{"id":15465,"date":"2025-03-26T11:27:13","date_gmt":"2025-03-26T11:27:13","guid":{"rendered":"https:\/\/site.itshrt.com\/worldnews\/masaki-kashiwara-japanese-mathematician-wins-2025-abel-prize\/"},"modified":"2025-03-26T11:27:13","modified_gmt":"2025-03-26T11:27:13","slug":"masaki-kashiwara-japanese-mathematician-wins-2025-abel-prize","status":"publish","type":"post","link":"https:\/\/site.itshrt.com\/worldnews\/masaki-kashiwara-japanese-mathematician-wins-2025-abel-prize\/","title":{"rendered":"Masaki Kashiwara, Japanese Mathematician, Wins 2025 Abel Prize"},"content":{"rendered":"<p> <script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-6606220950177433\"\r\n     crossorigin=\"anonymous\"><\/script>\r\n<!-- ItShrt World News -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:block\"\r\n     data-ad-client=\"ca-pub-6606220950177433\"\r\n     data-ad-slot=\"1882483372\"\r\n     data-ad-format=\"auto\"\r\n     data-full-width-responsive=\"true\"><\/ins>\r\n<script>\r\n     (adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\r\n<br \/>\n<\/p>\n<div data-testid=\"companionColumn-0\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Masaki Kashiwara, a Japanese mathematician, received this year\u2019s Abel Prize, which aspires to be the equivalent of the Nobel Prize in math. Dr. Kashiwara\u2019s highly abstract work combined algebra, geometry and differential equations in surprising ways.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">The Norwegian Academy of Science and Letters, which manages the Abel Prize, announced the honor on Wednesday morning.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cFirst of all, he has solved some open conjectures \u2014 hard problems that have been around,\u201d said Helge Holden, chairman of the prize committee. \u201cAnd second, he has opened new avenues, connecting areas that were not known to be connected before. This is something that always surprises mathematicians.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Mathematicians use connections between different areas of math to tackle recalcitrant problems, allowing them to recast those problems into concepts they better understand.<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-1\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">That has made Dr. Kashiwara, 78, of Kyoto University, \u201cvery important in many different areas of mathematics,\u201d Dr. Holden said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">But have uses been found for Dr. Kashiwara\u2019s work in solving concrete, real-world problems?<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cNo, nothing,\u201d Dr. Kashiwara said in an interview.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">The honor is accompanied by 7.5 million Norwegian kroner, or about $700,000.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Unlike <a class=\"css-yywogo\" href=\"https:\/\/www.nytimes.com\/article\/nobel-prizes-2024.html\" title=\"\">Nobel Prize laureates<\/a>, who are frequently surprised with <a class=\"css-yywogo\" href=\"https:\/\/www.nytimes.com\/interactive\/2015\/10\/04\/science\/where-where-you-nobel-prize-call-stories.html\" title=\"\">middle-of-the-night phone calls<\/a> just before the honors are publicly announced, Dr. Kashiwara has known of his honor for a week.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">The Norwegian academy informs Abel Prize recipients with ruses similar to those used to spring a surprise birthday party on an unsuspecting person. \u201cThe director of my institute told me that there is a Zoom meeting at 4 o\u2019clock in the afternoon, and please attend,\u201d Dr. Kashiwara recalled in an interview.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">On the video teleconference call, he did not recognize many of the faces. \u201cThere were many non-Japanese people in the Zoom meeting, and I\u2019m wondering what\u2019s going on,\u201d Dr. Kashiwara said.<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-2\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Marit Westergaard, secretary general of the Norwegian academy, introduced herself and told Dr. Kashiwara that he had been chosen for the year\u2019s Abel.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cCongratulations,\u201d she said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Dr. Kashiwara, who was having trouble with his internet connection, was initially confused. \u201cI don\u2019t completely understand what you said,\u201d he said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">When his Japanese colleagues repeated the news in Japanese, Dr. Kashiwara said: \u201cThat is not what I expected at all. I\u2019m very surprised and honored.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Growing up in Japan in the postwar years, Dr. Kashiwara was drawn to math. He recalled a common Japanese math problem known as tsurukamezan, which translates as the \u201ccrane and turtle calculation.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">The problem states: \u201cThere are cranes and turtles. The count of heads is X and the count of legs is Y. How many cranes and turtles are there?\u201d (For example, for 21 heads and 54 legs, the answer is 15 cranes and six turtles.)<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-3\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">This is a simple algebra word problem similar to what students solve in middle school. But Dr. Kashiwara was much younger when he encountered the problem and read an encyclopedia to learn how to come up with the answer. \u201cI was a kid, so I can\u2019t remember, but I think I was 6 years old,\u201d he said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">In college, he attended a seminar by Mikio Sato, a Japanese mathematician, and was fascinated by Sato\u2019s groundbreaking work in what is now known as algebraic analysis.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cAnalysis, that is described by the inequality,\u201d Dr. Kashiwara said. \u201cSomething is bigger or something is smaller than the other.\u201d Algebra deals with equalities, solving equations for some unknown quantity. \u201cSato wanted to bring the equality world into analysis.\u201d<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-4\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Phenomena in the real world are described by real numbers like 1, \u20134\/3 and pi. There are also what are known as imaginary numbers like <em class=\"css-2fg4z9 e1gzwzxm0\">i<\/em>, which is the square root of \u20131, and complex numbers, which are sums of real and imaginary numbers.