he added.
The ABEL award, which bears the name of the Norwegian mathematician Niels Henrik Abel (1802-1829), was created by the Norwegian government, partly in an attempt to compensate for the lack of a Nobel Prize in Mathematics.
Last year, the ABEL award fell to the Frenchman Michel Talagrand, a specialist in probability and functional analysis. Kashiwara will receive his award in Oslo on May 20.
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