{"id":605191,"date":"2026-04-14T00:50:14","date_gmt":"2026-04-14T00:50:14","guid":{"rendered":"https:\/\/www.newsbeep.com\/au\/605191\/"},"modified":"2026-04-14T00:50:14","modified_gmt":"2026-04-14T00:50:14","slug":"the-ai-revolution-in-math-has-arrived","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/au\/605191\/","title":{"rendered":"The AI Revolution in Math Has Arrived"},"content":{"rendered":"

As they related in a preprint on January 3, 2026, AlphaEvolve had found that the Bruhat intervals<\/a> in these particular permutation groups had a surprisingly special structure. When the researchers studied the intervals, they found that they formed higher-dimensional cubes called hypercubes. \u201cIf you look at what AlphaEvolve was thinking, I was super surprised,\u201d Libedinsky said. \u201cIf it was a human, it would be an extremely creative human.\u201d<\/p>\n

AlphaEvolve had answered a question they didn\u2019t know they had. \u201cWe didn\u2019t ask AlphaEvolve to find big hypercubes,\u201d Ellenberg said. \u201cWe asked it to find something else, and we thought about it and realized it was a gigantic hypercube which we had not anticipated was there.\u201d<\/p>\n

\"\" <\/p>\n

Excerpt from a prompt that mathematicians gave to AlphaEvolve, in which they asked it to construct an object called a Kakeya set. Mathematicians have found that AI performs better with encouragement.<\/p>\n

As Williamson put it, \u201cIt\u2019s a structure that\u2019s been sitting there for 50 years in front of our nose. We just hadn\u2019t noticed it.\u201d<\/p>\n

Older machine learning methods had previously enabled such serendipitous mathematical discoveries, too \u2014 uncovering patterns no one had thought to look for. But in the past, Williamson said, it was a \u201creal engineering effort. \u2026 You need to know how to code, spend a lot of time looking at details of neural network training. It was basically extremely difficult for a mathematician with no significant machine learning background to do this.\u201d<\/p>\n

With LLMs, \u201cI can suddenly do an experiment in 20 minutes that two years ago would have taken me two weeks,\u201d he said. Though \u201cmost of the time it doesn\u2019t work,\u201d AI can now be used like never before \u201cto discover the world that has riches beyond our imagination.\u201d<\/p>\n

Around Sphere<\/p>\n

Though Bruhat intervals seem like purely combinatorial objects, they also play an important role in a particularly abstract area of math called algebraic geometry, which Ravi Vakil<\/a>, a mathematician at Stanford University and the current president<\/a> of the American Mathematical Society, specializes in.<\/p>\n

Algebraic geometry is the study of shapes defined by polynomial equations like x3 + 2x2y + xz = 5, which involve a sum of variables raised to whole-number exponents. The degree of the equation is the highest exponent the polynomial has, in this case 3.<\/p>\n

\"Man <\/p>\n

Ravi Vakil and his colleagues recently came up with a novel proof idea while chatting with a bespoke version of Gemini. \u201cWho is that idea due to?\u201d he asked. \u201cIs it due to us? Is it due to the model?\u201d<\/p>\n

Vakil and his colleagues, Bal\u00e1zs Elek<\/a> of the University of New South Wales and Jim Bryan<\/a> of the University of British Columbia, were interested in studying how spheres can be embedded in special spaces called flag varieties. (Flag varieties appear in the Bruhat team\u2019s paper as well.) Each embedding \u2014 a way of associating each point on the sphere to a point within the flag variety \u2014 can be defined by a polynomial equation.<\/p>\n

There are lots of ways to embed the sphere. Mathematicians represent each embedding as its own point in a separate high-dimensional space. They then study the embeddings defined by polynomials of different degrees by analyzing the different spaces they form.<\/p>\n

As the degree increases, mathematicians want to understand how these spaces change. They knew that when the degree gets arbitrarily large \u2014 as it goes to infinity \u2014 the space resembles the space of all continuous embeddings, not just those defined by polynomials. But when does this resemblance come to pass?<\/p>\n

\"\" <\/p>\n

AlphaEvolve talked to itself as it attempted to solve a problem about the Bruhat intervals of permutation groups.<\/p>\n

Vakil and his colleagues had found examples that suggested, to their surprise, that it happens very quickly. \u201cThere was some consistency that was not supposed to happen until you reached infinity, and it already happened,\u201d he said.<\/p>\n

