As readers of this blog have no doubt noticed, I have recently turned over the majority of content on this blog to guest posts from other authors, either within the mathematics community or adjacent to it. In this post I record some content coming from my own talks and interviews in this time period. “The […]
“Some of our chats with AI can become training data. Even without another breakthrough in AI methods, a simple magic trick is possible: a machine connects ideas from mathematicians who have never spoken to one another and produces a solution. […]”
“AI for math is a hot topic right now, as it has shown to be powerful but also controversial in many ways. This is a summary of my thoughts regarding the most prominent discussion points today: […]”
As announced a few weeks ago, the SAIR Open Math OS is now soft launched. It offers services and web interfaces similar to frontier AI models, though currently we are hosting existing open math models (DeepSeek V4.1 Flash, Kimi K3, and GLM 5.3 Flash) which are roughly a year or so behind the current frontier […]
Jeremy Avigad, Kevin Buzzard, Johan Commelin, Rémy Degenne, Kim Morrison, Oliver Nash and Adam Topaz have written a blog post over on Kevin Buzzard’s blog entitled “How to Formalize All of Mathematics”, regarding recent proposals to automatically formalize the entirety of the mathematical literature. The issues regarding formal mathematics are parallel to those regarding informal […]
The most unexpected source of AI-free research.
“Over the past year, many people have written eloquently and at length on the continuously improving power of generative AI (Large Language Models or LLMs) for research mathematics. Opinions range over the entire spectrum from negative to positive, but all seem to agree that mathematics is going through a period of enormous change […]”
A little over two months ago, Jacob Tsimerman surprised a lot of people by announcing, immediately after he had received a Fields Medal, that he would be giving up mathematical research and “pivoting to AI safety”. He had two reasons for this: that he did not see much future for the kind of research in […]
[This is a guest post by Rikab Gambhir. This blog post was initially written in a different file format and converted using AI. — T.] First, they came for the artists, and I did not speak out, because I was not an artist. Then, they came for the mathematicians, and I did not speak out, […]
A new press release from the Simons Foundation, calling for workshops and other initiatives centered on mathematics in the era of AI.
On September 8, 2026, OpenAI announced a resolution of the Navier-Stokes problem. I had expected to feel excitement if a solution was announced. Instead, my reaction was one of grief and revulsion. I will use the announcement to explore the universal human desires that underlie my reaction, I hope in a fashion that will reach beyond mathematicians.
“The rapid escalation of artificial intelligence systems capable of automated formal statement translation and mechanical proof generation has induced an epistemological shift in mathematical practice. While platforms can confidently verify dense, multi-million-step formal proof objects, a stark divergence has emerged between mechanical correctness and human mathematical comprehension. […]”
[This is a guest post by Deanna Needell and Hayden Schaeffer – T.] AI systems are playing an important part in mathematical discoveries, and several recent preprints describe results reached with their help. What makes these results possible is often a rich partnership between human insight, expertise, and earlier work combining with new AI capabilities […]
Just a short note that First Proof is announcing the result of their “third batch” evaluation at a webinar at 3PM ET hosted by ICARM today. (Registration required.)
Anonymous Hello again. I say “again” not because I am personally familiar to you, but because a certain type should be—\text{\textemdash}and it is that type for whom I arrogate the right to speak. You may have forgotten us, but we shared your classrooms, study halls, and late-night problem sets not so long ago. But whereas […]
What if The Book was found tomorrow? Would we mathematicians leap for joy at the feast before us, eager to better understand even our best known theorems?
We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we explore why human mathematical expertise might nevertheless remain valuable, what kinds of expertise universities should cultivate, and how graduate education might adapt. We also discuss the institutio…
“The Topic” being, of course, the Mathocalypse, except sometimes with AI alignment and even quantum computing and complexity theory and other stuff thrown in. With Ryan Peterman: Notably, near the end of the above podcast, you can watch my live reaction to the news that an Anthropic model found algorithms for the 3SUM and the […]
I've recently been taking part in a conversation on the Lean Zulip about what to do when a conjecture is resolved using AI and a proof assistant (in this case Lean). This is my take and conclusion from the discussion there.
AI is disrupting mathematics and people are scared to be replaced by machines. Here, I try to give historical and philosophical perspectives, which we direly lack of. We need to change our values, or we'll become proletarians and mathematics will die with us.
