Amit Harlev, PhD student at the Cornell Center for Applied Mathematics In the last half year there has been a massive shift in the “Math and AI” discourse, primarily driven by changes in AI capabilities. In almost no time at all the collective opinion went from “AI can’t do research level mathematics” to “AI can […]
[This is a guest post by Amit Sahai. This blog post was initially written in a different file format and converted using AI. — T.] When I was an undergraduate student, I remember talking with several students who felt that the pace at which the top students could understand new math concepts was far too […]
Vladimir Lazić, Professor of Mathematics at Saarland University. Most days, for the last six months, I wake up feeling shame for the field we have become. Lined up towards a future most of us have not chosen; showing resistance on paper: signing petitions, creating initiatives, shouting in the wind. Led by people with no shame. […]
Alessandro Della Corte, Professor at Università di Camerino, and initiator of \begin{proof} Imagine that in Babylon, 600 BC, they had today’s AI technology: deep learning, transformers, GPUs. The training data would consist only of pre-Greek mathematics, like ancient Egyptian and Babylonian mathematical traditions. I doubt that anyone, given only those ingredients, would believe that this […]
[This is a guest post by Tapio Schneider. This blog post was initially written in a different file format and converted using AI. — T.] [This will be cross-posted on the CliMA blog.] The apparent proof of finite-time blow-up of the forced Navier-Stokes equation, announced by OpenAI on September 8, has brought into focus a […]
AI.MATH initiators With the AI.MATH initiative, we put forward draft positions on the future of mathematical research and mathematics degree programmes in the age of AI, alongside questions and possible answers. These are starting points for discussion. We also aim to make room for the uncertainties, hopes and concerns associated with this change. Received 23 […]
Tarik Aougab, Professor at Haverford College The premise for this post is simple: no matter what one thinks the central goals or purposes of mathematics are, the achievement of those goals by humans is impossible without ensuring that human beings have ample access and opportunity to study and think about mathematics. Of course, there are […]
[This is a guest post by Martin Hairer, cross-posted from Proofs and Prompts. — T.] There has been a lot of speculation regarding the “Advisory Group on Mathematics and Artifical Intelligence” agmai.org since it was announced on Monday. In this short blog post, I would like to explain in a bit more detail how the […]
Martin Hairer Professor of Pure Mathematics at EPFL and Imperial College London There has been a lot of speculation regarding the “Advisory Group on Mathematics and Artifical Intelligence” agmai.org since it was announced on Monday. In this short blog post, I would like to explain in a bit more detail how the group works, what […]
[This is a guest post by Antonio Auffinger. This blog post was initially written in a different file format and converted using AI. — T.] Despite writing papers in pure mathematics, much of my time in the past decade was spent talking (mostly listening, to be accurate) to biologists, computer scientists, and physicists. Theoretical physics […]
Marco Trombetti, Professor at Università degli Studi di Napoli Recent discussions around AI-generated mathematical papers have raised difficult questions about verification, attribution, authorship, and even about what it will mean to do mathematics in the coming years. I do not want to enter into the merits of any particular recent case. Instead, I would like to propose something […]
What is mathematics? Over the years I devoted a few dozen posts to the question “What is mathematics?”. Some posts in this category bring tears to my eyes like Christine Bjorner’s beautiful post: The Golden Room and the Golden Mountain, … Continue reading →
[This is a guest post by the Advisory Group on Mathematics and Artificial Intelligence. This blog post was initially written in a different file format and converted using AI. — T.] We would like to use this guest post to announce the creation of the Advisory Group on Mathematics and Artificial Intelligence hosted at the […]
Jonny Evans, Reader at the University of Lancaster I don’t use LLMS. I’m not going to say that you shouldn’t; it’s a choice. I don’t see the advent of LLMs as an existential challenge to mathematicians. Why would we lose our fascination with deep truths, patterns and connections just because computers can help? That, too, […]
Saksham Sharma, Postdoc at Caltech It is as if there existed, for what seems like millennia, tracing back to the very origins of mathematics and of other arts and sciences, a sort of “conspiracy of silence” surrounding these “unspeakable labors” which precede the birth of each new idea, both big and small, and which thereby […]
Indira Chatterji, Professor at Université Côte d’Azur The noise. The slop. The conversation dominated by AI stuff. I guess that’s a welcomed break from mulling over the fact that we are all dying, if not quickly cooked then slowly poisoned. Meanwhile our institutions want us to answer the following question: “Is AI killing math?” First […]
[This is a guest post by Po-Shen Loh, crossposted from his blog, where an illustrated version appears. This blog post was initially written in a different file format and converted using AI. — T.] Similar logic applies to every industry and every job. And it comes to the conclusion that we won’t have enough people […]
David Craven, professor at the University of Birmingham A mathematician sits down to work on a problem. She knows the rough outline of the proof. First, she gets her LLM to check the literature to make sure that she hasn’t been scooped recently, then feeds the intermediate lemmas into the LLM to get its opinion […]
[This is a guest post by Grant Sanderson. This blog post was initially written in a different file format and converted using AI. — T.] A sentiment echoing throughout the mathematics community right now is that solving problems and generating proofs have always served as proxies for the true goal of mathematicians, which is to […]
Last year I co-founded the Foundation for Science and AI Research (SAIR) with some private donors to create a non-profit organization that could support responsible uses of AI in mathematics and the other sciences, independent of the major AI companies. Initially, our resources were rather limited, and our main activities consisted primarily of podcasts, short […]
