{"id":8115,"date":"2022-10-05T12:40:58","date_gmt":"2022-10-05T03:40:58","guid":{"rendered":"https:\/\/www.waseda.jp\/fsci\/wise\/?p=8115"},"modified":"2022-10-20T14:41:52","modified_gmt":"2022-10-20T05:41:52","slug":"%e5%bd%93%e3%81%9f%e3%82%8a%e5%89%8d%e3%81%ab%e5%88%a9%e7%94%a8%e3%81%95%e3%82%8c%e3%82%8b%e7%94%bb%e5%83%8f%e9%80%9a%e4%bf%a1%e6%8a%80%e8%a1%93%e3%81%a7%e7%a4%be%e4%bc%9a%e3%81%ab-2-2","status":"publish","type":"post","link":"https:\/\/www.waseda.jp\/fsci\/wise\/other\/2022\/10\/05\/8115\/","title":{"rendered":"\u6570\u5b66\u3068\u3044\u3046\u8a00\u8a9e\u3067\u81ea\u7136\u79d1\u5b66\u306e\u771f\u7406\u3092\u63a2\u7a76\u3059\u308b \/ Harnessing the Language That Is Mathematics to Search for the Truths of Natural Science\u3010\u57fa\u5e79\u7406\u5de5\u5b66\u90e8 \u6570\u5b66\u79d1\u30fb\u5c0f\u8597\u82f1\u96c4\u6559\u6388\u3011"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-8116 aligncenter\" 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\/><\/p>\n<h3>\u6570\u5b66\u306f\u81ea\u7136\u79d1\u5b66\u3092\u8aac\u660e\u3059\u308b\u8a00\u8a9e<\/h3>\n<p>\u5fae\u7a4d\u5206\u306f\u30a2\u30a4\u30b6\u30c3\u30af\u30fb\u30cb\u30e5\u30fc\u30c8\u30f3\u304c\u751f\u307f\u51fa\u3057\u305f\u3082\u306e\u3067\u3001\u3082\u3068\u3082\u3068\u306f\u7269\u7406\u73fe\u8c61\u3092\u6570\u5b66\u3067\u8a18\u8ff0\u3057\u305f\u3044\u3068\u3044\u3046\u52d5\u6a5f\u304b\u3089\u8003\u3048\u51fa\u3055\u308c\u305f\u3002\u305d\u306e\u305f\u3081\u3001\u6570\u5b66\u3068\u7269\u7406\u5b66\u306f\u5bc6\u63a5\u306a\u95a2\u4fc2\u306b\u3042\u308a\u3001\u76f8\u4e92\u767a\u5c55\u3057\u3066\u304d\u305f\u3068\u3044\u3046\u6b74\u53f2\u304c\u3042\u308b\u3002<\/p>\n<p>\u300c\u30b1\u30d7\u30e9\u30fc\u306f\u3001\u60d1\u661f\u304c\u6955\u5186\u8ecc\u9053\u3092\u63cf\u3044\u3066\u3044\u308b\u3053\u3068\u3092\u89b3\u6e2c\u304b\u3089\u767a\u898b\u3057\u3001\u30cb\u30e5\u30fc\u30c8\u30f3\u306f\u305d\u308c\u3092\u6570\u5f0f\u3067\u8868\u3057\u3066\u307f\u305b\u307e\u3057\u305f\u3002\u60d1\u661f\u306e\u904b\u52d5\u304c\u65b9\u7a0b\u5f0f\u3072\u3068\u3064\u3067\u30d0\u30b7\u30c3\u3068\u51fa\u3066\u304f\u308b\u3001\u3053\u308c\u306f\u7269\u51c4\u3044\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u7269\u7406\u5b66\u3067\u767a\u898b\u3057\u305f\u73fe\u8c61\u3092\u30e2\u30c7\u30eb\u5316\u3057\u305f\u308a\u89e3\u3044\u305f\u308a\u3059\u308b\u306e\u304c\u6570\u5b66\u3067\u3001\u305d\u308c\u304c\u6211\u3005\u306e\u6700\u7d42\u7684\u306a\u76ee\u6a19\u3067\u3059\u3002\u305d\u306e\u610f\u5473\u3067\u3001\u6570\u5b66\u306f\u81ea\u7136\u79d1\u5b66\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u8a00\u8a9e\u3068\u3044\u3048\u308b\u3068\u601d\u3044\u307e\u3059\u300d\uff08\u5c0f\u8597\u6559\u6388\uff09<\/p>\n<p>\u300c\u79c1\u304c\u3084\u3063\u3066\u3044\u308b\u5206\u91ce\u306f\u7d14\u7c8b\u6570\u5b66\u3067\u3059\u304b\u3089\u3001\u76f4\u63a5\u7684\u306b\u793e\u4f1a\u306e\u5f79\u306b\u7acb\u3064\u3053\u3068\u304c\u76ee\u7684\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3082\u3061\u308d\u3093\u3001\u7d50\u679c\u3068\u3057\u3066\u5f79\u306b\u7acb\u3064\u3053\u3068\u306f\u3042\u308b\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u305d\u308c\u304c\u76ee\u7684\u3067\u306f\u306a\u3044\u3002\u3067\u3082\u3001\u81ea\u7136\u79d1\u5b66\u3063\u3066\u305d\u3046\u3044\u3046\u3082\u306e\u3067\u3059\u3088\u306d\u3002\u4f8b\u3048\u3070\u3001\u6697\u53f7\u306b\u306f\u7d20\u6570\u304c\u4f7f\u308f\u308c\u307e\u3059\u304c\u3001\u6697\u53f7\u3092\u3064\u304f\u308a\u305f\u304f\u3066\u7d20\u6570\u306e\u7814\u7a76\u3092\u3057\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u308f\u3051\u3067\u3059\u300d\uff08\u5c0f\u8597\u6559\u6388\uff09<\/p>\n<p>\u3067\u306f\u3001\u7814\u7a76