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Joint Statement about Mathathon
Summary
A coalition of Caltech Mathematicians. Also cross-posted at Terry Tao’s blog. Mathathon is centered around one question: how can we use AI to augment human understanding of mathematics? This past week, the original organizers of Mathathon, two coauthors of Open Letter about the Mathathon, and other members of the Caltech community engaged in a conversation…
3 comments on Joint Statement about Mathathon -
Applied mathematics has met the machine before
by Denys DutykhSummary
Why does AI worry applied mathematicians less? We have met the machine before: human computers moved up to designing algorithms, and a computer run led to the solution. Driven by problems rather than great conjectures, we expect AI, used with careful verification and validation, to make us better mathematicians.
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The Loss of Singularity
by Benoit HenrySummary
This essay was, in some sense, written as a way to grapple with the questions raised by AI about my own value as a researcher. It is a reflection on the effects these changes were having on me, on my practice of mathematics, and on how I might learn to cope with them.
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Knowing vs. Understanding: Humans and Machines in Puzzle-land
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We can use puzzles as a philosophical playground to think about the nature of insight, and compare human and artificial approaches. And we can explore what understanding means to us as human beings—both when we struggle toward it ourselves, and when we share it with each other.
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On using LLMs without telling which ones
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Some Mathematician. Some mathematicians don’t use LLMs at all. Some others use LLMs and desire to state which models they use in their papers. But if you use LLMs and do not hold this desire, you may choose to state “I used some LLMs to do this and that” without specifying which models you used.…
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From non-sofic to non-hyperlinear groups: the new messiness of discovering and announcing big results
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The very human story of the discovery of non-sofic, non-MF and non-hyperlinear groups over the past two months.
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Dear conferences, journals, and hiring committees: don’t wait for everyone else
by Amit HarlevSummary
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…
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Rulers of the childless land: A response to the AGMAI
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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.…
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All the math we will not see
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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…
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AI.MATH: announcement
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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…
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Navigating the AI crisis: a humble guide for students
by Tarik AougabSummary
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…
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Why I agreed to join AGMAI
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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…
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Many choices lie ahead
by Jonny EvansSummary
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,…
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History and Future of Fluid Dynamics
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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…
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Thoughts on death and a beautiful future
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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…
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Where will all the papers go?
by David CravenSummary
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…
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Two responses to “A Severe Misalignment of AI in Mathematics”
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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…
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Existential Risk from AI: An Exposition for Mathematicians (excerpt)
by Xiaoyu HeSummary
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,…
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The Fate of the Riemann Hypothesis: Revisited
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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…
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Open Letter to Sir Paul Nurse, President of the Royal Society
by Ben GreenSummary
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…
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One month of Proofs and Prompts
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We look back on one month of blogposts, give some updates, and tell the readers what we’d like to see more of.
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When inventing is not enough
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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…
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A beginning for mathematics
by Daniel LittSummary
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…
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Nothing changed
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Martin Drohmann, former postdoc at the Sandia National Laboratories Mathematics always was the story of humans searching for truth. Truth that is so compelling and universally verifiable that it is difficult to deny. Not always easy to believe: Although the details are lost, it took Pythagoras and his followers some significant time and effort to accept the…
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The Platonist view
by Uri BaderSummary
Uri Bader, Professor at Maryland University and Weizmann Institute Math exists. We explore it.We do not invent math. We invent ways of understanding and communicating it. We choose which parts of it to study, and we develop an adequate language for that that suits us, humans. But we explore an objectively existing domain. Empirical fact: our abstract…
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The Association for Human Mathematics
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AHM communications group This is a short announcement about the birth of the Association for Human Mathematics (AHM), an organization run collectively by mathematicians at all career stages. Its main goal is to protect mathematics and its practitioners from the jaws of AI companies, whose actions are increasingly destructive to our discipline, to the environment, and to…