Note from P&P: On 11 September 2026, 25 Fields Medallists co-authored the declaration “A Severe Misalignment of AI in Mathematics“, which at the time of posting has over 7000 signatures. Below are are two separate and independent submissions we received, respectively, on 15 and 16 September 2026, responding to this declaration. The first one is […]
Xiaoyu He, Assistant Professor at Georgia Institute of Technology What follows is an edited and abridged version of a longer essay. The full version is available at alkjash.github.io/ai-risk. It has been a topic of heated discussion in the mathematical community whether AI progress spells the end of mathematics as a human profession. In this essay, […]
[This is a guest post by Dimitris Koukoulopoulos. This blog post was initially written in a different file format and converted using AI. — T.] At the 2026 World Cup semifinal, England led Argentina 1-0 with less than twenty minutes left. And then the momentum completely changed: England switched to a much more defensive formation, […]
[This is a guest post by Timothy Gowers, crossposted from his blog. This blog post was initially written in a different file format and converted using AI. — T.] When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as […]
[This is a guest post by Talia Ringer. This blog post was initially written in a different file format and converted using AI. — T.] When I was wrapping up graduate school in computer science in Spring 2021, I was given access to a curious little programming model on OpenAI’s “playground.” The model, called Codex, […]
Richard Evan Schwartz, Professor at Brown University My short story, The Fate of the Riemann Hypothesis, recently got a lot of attention on social media. Many people liked the story and many people did not. The story precisely expresses my feelings about AI-driven mathematics but my scientific views about it are more nuanced. In this […]
When I was around 11 I heard for the first time about Fermat’s Last Theorem. I was immediately captivated by the problem statement, as well as by the accompanying story, and made a fairly serious attempt to prove it. And while, unsurprisingly, I failed, I learned a lot from the attempt. Blissfully ignorant of the […]
Ben Green, Professor at the University of Oxford The rapid development of AI is of enormous public interest right now, with the possible existential risk to humanity being reported by mainstream news organisations. However, the discussion is often tempered with questions such as ‘haven’t we heard this before?’ or ‘isn’t this just hype from the […]
We’re excited to launch Stage 1 of the Lean Kernel Challenge, a multi-stage competition to improve the performance of verified computation in the Lean 4 kernel that the whole community can benefit from. The Lean Kernel Challenge brings the community together to develop faster algorithms and better representations for verified computation. Through these collective contributions, […]
[This is a guest post by the editors of the communal blog Proofs and Prompts. This blog post was initially written in a different file format and converted using AI. — T.] In the mathematical community, AI became a central conversation topic months before we started our communal blog, called Proofs and Prompts. Some of […]
[This is a guest post by Noah Giansiracusa. This blog post was initially written in a different file format and converted using AI. — T.] Imagine a tech company announces new robot workers that can prepare food better than human chefs. If you think of dining out as sitting at a table and having your […]
[This is a guest post by Ben Green. I support the letter, and am also a (corresponding) Fellow, but I have worked in various collaborations with the AI industry and so was not eligible to be a signatory. — T.] The rapid development of AI is of enormous public interest right now, with the possible existential […]
The hosts of Proofs and Prompts A little more than a month ago, we started this blog. It has grown a lot faster than we could have ever anticipated. We are grateful to everyone for the trust they have put in this project and in us. We are amazed by the engagement and the interest […]
Twenty years ago, when the idea of AI taking over the world in our lifetimes still struck most of us as the unconstrained fantasy of those who knew too much science fiction and too little science, many of us would say things like: Look, the part of the story that’s wildly implausible is that a […]
[This is a guest post by Ben Antieau, crossposted from his blog. This blog post was initially written in a different file format and converted using AI. — T.] To resolve a central tension in the practice of mathematics by academics, I suggest the parallel with fast food and its attendant slow food movement. Three […]
[This is a guest post by Henry Cohn. This blog post was initially written in a different file format and converted using AI. — T.] In this essay I’d like to discuss the role of AI-generated solutions in mathematics and why many mathematicians are justifiably concerned about a mismatch of values. Let’s start with the […]
Lisa Valentini, PhD student at the University of Cambridge We are mathematicians: we seek answers to problems that, at present, have no solution. To do so, we study the work of other colleagues, adapt it to the context we are interested in and, starting from there, look for new solutions. Now, the problem to be […]
[This is a guest post by Emily Riehl. This blog post was initially written in a different file format and converted using AI. — T.] Like many mathematicians, I was drawn to the field as a little girl by its aesthetics: questions that I found endlessly fascinating and arguments that struck me as delightful and […]
Daniel Litt, professor at the University of Toronto Three years ago, AI systems could not reliably add two numbers. A year ago, internal models at OpenAI and DeepMind received the equivalent of a gold-medal score on the IMO. Now, these systems are autonomously resolving major open questions. It’s hard to imagine this trend continuing for […]
[This is a guest post by Bryna Kra. This blog post was initially written in a different file format and converted using AI. — T.] For generations, mathematicians have treated the production of theorems as a clear measure of success. The stronger the theorem, the deeper the proof, the more surprising the connections, the greater […]