\u306e\u30e2\u30c1\u30d9\u30fc\u30b7\u30e7\u30f3\u306f\u4f55\u304b\u3068\u306e\u8cea\u554f\u306b\u3001\u300c\u304b\u3063\u3053\u3088\u304f\u8a00\u3048\u3070\u771f\u7406\u306e\u63a2\u7a76\u3067\u3059\u300d\u3068\u7b54\u3048\u305f\u5c0f\u8597\u6559\u6388\u3002\u6700\u5f8c\u306b\u3001\u4eca\u5f8c\u306e\u5c55\u671b\u306b\u3064\u3044\u3066\u4f3a\u3063\u305f\u3002<\/p>\n<p>\u300c\u30ca\u30d3\u30a8-\u30b9\u30c8\u30fc\u30af\u30b9\u65b9\u7a0b\u5f0f\u306f\u30df\u30ec\u30cb\u30a2\u30e0\u554f\u984c\u306b\u3082\u306a\u308b\u304f\u3089\u3044\u3067\u3059\u304b\u3089\u3001\u305d\u3046\u7c21\u5358\u306b\u89e3\u3051\u308b\u554f\u984c\u3067\u306f\u306a\u3044\u306e\u3067\u3059\u304c\u3001\u6700\u7d42\u7684\u306b\u306f\u3001\u3069\u3093\u306a\u521d\u671f\u6761\u4ef6\u3092\u4e0e\u3048\u3066\u3082\u89e3\u3051\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002\u6700\u8fd1\u3001\u6761\u4ef6\u306e\u7bc4\u56f2\u3092\u3042\u307e\u308a\u5e83\u3052\u3059\u304e\u308b\u3068\u89e3\u3051\u306a\u304f\u306a\u308b\u3068\u3044\u3063\u305f\u3053\u3068\u304c\u3088\u304f\u7814\u7a76\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3067\u3059\u304b\u3089\u3001\u3069\u3053\u307e\u3067\u306a\u3089\u5e83\u3052\u3089\u308c\u308b\u306e\u304b\u3001\u6761\u4ef6\u306e\u95be\u5024\u3001\u5883\u76ee\u3092\u898b\u3064\u3051\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u300d\uff08\u5c0f\u8597\u6559\u6388\uff09<\/p>\n<h5>\u30d7\u30ed\u30d5\u30a3\u30fc\u30eb<\/h5>\n<p>\u5c0f\u8597\u82f1\u96c4 \u6559\u6388\uff08\u57fa\u5e79\u7406\u5de5\u5b66\u90e8 \u6570\u5b66\u79d1\uff09<\/p>\n<p>\u3053\u305e\u306e\u30fb\u3072\u3067\u304a\uff0f1958\u5e74\u751f\u307e\u308c\u300281\u5e74\u5317\u6d77\u9053\u5927\u5b66\u7406\u5b66\u90e8\u6570\u5b66\u79d1\u5352\u300187\u5e74\u540c\u5927\u5b66\u9662\u7406\u5b66\u7814\u7a76\u79d1\u535a\u58eb\u8ab2\u7a0b\u4fee\u4e86\u3002\u7406\u5b66\u535a\u58eb\u300293\u5e74\u540d\u53e4\u5c4b\u5927\u5b66\u52a9\u6559\u6388\u300199\u5e74\u6771\u5317\u5927\u5b66\u6559\u6388\u306a\u3069\u3092\u7d4c\u3066\u300112\u5e74\u65e9\u7a32\u7530\u5927\u5b66\u7406\u5de5\u5b66\u8853\u9662\u6559\u6388\u300202\u5e74\u30c9\u30a4\u30c4\u5927\u7d71\u9818\u304b\u3089\u30b7\u30fc\u30dc\u30eb\u30c8\u8cde\u3092\u8d08\u3089\u308c\u308b\u300214\u5e74\u65e5\u672c\u6570\u5b66\u4f1a\u8cde\u79cb\u5b63\u8cde\u300116\u5e74\u6587\u90e8\u79d1\u5b66\u5927\u81e3\u8868\u5f70\u30fb\u79d1\u5b66\u6280\u8853\u8cde\u3092\u53d7\u8cde\u3002\u5c02\u9580\u306f\u975e\u7dda\u5f62\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3002<\/p>\n<p>\u6240\u5c5e\u5b66\u4f1a<br \/>\n\u65e5\u672c\u6570\u5b66\u4f1a<\/p>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/jSDfMBfBlcI\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Equations That Support Weather Forecasts<\/h3>\n<p>Mathematics can be divided into four overarching fields: algebra, geometry, analysis, and practical applications. Professor Hideo Kozono is part of the Department of Mathematics within the School of Fundamental Science and Engineering. He specializes in analysis, particularly using differential equations.<\/p>\n<p>&#8220;The theme of my research is nonlinear partial differential equations. More specifically, I&#8217;m doing mathematical research on the Navier-Stokes equations, which describe the motion of fluids. Differential equations are specified through initial or boundary conditions, which you use to solve them. So, what kinds of initial conditions will uniquely determine a solution? If we take a broad set of initial conditions that are similar, will the solutions also be similar? These kinds of questions\u2014the relevance of differential equations\u2014are what I&#8217;m studying,&#8221; Prof. Kozono shared.