So, together with Freddie Manners<\/a> and George Salafatinos<\/a>, who were then working for DeepMind, they set out to prove it using two specialized modules built atop Google Gemini: DeepThink, which is publicly available, and a system developed by Salafatinos, called FullProof, which is not. They started with a simpler case. \u201cThe proof it gave was very elegant, correct, beautifully written. We could follow it line by line,\u201d Vakil said. \u201cIt made clear a structure that was not obvious at the time. From that, we realized how the whole argument and significant generalization should potentially work.\u201d<\/p>\n

Vakil and his colleagues then went back to the AI model, sketching a proof of the general case and asking it to fill in the details. As they reported in a preprint on January 12, 2026<\/a>, it succeeded. \u201cTo me,\u201d Vakil said, \u201cthe real thing was the first thing\u201d \u2014 DeepMind\u2019s proof of the simpler case. \u201cThe clarity of the argument gave us a new idea.\u201d But he wonders: \u201cWho is that idea due to? Is it due to us? Is it due to the model?\u201d<\/p>\n

However one ascribes credit, Vakil said, \u201cI believe I would have come up with the proof given enough time.\u201d<\/p>\n

But then he hesitated. \u201cI think so. I\u2019m not sure. I don\u2019t know. Maybe I would have done it in a clunky way. Very possibly, the paper wouldn\u2019t have happened without the assistance.\u201d<\/p>\n

And finally: \u201cWe needed to go back and forth. AI models will help us do mathematics by letting us do things we did not have time to do before.\u201d<\/p>\n

This is perhaps a paradigmatic example of how AI can be useful today.\u00a0A group of expert mathematicians, with help from a big tech company, figures something out faster than they likely would have otherwise \u2014 and they are sure it is correct, because they can check it line by line.<\/p>\n

All Ye Need To Know <\/p>\n

In asking what AI is doing to mathematical research, we shouldn\u2019t only look at the successes. Litt cautioned that \u201cthere is a lot of pollution of the commons by AI-generated nonsense.\u201d Joel David Hamkins<\/a> of the University of Notre Dame said he is \u201cdespairing of this ocean of slop that is overwhelming our journal systems.\u201d<\/p>\n

Mathematicians are pinning their hopes on formal proof<\/a> as the way to navigate this ocean of slop. They\u2019re converting proofs into a language that computers can understand, and then using computer programs to verify that all the logic in the proof pans out. \u201cAI without validation is too unreliable to be of use in any serious application,\u201d Tao said.<\/p>\n

\"Man <\/p>\n

\u201cIt\u2019s very likely that this technology is\u00a0bigger than the computer,\u201d Daniel Litt wrote in a recent analysis of AI\u2019s potential impact on mathematics.<\/p>\n

Currently, formalizing mathematical proofs in this way is a time-consuming, intricate process that itself takes substantial mathematical knowledge and is a bit of a craft. And so mathematicians are increasingly turning to \u201cautoformalization,\u201d in which AI models translate mathematical statements into formal, logical ones and then prove them. \u201cFor the first time,\u201d Tao said, \u201cit does feel like we could formalize a significant fraction of mathematics through AI.\u201d<\/p>\n

The other major challenge that many mathematicians see as a consequence of AI\u2019s increasing ability to do math is how it will affect the way students learn. Even the most ardent proponents of AI are concerned. Ken Ono, a professor at the University of Virginia who recently took a leave of absence to become the \u201cfounding mathematician\u201d at Axiom, told me he sees \u201ca rosy picture about how AI can help mathematics research, but I am deeply concerned about the role of AI in the future of work and training at all levels.\u201d<\/p>\n

Tao said, \u201cMany of the problems we assign, AI can solve instantly. This can discourage a lot of the students from building up their mental muscles.\u201d<\/p>\n

Hamkins agreed. \u201cI used to assign quite a bit of homework. I just can\u2019t do it anymore,\u201d he said; a substantial fraction of the assignments students turn in are written by AI. \u201cI don\u2019t want to read it. I don\u2019t want to be the AI cop.\u201d Though homework was highly pedagogically valuable, now \u201ceverything has to be in-class quizzes and work. It\u2019s a problem for the entire academic profession.\u201d<\/p>\n

As another mathematician at a leading research university told me, \u201cThere is a serious risk that, in parallel with accelerating the progress of serious mathematical researchers, AI prevents us from making more mathematical researchers.\u201d<\/p>\n

\n New Coauthors\n <\/p>\n

The use of AI to conduct math research is quickly becoming routine, and will, if current trends continue, soon be no more noteworthy than the use of the LaTeX typesetting language, which mathematicians use to format technical expressions. Aside from the results discussed in this article, there have been dozens of others in recent months.<\/p>\n