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On the impact of AI on the mathematical practice
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Manuel Rivera, Associate Professor at Purdue University I’ve been recently following some interesting debates about the future of mathematics in the age of AI. I think many discussions about how AI is “disrupting” or “changing” (pure) mathematics tend to conflate, or at least fail to distinguish between, three interlocked interpretations of mathematics: (1) Mathematics itself,…
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Protesting the protests
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Galyna V. Livshyts, associate professor at Georgia Tech When you realize that your opinion differs from seemingly everyone else’s, your first instinct is to keep quiet. But that is the wrong instinct. So I shall speak up. Imagine two high school kids taking a quiz that involves computing a derivative. They finish almost simultaneously. Suddenly,…
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We Need a Stockfish for Math
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Oren Hartstein, undergraduate at Columbia University and author of a blog LLMs have become shockingly good at math. They solve competition problems, assist with research, and are improving fast enough that some fear human mathematicians are becoming marginal. I want to make the opposite critique: LLMs aren’t nearly good enough at math, and the way…
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A somewhat optimistic view of AI in mathematics
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Robert Wegner, PostDoc at Karlsruhe Institute of Technology I have the impression that recent advances in the deployment of AI for the purpose of mathematical research have made many people uncomfortable. I want to present my personal view on these matters, which is more optimistic. Let me get the following assumption out of the way:…
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A response from Mathathon
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Mathathon Organizers: Alvan Arulandu, Sathvik Rodrothu, Caiman Moreno-Earle, Avni Garg, Brian Zhao. On September 4th, we announced Mathathon, an event allocating compute credits across 100 teams of mathematicians tasked with solving and presenting an open problem in 40 hours. As of September 10th, we have received over a thousand applications from undergraduates, Ph.D. students, postdocs,…
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Open Letter about the Mathathon
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A coalition of current and former Caltech mathematicians Note: The Mathathon organizers have published a response, available here. On October 30th, 2026, Caltech will begin hosting the Caltech Mathathon, a math hackathon in which participants are encouraged to solve open research problems by prompting LLMs. Two prominent AI companies, Anthropic and OpenAI, will supply participants…
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How to welcome LLM use into student research mentorship
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Joshua Siktar, Visiting professor at Texas A&M University A lot of the conversation in the faculty coffee room lately has been about how to answer the question, “how do I discourage/prevent my students from cheating on homework using LLMs?” That’s a great (and loaded!) question but it only captures one of the two main ways…
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What’s not new
by Orr ShalitSummary
Orr Shalit, Professor at the Technion There is nothing new under the sun. Yes, we are living through a technological revolution of dramatic consequences. We who have lived through the birth of personal computers, the rise of the internet, the invention of smartphones, the disruptive eruption of social media, the promise of mass open online…
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(auto)formalization, but why
by Seewoo LeeSummary
Seewoo Lee, postdoc at EPFL. I want to share some thoughts on (auto)formalization based on personal experience, and propose some possible positive and negative usages of it. Disclaimer: I mostly focus on formalizations in Lean, due to my limited experience and knowledge. But most of the discussion can be applied to formalizations using other proof…
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What is mathematics now, and what should it be?
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Jeremy Avigad, Professor of Mathematics and Philosophy at Carnegie Mellon Abstract: Advances in neural theorem provers have been impressive, but the successes obscure a broader vision of what AI can do for mathematics and how mathematicians can engage with AI. This essay advances a more expansive and optimistic point of view. Worries about AI Over…
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On proof and progress in mathematics in the age of generative LLMs
by Andrew NgSummary
We should redefine mathematician to mean somebody who strives to understand human understanding of mathematics. Our work and how we obtain credit for it should change accordingly. We should do a better job of explaining what we do to each other as well as to the public.
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AI and maths communication
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Trevor Cheung, aka Mathemaniac and PhD student at the University of Nottingham Given the recent progress in AI solving many long-standing open problems in maths, there is no doubt there are many schools of thought around the use of AI in maths academia. However, I want to provide a different perspective of the worrying role…
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Rethinking Maths education: A perspective from Olympiad and higher education
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Baptiste Serraille, PhD student at ETH Zurich In the present text, I wish to express some thoughts about teaching and AI. These thoughts come from personal experience and the reader will notice the lack of references. My goal is to highlight some aspects of teaching mathematics that I think we should keep in mind, how…
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On analogies, parallels and thought experiments
by Nilima NigamSummary
Nilima Nigam, Professor at Simon Fraser University (What follows are long-winded personal reflections around AI and mathematics. I’ll conflate ‘AI’ with LLMs for the most part for the rest of this.) Cursed as we are to live in ‘interesting times’ which are changing rapidly thanks to AI, we reach for historical parallels and analogies. As…
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Invest in Human Mathematicians!
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If we want to make sure that mathematics survives the AI era, and if we want our field to continue to attract human talent and humans hoping to build a better and stronger community, then we need to heavily invest in humans, and vociferously celebrate the human contributions by the great people that have built…
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Care for a little more AI?
