{"id":78923,"date":"2026-03-25T14:39:45","date_gmt":"2026-03-25T14:39:45","guid":{"rendered":"https:\/\/youzum.net\/this-startup-wants-to-change-how-mathematicians-do-math\/"},"modified":"2026-03-25T14:39:45","modified_gmt":"2026-03-25T14:39:45","slug":"this-startup-wants-to-change-how-mathematicians-do-math","status":"publish","type":"post","link":"https:\/\/youzum.net\/it\/this-startup-wants-to-change-how-mathematicians-do-math\/","title":{"rendered":"This startup wants to change how mathematicians do math"},"content":{"rendered":"<p>Axiom Math, a startup based in Palo Alto, California, has released a <a href=\"https:\/\/axiommath.ai\/territory\/axplorer\">free new AI tool for mathematicians<\/a>, designed to discover mathematical patterns that could unlock solutions to long-standing problems.<\/p>\n<p>The tool, called Axplorer, is a redesign of an<a href=\"https:\/\/arxiv.org\/pdf\/2411.00566\"> existing one called PatternBoost<\/a> that Fran\u00e7ois Charton, now a research scientist at Axiom, co-developed in 2024 when he was at Meta. PatternBoost ran on a supercomputer; Axplorer runs on a Mac Pro.<\/p>\n<p>The aim is to put the power of PatternBoost, which was used to crack a hard math puzzle known as the Tur\u00e1n four-cycles problem, in the hands of anyone who can install Axplorer on their own computer.<\/p>\n<p>Last year, the US Defense Advanced Research Projects Agency set up a new initiative called expMath\u2014short for Exponentiating Mathematics\u2014to encourage mathematicians<a href=\"https:\/\/www.technologyreview.com\/2025\/06\/04\/1117753\/whats-next-for-ai-and-math\/\"> to develop and use AI tools<\/a>. Axiom sees itself as part of that drive.<\/p>\n<p>Breakthroughs in math have enormous knock-on effects across technology, says Charton. In particular, new math is crucial for advances in computer science, from building next-generation AI to improving internet security.<\/p>\n<p>Most of the successes with AI tools have involved finding solutions to existing problems. But finding solutions is not all that mathematicians do, says Axiom Math founder and CEO Carina Hong. Math is exploratory and experimental, she says.\u00a0<\/p>\n<p><em>MIT Technology Review <\/em>met with Charton and Hong last week for an exclusive video chat about their new tool and how AI in general could change mathematics.\u00a0<\/p>\n<p><strong>Math by chatbot<\/strong><\/p>\n<p>In the last few months, a number of mathematicians have used LLMs, such as OpenAI\u2019s GPT-5, to find solutions to unsolved problems, especially ones set by the 20th-century mathematician Paul Erd\u0151s, who left behind hundreds of puzzles when he died.<\/p>\n<p>But Charton is dismissive of those successes. \u201cThere are tons of problems that are open because nobody looked at them, and it\u2019s easy to find a few gems you can solve,\u201d he says. He\u2019s set his sights on tougher challenges\u2014\u201cthe big problems that have been very, very well studied and famous people have worked on them.\u201d Last year, Axiom Math used another of its tools, called AxiomProver, to <a href=\"https:\/\/www.wired.com\/story\/a-new-ai-math-ai-startup-just-cracked-4-previously-unsolved-problems\/\">find solutions<\/a> to four such problems in mathematics.\u00a0\u00a0\u00a0<\/p>\n<p>The Tur\u00e1n four-cycles problem that PatternBoost cracked is another big problem, says Charton. (The problem is an important one in graph theory, a branch of math that\u2019s used to analyze complex networks such as social media connections, supply chains, and search engine rankings. Imagine a page covered in dots. The puzzle involves figuring out how to draw lines between as many of the dots as possible without creating loops that connect four dots in a row.)<\/p>\n<p>\u201cLLMs are extremely good if what you want to do is derivative of something that has already been done,\u201d says Charton. \u201cThis is not surprising\u2014LLMs are pretrained on all the data that there is. But you could say that LLMs are conservative. They try to reuse things that exist.\u201d<\/p>\n<p>However, there are lots of problems in math that require new ideas, insights that nobody has ever had. Sometimes those insights come from spotting patterns that hadn\u2019t been spotted before. Such discoveries can open up whole new branches of mathematics.<\/p>\n<p>PatternBoost was designed to help mathematicians find new patterns. Give the tool an example and it generates others like it. You select the ones that seem interesting and feed them back in. The tool then generates more like those, and so on.