Norms are still emerging about how to account for AI contributions. Some papers include detailed supplemental information about how human mathematicians interacted with LLMs, including transcripts of conversations. Some mention an AI\u2019s contribution prominently in the abstract; others make only brief mention of an AI\u2019s assistance in the acknowledgments. Some mathematicians take pains to point out that though AI helped with the research, they wrote the paper themselves; others credit AI with the writing as well.<\/p>\n

Even with the rapid changes of the past year, none of the mathematicians I spoke to in reporting this piece fear that the subject will become obsolete. Tao gave the analogy of mathematicians trying to climb \u201ca big mountain range with lots of tall mountains and lots of foothills.\u201d Humans can only climb one step at a time, but they can plan a route to the top of a mountain like Everest. Meanwhile, Tao said, current AIs are like jumping robots. They can sometimes \u201cparkour their way to the top of a 6-foot wall\u201d that a human couldn\u2019t climb. But they can\u2019t do long-term strategic planning. Those 6 feet might become 10 feet, or 100, Tao imagines, but \u201cthe little jumping robots are nowhere near the Mount Everests of math.\u201d<\/p>\n

Pak thinks that certain Everests \u2014 such as a major problem in number theory about whether sums like \u03c0 + e can be written as fractions \u2014 will remain unresolved for centuries. \u201cI\u2019m really doubtful AI can make any dents there at all,\u201d he said. \u201cThis is not something that AI would be able to do. But I\u2019m quite positive that if humanity survives, eventually we will figure it out.\u201d<\/p>\n

Of course, a lot depends on how the capabilities of AI algorithms change and improve in coming years. Even the most astute and careful observers can\u2019t say for sure how the models will develop. Few see signs of stagnation. \u201cThings are moving very fast. I don\u2019t see any sign they are slowing down,\u201d Litt said. The first few months of 2026 have already seen a steady stream of new results from big companies like Google<\/a> and OpenAI<\/a> and small ones like Axiom<\/a>, as well as from academics<\/a> and even hobbyists<\/a>.<\/p>\n

\u201cMy expectation is surely in 20 years we are going to see AI tools generating mathematics that in many measurable ways are better than every human mathematician,\u201d Litt said. \u201cI would be shocked if that doesn\u2019t happen.\u201d<\/p>\n

But as Venkatesh told me, \u201cIn the end, there are infinitely many ways to formulate any piece of math.\u201d The choices we make, he said, are governed by human values and shaped by the fact that mathematics is not only a science but also an art.<\/p>\n

That balance between science and art is in large measure what gives math its beauty \u2014 one of the \u201cvaluable things in our culture\u201d that Venkatesh wants to retain. If AI pushes mathematics away from its artistic heritage, the discipline will be diminished, even if more theorems are proved each month. After all, no poet talks seriously about doing statistical regression on sonnets to find the optimal ones.<\/p>\n

The best hope for AI is that it will help mathematicians find and prove things that would otherwise have remained mysteries. Most mathematicians agree that that\u2019s what computers have done for the past 80 years. But the scale of the change now underway has left many feeling unsettled.<\/p>\n

The biggest annual mathematics conference in the world is held every year in early January. In 2026, in Washington, D.C., nervous jokes about being made obsolete by AI were plentiful, even if, on the record, everyone insisted that AI will be a helpmate to human mathematicians. Williamson \u2014 who has been working with AI for years and is very excited by it \u2014 was chosen to deliver a series of prestigious lectures<\/a> about AI and math to the entire conference. He told the audience that it\u2019s a mistake to react to AI developments with ignorance and fear.<\/p>\n

But he said he understands where the fear comes from. He sees mathematics as a \u201ccraft that people have spent their lives\u00a0\u2014 dedicated their lives \u2014 towards. There is some possibility that its value may be greatly diminished in the future.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"As they related in a preprint on January 3, 2026, AlphaEvolve had found that the Bruhat intervals in…\n","protected":false},"author":2,"featured_media":605192,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[256,254,255,64,63,105],"class_list":{"0":"post-605191","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-artificial-intelligence","8":"tag-ai","9":"tag-artificial-intelligence","10":"tag-artificialintelligence","11":"tag-au","12":"tag-australia","13":"tag-technology"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/605191","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/comments?post=605191"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/posts\/605191\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media\/605192"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/media?parent=605191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/categories?post=605191"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/au\/wp-json\/wp\/v2\/tags?post=605191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}