{"id":21557,"date":"2026-09-08T21:42:41","date_gmt":"2026-09-08T21:42:41","guid":{"rendered":"https:\/\/8657085.xyz\/?p=21557"},"modified":"2026-09-08T21:42:41","modified_gmt":"2026-09-08T21:42:41","slug":"openai-says-it-cracked-90-year-old-maths-problem-in-88-hours","status":"publish","type":"post","link":"https:\/\/8657085.xyz\/?p=21557","title":{"rendered":"OpenAI says it cracked 90-year-old maths problem in 88 hours"},"content":{"rendered":"<p> <div style=\"display: grid; grid-template-columns: 300px 160px; gap: 2px; width: 460px; background: #eee; padding: 2px;\">\r\n\r\n  <!-- \u6574\u884c\u5bbd\u5e7f\u544a -->\r\n  <div style=\"grid-column: 1\/-1; width: 460px; height: 250px; background: #ccc; display: grid; place-items: center;\">\r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e2\" data-zoneid=\"5876674\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n  <\/div>\r\n  <div style=\"grid-column: 1\/-1; width: 460px; height: 90px; background: #ccc; display: grid; place-items: center;\">\r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e2\" data-zoneid=\"5876676\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n  <\/div>\r\n\r\n  <!-- \u5de6\u4fa7\u7ad6\u6392 -->\r\n  <div style=\"height: 250px; background: #ccc; display: grid; place-items: center;\">\r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e2\" data-zoneid=\"5876672\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n  <\/div>\r\n  <div style=\"height: 500px; background: #ccc; display: grid; place-items: center;\">\r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e2\" data-zoneid=\"5876680\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n  <\/div>\r\n\r\n  <!-- \u53f3\u4fa7\u6469\u5929\u697c\uff08\u548c\u5de6\u4fa7\u5b8c\u5168\u5bf9\u9f50\uff09 -->\r\n  <div style=\"grid-row: 3\/5; height: 750px; background: #ccc; display: grid; place-items: center;\">\r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e2\" data-zoneid=\"5876678\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n  <\/div>\r\n  \r\n  <script async type=\"application\/javascript\" src=\"https:\/\/a.magsrv.com\/ad-provider.js\"><\/script> \r\n <ins class=\"eas6a97888e6\" data-zoneid=\"5876682\"><\/ins> \r\n <script>(AdProvider = window.AdProvider || []).push({\"serve\": {}});<\/script>\r\n<\/div><br \/>\n<\/p>\n<div>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\"><b class=\"ssrcss-1xjjfut-BoldText e5tfeyi3\">OpenAI says it has found a solution to a decades-old advanced maths problem in a matter of hours using a new artificial intelligence (AI) model and thousands of AI bots.<\/b><\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The ChatGPT-maker said on Tuesday<span class=\"visually-hidden ssrcss-i2z2ig-VisuallyHidden e16en2lz0\">, <!-- -->external<\/span> that by focusing a group of roughly 10,000 AI agents, or AI bots that undertake tasks somewhat autonomously, it solved a notoriously difficult maths problem in just 88 hours.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The problem was part of the Navier-Stokes equations<span class=\"visually-hidden ssrcss-i2z2ig-VisuallyHidden e16en2lz0\">, <!-- -->external<\/span>, which concern how fluids move. For 90 years important aspects of the problems have lacked a proof, the argument underlying a correct math equation.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">OpenAI called the solution which it found a &#8220;milestone&#8221; and evidence that AI tools are improving quickly.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">OpenAI&#8217;s solution has yet to be verified independently or publicly accepted by The Clay Mathematics Institute, a maths organization based in the US which runs the Millennium Prize that offers big money to the first to solve certain mathematical conundrums.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The company said that at the end of August, it started to train a new model that quickly showed that it was adept at maths. AI models are computer programs trained on huge amounts of data to recognize and predict patterns in information.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">While the new OpenAI model remains a tool only used within the company, as it is &#8220;significantly more capable&#8221; than the company&#8217;s most recent AI model release, its researchers decided to use it on certain notable advanced maths problems.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">OpenAI admitted that last week on 1 September, it had &#8220;heard rumors that two Millennium Prize problems had been resolved&#8221; and so decided to put thousands of AI bots trained on the new internal model to work attempting to solve some of the remaining problems.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">By Sept 5, or roughly 88 hours after it had set 10,000 AI bots to the task, OpenAI had found a solution to what&#8217;s referred to as the Navier\u2013Stokes existence and smoothness problem.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The problem is at the heart of turbulence, which is a phenomenon that is still not well understood.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Although it took the AI bots seemingly little time to reach a solution, OpenAI said the bots exchanged nearly 3 million messages and used up 130 billion output tokens, or the individual lines of text and code an AI model produces in answers, on Navier\u2013Stokes alone.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Such an effort would have cost roughly $10m (\u00a37.3m), based on OpenAI&#8217;s own pricing<span class=\"visually-hidden ssrcss-i2z2ig-VisuallyHidden e16en2lz0\">, <!-- -->external<\/span> for output from its most advanced models. <\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The solution that OpenAI says it has now reached for the Navier\u2013Stokes existence and smoothness problem resolved two out of the four statements in the proof that the Millennium Prize had demanded. The prize is worth $1m to a winner.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">&#8220;Our goal in releasing this result is to report on the substantial progress of our AI models&#8221;, OpenAI said on Tuesday. &#8220;We do not intend to claim the Millennium Prize for this result.&#8221;<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Already the company&#8217;s claim is stirring some controversy.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Tristan Buckmaster, a mathematics professor at New York University, said on Tuesday<span class=\"visually-hidden ssrcss-i2z2ig-VisuallyHidden e16en2lz0\">, <!-- -->external<\/span> that he and Levent Alp\u00f6ge, a mathematician working for OpenAI rival Anthropic, had also been working toward solutions for the problem.<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The duo had been using OpenAI&#8217;s tool Codex in their work. But Buckmaster said that on 3 September, he found out that &#8220;information about our progress had been passed to OpenAI.&#8221; <\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Buckmaster&#8217;s statement came the same day, but hours before, OpenAI published its Navier\u2013Stokes work. He claimed that OpenAI did not begin working on the Navier\u2013Stokes equations until &#8220;after information about our work had reached OpenAI.&#8221; He included text from emails exchanged with OpenAI over the work and his questions of the company&#8217;s timing and methods. <\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">Buckmaster added that he had not yet read OpenAI&#8217;s full proof, but felt compelled to go public with &#8220;what I was told, when, and what was proposed to me&#8230;because the alternative is to let a sequence of announcements say something I know to be false.&#8221;<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">OpenAI on Tuesday congratulated the &#8220;concurrent work&#8221; of Buckmaster and Alp\u00f6ge, calling it &#8220;remarkable.&#8221;<\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">The company said it had not seen &#8220;any of their work through any means until they released it publicly&#8221; and that no user data was accessed in its work on the Navier\u2013Stokes problem. <\/p>\n<p class=\"ssrcss-1q0x1qg-Paragraph e1jhz7w10\">&#8220;While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models\u2060&#8221;, the company added. &#8220;However, our proofs differ significantly and even the precise results proved are different.&#8221;<\/p>\n<\/div>\n<p><!-- \u603b\u5bb9\u5668\uff1a\u6700\u5927\u5bbd908px Grid\u7d27\u51d1\u5e03\u5c40 -->\r\n<div style=\"display: grid; 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