\u00a0\u00a0<\/p>\n<p>It\u2019s a similar idea to Google DeepMind\u2019s AlphaEvolve, a <a href=\"https:\/\/www.technologyreview.com\/2025\/05\/14\/1116438\/google-deepminds-new-ai-uses-large-language-models-to-crack-real-world-problems\/\">system that uses an LLM to come up with novel solutions to a problem<\/a>. AlphaEvolve keeps the best suggestions and asks the LLM to improve on them.<\/p>\n<p><strong>Special access<\/strong><\/p>\n<p>Researchers have already used both AlphaEvolve and PatternBoost to discover new solutions to long-standing math problems. The trouble is that those tools run on large clusters of GPUs and are not available to most mathematicians.<\/p>\n<p>Mathematicians are excited about AlphaEvolve, says Charton. \u201cBut it\u2019s closed\u2014you need to have access to it. You have to go and ask the DeepMind guy to type in your problem for you.\u201d<\/p>\n<p>And when Charton solved the Tur\u00e1n problem with PatternBoost, he was still at Meta. \u201cI had literally thousands, sometimes tens of thousands, of machines I could run it on,\u201d he says. \u201cIt ran for three weeks. It was embarrassing brute force.\u201d<\/p>\n<p>Axplorer is far faster and far more efficient, according to the team at Axiom Math. Charton says it took Axplorer just 2.5 hours to match PatternBoost\u2019s Tur\u00e1n result. And it runs on a single machine.<\/p>\n<p>Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.)<\/p>\n<p>Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. \u201cIt remains to be seen how significant these improvements are,\u201d he says.<\/p>\n<p>\u201cWe are in a strange time at the moment, where lots of companies have tools that they\u2019d like us to use,\u201d Williamson adds. \u201cI would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.\u201d<\/p>\n<p>Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That\u2019s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you want to do step by step, she says.<\/p>\n<p>The code for Axplorer is open source and <a href=\"https:\/\/github.com\/AxiomMath\/axplorer\">available via GitHub<\/a>. Hong hopes that students and researchers will use the tool to generate sample solutions and counterexamples to problems they\u2019re working on, speeding up mathematical discovery.<\/p>\n<p>Williamson welcomes new tools and says he uses LLMs a lot. But he doesn\u2019t think mathematicians should throw out the whiteboards just yet. \u201cIn my biased opinion, PatternBoost is a lovely idea, but it is certainly not a panacea,\u201d he says. \u201cI\u2019d love us not to forget more down-to-earth approaches.\u201d<\/p>","protected":false},"excerpt":{"rendered":"<p>Axiom Math, a startup based in Palo Alto, California, has released a free new AI tool for mathematicians, designed to discover mathematical patterns that could unlock solutions to long-standing problems. The tool, called Axplorer, is a redesign of an existing one called PatternBoost that Fran\u00e7ois Charton, now a research scientist at Axiom, co-developed in 2024 when he was at Meta. PatternBoost ran on a supercomputer; Axplorer runs on a Mac Pro. The aim is to put the power of PatternBoost, which was used to crack a hard math puzzle known as the Tur\u00e1n four-cycles problem, in the hands of anyone who can install Axplorer on their own computer. Last year, the US Defense Advanced Research Projects Agency set up a new initiative called expMath\u2014short for Exponentiating Mathematics\u2014to encourage mathematicians to develop and use AI tools. Axiom sees itself as part of that drive. Breakthroughs in math have enormous knock-on effects across technology, says Charton. In particular, new math is crucial for advances in computer science, from building next-generation AI to improving internet security. Most of the successes with AI tools have involved finding solutions to existing problems. But finding solutions is not all that mathematicians do, says Axiom Math founder and CEO Carina Hong. Math is exploratory and experimental, she says.\u00a0 MIT Technology Review met with Charton and Hong last week for an exclusive video chat about their new tool and how AI in general could change mathematics.