<\/p>\n<p>Navier-Stokes equations can show us how fluids\u2014such as water and air\u2014change over time. These equations are commonplace in fluid mechanics and used extensively in the field of engineering, but they&#8217;re actually an essential part of our daily lives too. One place they&#8217;re used is in weather forecasts.<\/p>\n<p>Weather is the state of the atmosphere in a given time and place. Namely, it&#8217;s air temperature, atmospheric pressure, wind direction, wind speed, cloud cover, and precipitation described in physical quantities. Weather forecasts determine how those physical quantities will change over time to predict future atmospheric conditions.<\/p>\n<p>&#8220;How the atmosphere moves are entirely described by fluid dynamics. We can create and solve Navier-Stokes equations to predict physical quantities like the direction the wind will blow in tomorrow and how the air temperature and atmospheric pressure will change. Computers do the actual calculations, but mathematics is what ensures those calculations are correct. So, when initial or boundary conditions have been specified, can we predict the weather correctly in X number of seconds? In simple terms, that&#8217;s what I&#8217;m working on,&#8221; explained Prof. Kozono.<\/p>\n<h3>The &#8220;Unsolved Problem&#8221; of Navier-Stokes Equations<\/h3>\n<p>Although Navier-Stokes equations are used all around us, some problems using them remain mathematically unsolved. Prof. Kozono explained this as follows:<\/p>\n<p>&#8220;Navier-Stokes equations are solvable when the conditions are limited to a narrow range, but they become impossible to solve as that range is widened. As an example, the less viscous a fluid is, the more turbulent it is and the more the range of initial conditions widens. Conversely, if a liquid is highly viscous and the initial turbulence is low, the range of conditions will be narrow and we can figure out how it&#8217;ll move in the future. What I want to demonstrate mathematically is that we can solve any of these equations, no matter how low a liquid&#8217;s viscosity is or how turbulent it is initially\u2014basically, no matter what the initial conditions are.&#8221;<\/p>\n<p>This problem is actually also one of the Millennium Prize Problems. The Millennium Prize Problems are a series of seven unsolved problems that are important in mathematics. They were selected by the US&#8217; Clay Mathematics Institute in 2000. One of them\u2014the Poincar\u00e9 conjecture\u2014has been solved, but the other six remain unsolved. What would happen if someone solved this problem?<\/p>\n<p>Prof. Kozono had this to say: &#8220;Navier-Stokes equations are quite reliable ones that show us a complete picture of how fluids move. In other words, we could use them to forecast the weather for eternity.&#8221;<\/p>\n<h3>Mathematics: A Language That Explains Natural Science<\/h3>\n<p>Isaac Newton originally invented calculus because he wanted to find a way to describe physical phenomena using mathematics. Thus, mathematics and physics have long been closely related, and they developed in tandem over time.<\/p>\n<p>&#8220;Kepler discovered that planets have elliptical orbits by observing them, and Newton tried to represent that in a mathematical expression. He described how the planets move perfectly with a single equation, which is truly amazing. As with that example, we use mathematics to model and understand the phenomena discovered through physics. That&#8217;s our end goal. So, I think you can definitely call mathematics a language that explains natural science,&#8221; Prof. Kozono remarked.