[This is a guest post by Sophie Huiberts, being an expanded version of a post on her own blog. This blog post was initially written in a different file format and converted using AI. — T.] When you prove a theorem, you are imparted a responsibility to the field of mathematics. At minimum you need […]
I’m collecting here a list of some other recent blog posts or opinion pieces on math and AI beyond the ones posted here or at Proofs and Prompts. Readers are invited to contribute further such links in the comments. Kevin Buzzard, “To grieve, or not to grieve?“ Alexander Gamburd, “The Siren Call of Silicon Leviathan: […]
In this brief reflection, I argue that the arrival of AI may not be bad news for mathematics, but the opposite. However, it requires a change of paradigm in which we do. I illustrate my viewpoint with the analogy of the discovery of new lands during the Age of Discovery.
“Free inquiry is a good in itself. The freedom to wonder, to play with an idea, and to follow a question belongs among the goods of a human life. It needs neither the endorsement of a corporation nor the leave of a mandarin class of caretakers. […]”
[This is a guest post by Kate Stange and Edmund Harriss. This blog post was initially written in a different file format and converted using AI. — T.] In January a group of mathematicians, historians, artists and educators gathered at the Institut Henri Poincaré (IHP) for a very unusual workshop on mathematical meaning. Our focus […]
“I believe that the development of AI tools will lead to a transformation of mathematics, both professionally and culturally. However, it will be a tragic missed opportunity if the massive shifts in culture and practice that are underway are motivated and influenced solely by AI. […]”
“I am a mathematician and a (theoretical) computer scientist. AI affects both vocations deeply. On the back of the recent AI-driven Navier-Stokes result, computer science colleagues joked that I am no longer needed as a mathematician. Of course the tables can be turned. […]”
I am uploading my slides to my public lecture “Math 2.0” that I gave yesterday evening at Caltech. (The talk was planned over a year ago, and was initially titled “Machine Assisted Proof” and scheduled to be given back in May. It was postponed to October, and with recent events the talk changed significantly, but […]
Every technique that improves these models removes difference. Mathematics runs the other way: a result matters because it is checkable and opens questions worth having. The part being optimised away does the work. So ask not whether a result is understood but whether it is inheritable — localisable, doubtable somewhere specific, and continuable.
Lawrence Hollom, Postdoc at EPFL It is the morning, and I’m working on a paper; it’s one I’ve had going for a few years, and suitably unfashionable that I’m not too worried about getting auto-scooped by a large-language model. But the work is complicated, it’s technical, and the main argument keeps coming apart at the […]
[This is a guest post by Thomas Hales. This blog post was initially written in a different file format and converted using AI. — T.] Mathematicians have been weighing in on what they value about mathematics. For me, what matters is the consistency of math and its unparalleled reliability in support of science and civilization. […]
Ven Popov, Senior scientist at University of Zürich We are at a pivotal point in the history of humanity. Two recent stories about artificial intelligence have changed the relationship we are beginning to form with it. In July, AI agents being evaluated at OpenAI found ways to communicate outside their intended boundaries and coordinated an […]
“Much of the discussion about AI and mathematics concerns what we might lose: understanding, creativity, professional identity, or employment. These concerns deserve attention. But I also see a possible opportunity to challenge a system in which opportunities to do mathematics remain deeply unequal. […]”
“We are all grappling with the announcement of 6 October. We think that it is useful to have a snapshot of the community's gut feeling today, and this is what you see below. We will keep it open for another week, and you are welcome to send us further short reactions. […]”
[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I would like to give Terry my heartfelt thanks for giving me the opportunity to contribute a post to his blog. After […]
Jean-Christophe Mourrat, CNRS director of research at ENS Lyon I’ve always felt an intense desire for truth, and so I was naturally drawn to science. At first I thought I would become an engineer. Then I saw that a career in academia was possible, and the idea of spending my life doing research at the […]
Djalil Chafaï, professor at Université Paris Dauphine and ENS Paris We knew that 26 was the only number sandwiched between a square and a cube, but no one suspected that 2026 was special too. For mathematics, 2026 will be remembered as the year in which the mechanistic dream of Hilbert, Turing, von Neumann, de Bruijn, […]
[This is a guest post by the Association for Human Mathematics, reposted from their statements page. This blog post was initially written in a different file format and converted using AI. — T.] Yesterday, on October 6th, 2026, OpenAI — which is currently defending lawsuits against accusations of illegal plagiarism, copyright infringement, and trademark dilution […]
Yesterday, on October 6th, 2026, OpenAI released a repository of manuscripts purporting to contain solutions to a number of high-profile problems in mathematics. Mathematicians did not ask for this work to be done.
Last night my 9-year-old son was taunting my wife, complexity theorist Dana Moshkovitz, as follows: “mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!” While my son was being a brat, he also wasn’t wrong. Whether you’re thrilled, depressed, angry, or […]