\u00a0 Math by chatbot In the last few months, a number of mathematicians have used LLMs, such as OpenAI\u2019s GPT-5, to find solutions to unsolved problems, especially ones set by the 20th-century mathematician Paul Erd\u0151s, who left behind hundreds of puzzles when he died. But Charton is dismissive of those successes. \u201cThere are tons of problems that are open because nobody looked at them, and it\u2019s easy to find a few gems you can solve,\u201d he says. He\u2019s set his sights on tougher challenges\u2014\u201cthe big problems that have been very, very well studied and famous people have worked on them.\u201d Last year, Axiom Math used another of its tools, called AxiomProver, to find solutions to four such problems in mathematics.\u00a0\u00a0\u00a0 The Tur\u00e1n four-cycles problem that PatternBoost cracked is another big problem, says Charton. (The problem is an important one in graph theory, a branch of math that\u2019s used to analyze complex networks such as social media connections, supply chains, and search engine rankings. Imagine a page covered in dots. The puzzle involves figuring out how to draw lines between as many of the dots as possible without creating loops that connect four dots in a row.) \u201cLLMs are extremely good if what you want to do is derivative of something that has already been done,\u201d says Charton. \u201cThis is not surprising\u2014LLMs are pretrained on all the data that there is. But you could say that LLMs are conservative. They try to reuse things that exist.\u201d However, there are lots of problems in math that require new ideas, insights that nobody has ever had. Sometimes those insights come from spotting patterns that hadn\u2019t been spotted before. Such discoveries can open up whole new branches of mathematics. PatternBoost was designed to help mathematicians find new patterns. Give the tool an example and it generates others like it. You select the ones that seem interesting and feed them back in. The tool then generates more like those, and so on.\u00a0\u00a0 It\u2019s a similar idea to Google DeepMind\u2019s AlphaEvolve, a system that uses an LLM to come up with novel solutions to a problem. AlphaEvolve keeps the best suggestions and asks the LLM to improve on them. Special access Researchers have already used both AlphaEvolve and PatternBoost to discover new solutions to long-standing math problems. The trouble is that those tools run on large clusters of GPUs and are not available to most mathematicians. Mathematicians are excited about AlphaEvolve, says Charton. \u201cBut it\u2019s closed\u2014you need to have access to it. You have to go and ask the DeepMind guy to type in your problem for you.\u201d And when Charton solved the Tur\u00e1n problem with PatternBoost, he was still at Meta. \u201cI had literally thousands, sometimes tens of thousands, of machines I could run it on,\u201d he says. \u201cIt ran for three weeks. It was embarrassing brute force.\u201d Axplorer is far faster and far more efficient, according to the team at Axiom Math. Charton says it took Axplorer just 2.5 hours to match PatternBoost\u2019s Tur\u00e1n result. And it runs on a single machine. Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.) Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. \u201cIt remains to be seen how significant these improvements are,\u201d he says. \u201cWe are in a strange time at the moment, where lots of companies have tools that they\u2019d like us to use,\u201d Williamson adds. \u201cI would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.\u201d Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That\u2019s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you want to do step by step, she says. The code for Axplorer is open source and available via GitHub. Hong hopes that students and researchers will use the tool to generate sample solutions and counterexamples to problems they\u2019re working on, speeding up mathematical discovery. Williamson welcomes new tools and says he uses LLMs a lot. But he doesn\u2019t think mathematicians should throw out the whiteboards just yet. \u201cIn my biased opinion, PatternBoost is a lovely idea, but it is<\/p>","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_pvb_checkbox_block_on_post":false,"footnotes":""},"categories":[52,5,7,1],"tags":[],"class_list":["post-78923","post","type-post","status-publish","format-standard","hentry","category-ai-club","category-committee","category-news","category-uncategorized","pmpro-has-access"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3 - 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