<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-5\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Real numbers are a subset of complex numbers. The real world, described by the mathematical functions of real numbers, \u201cis surrounded by a complex world\u201d involving functions of complex numbers, Dr. Kashiwara said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">For some equations with singularities \u2014 points where the answers turn into infinity \u2014 looking at the nearby behavior with complex numbers can sometimes provide insight. \u201cSo<strong class=\"css-8qgvsz ebyp5n10\"> <\/strong>the inference from the complex world is reflected to the singularities in the real world,\u201d Dr. Kashiwara said.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">He wrote \u2014 by hand, in Japanese \u2014 a master\u2019s thesis using algebra to study partial differential equations, developing techniques that he would employ throughout his career.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Dr. Kashiwara\u2019s work also pulled in what is known as representation theory, which uses knowledge of symmetries to help solve a problem. \u201cImagine you have a figure drawn on the floor,\u201d Olivier Schiffmann, a mathematician at the University of Paris-Saclay and the French National Center for Scientific Research. \u201cUnfortunately, it is all covered in mud and all you can see is, say, a 15-degree sector of it.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">But if one knows that the figure remains unchanged when rotated by 15 degrees, one can reconstruct it through successive rotations. Because of the symmetry, \u201cI only need to know a small part in order to understand the whole,\u201d Dr. Schiffman said. \u201cRepresentation theory allows you to do that in much more complex situations.\u201d<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-6\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Another invention of Dr. Kashiwara\u2019s was called crystal bases. He drew inspiration from statistical physics, which analyzes critical temperatures when materials change phases, like when ice melts to water. The crystal bases allowed complex, seemingly impossible calculations to be replaced with much simpler graphs of vertices connected by lines.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cThis purely combinatorial object in fact encodes a lot of information,\u201d Dr. Schiffmann said. \u201cIt opened up a whole new area of research.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Confusingly, however, the crystals of crystal bases are completely different from the sparkly faceted gemstones that most people think of as crystals.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cPerhaps crystal is not a good word,\u201d Dr. Kashiwara admitted.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Dr. Holden said Dr. Kashiwara\u2019s work was difficult to explain to non-mathematicians, because it was much more abstract than that of some earlier Abel prize laureates.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">For example, the research of <a class=\"css-yywogo\" href=\"https:\/\/www.nytimes.com\/2024\/03\/20\/science\/abel-prize-mathematics-randomness.html\" title=\"\">Michel Talagrand<\/a>, last year\u2019s laureate, studied randomness in the universe like the heights of ocean waves, and the work of <a class=\"css-yywogo\" href=\"https:\/\/www.nytimes.com\/2023\/03\/22\/science\/abel-prize-math-luis-caffarelli.html\" title=\"\">Luis Caffarelli<\/a>, who was honored two years ago, can be applied to phenomena like the melting of a piece of ice.<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<div data-testid=\"companionColumn-7\">\n<div class=\"css-53u6y8\">\n<p class=\"css-at9mc1 evys1bk0\">Dr. Kashiwara\u2019s work is more like tying together several abstract ideas of mathematics into more abstract combinations that are insightful to mathematicians tackling a variety of problems.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cI think it\u2019s not easy,\u201d Dr. Kashiwara said. \u201cI\u2019m sorry.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">Dr. Holden pointed to one particular work, in which Dr. Kashiwara deduced the existence of crystal bases, as a \u201cmasterpiece of a theorem,\u201d with 14 steps of induction, using inference to recursively prove a series of assertions.<\/p>\n<p class=\"css-at9mc1 evys1bk0\">\u201cHe has to solve one by solving the others, and they\u2019re all connected,\u201d Dr. Holden said. \u201cAnd if one falls, the whole thing falls. So he is able to combine them in a very deep and very clever way.\u201d<\/p>\n<p class=\"css-at9mc1 evys1bk0\">But Dr. Holden said he could not provide a simple explanation of the proof. \u201cThat\u2019s hard,\u201d he said. \u201cI can see the 14 steps.\u201d<\/p>\n<\/div>\n<aside class=\"css-ew4tgv\" aria-label=\"companion column\"\/><\/div>\n<p><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-6606220950177433\"\r\n     crossorigin=\"anonymous\"><\/script>\r\n<!-- ItShrt World News -->\r\n<ins class=\"adsbygoogle\"\r\n     style=\"display:block\"\r\n     data-ad-client=\"ca-pub-6606220950177433\"\r\n     data-ad-slot=\"1882483372\"\r\n     data-ad-format=\"auto\"\r\n     data-full-width-responsive=\"true\"><\/ins>\r\n<script>\r\n     (adsbygoogle = window.adsbygoogle || []).push({});\r\n<\/script>\r\n<br \/>\n<br \/><a href=\"https:\/\/www.nytimes.com\/2025\/03\/26\/science\/abel-prize-math-masaki-kashiwara.html\">Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Masaki Kashiwara, a Japanese mathematician, received this year\u2019s Abel Prize, which aspires to be the equivalent of the Nobel Prize<\/p>\n","protected":false},"author":1,"featured_media":15466,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[38],"tags":[4931,4932,4933,760,4929,4930,848,4934,188],"class_list":["post-15465","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-science","tag-abel-prize","tag-awards","tag-decorations-and-honors","tag-japan","tag-kashiwara","tag-masaki","tag-mathematics","tag-norwegian-academy-of-science-and-letters","tag-your-feed-science"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Masaki Kashiwara, Japanese Mathematician, Wins 2025 Abel Prize - World News<\/title>\n<meta name=\"robots\" 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