<\/p>\n<p>&#8220;I work in pure mathematics, so my goal isn&#8217;t to be helpful to society directly. Sometimes the results may end up being useful, but that&#8217;s not why I do what I do. That&#8217;s how it goes with natural science, though. Prime numbers, for example, are used in encrypting, but that doesn&#8217;t mean that we research them to create ciphers,&#8221; he explained.<\/p>\n<p>When asked what motivates his research, Prof. Kozono answered, &#8220;A cool way to say it is that I&#8217;m searching for the truth.&#8221; Finally, he told us about his future prospects.<\/p>\n<p>&#8220;Navier-Stokes equations are complex enough to be Millennium Problems, so they&#8217;re obviously not very easy to solve, but I want to prove that they can be solved no matter what the initial conditions are. Recent research has clearly shown that these equations are impossible to solve when the range of conditions is too wide, so I want to find the threshold\u2014or the limit\u2014that they can be widened to,&#8221; he said.<\/p>\n<h5>Profile<\/h5>\n<p>Professor Hideo Kozono<br \/>\nDepartment of Mathematics, School of Fundamental Science and Engineering<\/p>\n<p>Born in 1958, Prof. Kozono graduated from the Mathematics Department in the School of Science at Hokkaido University in 1981. He went on to receive a Doctor of Science degree upon completing the doctoral course at the same university&#8217;s Faculty of Science in 1987. He became an associate professor at Nagoya University in 1993, and in 1999, he become a professor at Tohoku University. He then moved through other various positions before becoming a professor at Waseda University&#8217;s Faculty of Science and Engineering in 2012. Germany&#8217;s president awarded him the Philipp Franz von Siebold Award in 2002. He received the Autumn Prize from the Mathematical Society of Japan in 2014, and in 2016, he received a Commendation for Science and Technology from MEXT. He specializes in nonlinear partial differential equations.<\/p>\n<p>Academic affiliations:<br \/>\nThe Mathematical Society of Japan<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5929\u6c17\u4e88\u5831\u3092\u652f\u3048\u308b\u65b9\u7a0b\u5f0f \u6570\u5b66\u306f\u3001\u5927\u304d\u304f4\u3064\u306e\u5206\u91ce\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u4ee3\u6570\u5b66\u3001\u5e7e\u4f55\u5b66\u3001\u89e3\u6790\u5b66\u3001\u305d\u3057\u3066\u5fdc\u7528\u3060\u3002\u57fa\u5e79\u7406\u5de5\u5b66\u90e8 \u6570\u5b66\u79d1\u306e\u5c0f\u8597\u82f1\u96c4\u6559\u6388\u306f\u3001\u89e3\u6790\u5b66\u3001\u3068\u304f\u306b\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u5c02\u9580\u3068\u3057\u3066\u3044\u308b\u3002 \u300c\u79c1\u306e\u7814\u7a76\u30c6\u30fc\u30de\u306f\u975e\u7dda\u5f62\u504f\u5fae\u5206 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":8119,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[96],"tags":[28],"class_list":["post-8115","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-other","tag-research"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/posts\/8115","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/comments?post=8115"}],"version-history":[{"count":1,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/posts\/8115\/revisions"}],"predecessor-version":[{"id":8163,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/posts\/8115\/revisions\/8163"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/media\/8119"}],"wp:attachment":[{"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/media?parent=8115"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/categories?post=8115"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.waseda.jp\/fsci\/wise\/wp-json\/wp\/v2\/tags?post=8115"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}