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Hugo Duminil-Copin, Professor at Université de Genève and IHES Disclaimer. The effects of AI are vast, and there is much to be said about its broader impact on society. One should also remind that mathematicians have a role to play in advancing research on AI safety. I do not feel sufficiently qualified to address these…
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The AI-assisted mathematician’s dilemma
by Ruodu WangSummary
Ruodu Wang, Professor at the University of Waterloo I am a mathematical statistician and mathematical economist. I have been a full professor for many years, so I am less affected by what I will describe below than young scholars are. But their well-being concerns me the most. I would like to share some thoughts, based…
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Evaluating mathematical merit
by Qi GuoSummary
AI-Reproducible Work, Human Mathematical Contribution, and a Residual Evaluation Framework by Qi Guo, Associate professor at the School of Mathematics, Renmin University of China Personal principles. AI is a tool. In evaluating a paper as a human research contribution, every component that standard AI tools can reproduce should be subtracted, even if a human happened…
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Statement on AI usage for PhD students
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Manuel Rivera, Associate Professor at Purdue University With the growing use of AI tools in mathematics research, I recently drafted the following statement for my graduate students, which I’m sharing here in case it’s useful to others navigating the same questions. As you are probably aware, AI agents and LLMs are becoming both a valuable…
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The reverse-centaur problem: LLMs and the choices ahead
by Mark WildonSummary
Mark Wildon, Professor at the University of Bristol and Heilbronn research fellow In The reverse centaur’s guide to life after AI: How to think about artificial intelligence before it’s too late, the science-fiction writer and futurist Cory Doctorow draws a distinction between two ways people interact with AI. Centaurs are people whose skills are boosted…
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Shannon, Orwell, and the Thinking Machine
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Amites Sarkar, Professor at Western Washington University A Literary Experiment In 1948, Claude Shannon published his groundbreaking paper A Mathematical Theory of Communication. This work appeared, in two parts, in Volume 27 of the Bell System Technical Journal, and it’s hard to overstate its importance. For example, it’s instinctive for most of us to measure…
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Where to Point the Telescope
by Shaowu ZhangSummary
AI, Mathematical Judgment, and M23M_{23} Shaowu Zhang (Ivan), PhD student at Caltech The inverse Galois problem asks whether every finite group occurs as the Galois group of some finite Galois extension of ℚ\mathbb{Q}. The program to realize the sporadic finite simple groups as Galois groups over ℚ\mathbb{Q} began in 1984. Over the following years, every…
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Response to “The AI dissenter viewpoint”
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Anatoly Vitold Stankyavichyus, data scientist Recently I wrote a reply to “The AI dissenter viewpoint” and was encouraged by the author and Yemon Choi to contribute my response as a separate post. I’ve also become concerned with the extent of absolutist and highly-charged comments regarding those who do not conform to others’ views on this…
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Changes in the classroom in the AI Era
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Benjamin Jaye and Galyna V. Livshyts, associate professors at Georgia Tech As the nature of mathematical work evolves rapidly, many of us are asking: how should we prepare our students for successful careers? Which skills will be crucial for mathematicians ten years from now — or one year from now, or even one month from…
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How dare you?
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by Vadim Lebovici
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Mathematicians, machines, and the Earth
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The large language model crisis arises from the same capitalistic ideology as the climate crisis, and contributes to it. Mathematicians have a special responsibility regarding LLMs. We must act: collectively, by working towards mitigating the negative impacts of LLMs on society, and individually, by refusing to adopt destructive technology.
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On The Brutal Mathematics of Slop
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Simon Hayward, data scientist and MSc student at the Open University This article is written in response to the announcement of OpenAI’s “Sol” model making 10 mathematical “breakthroughs”. These events have been well covered elsewhere and I don’t intend to cover them in any detail. Instead I intend to focus on the likely trajectory of…
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Keeping the learner in the loop
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Amruth Srivathsan, student researcher at the University of Cambridge One thing I have noticed while teaching and just generally from observing people learn maths (or in fact anything) nowadays is how quickly they reach for AI tools to make difficulty disappear. In the past, when a student gets stuck on a problem there were only…
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The end of an era in mathematical research
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Alonso Castillo-Ramirez, Professor and Researcher at Universidad de Guadalajara For more than two thousand years, research in pure mathematics has retained basically the same structure. Euclid began with definitions and axioms, and from them he proved theorems through logical arguments. Essentially, we still do the same today. Of course, this does not mean that mathematical research…
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Prompting Toward a Conjecture
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Guanyang Wang, Assistant professor at Rutgers University and author of a blog TL;DR: A controlled experiment suggests that one general instruction to search broadly across the literature can dramatically affect whether an LLM finds a proof. A second promising route is for humans to provide the proof roadmap while LLMs fill in difficult intermediate steps.…
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The question of reasoning traces
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Segev Gonen Cohen, PhD student at ETH Zurich I want to raise a specific question that I think has not received enough attention, and that might become more important over time. As will be clear, it is intimately related to many other pertinent questions, and as such can lead to interesting conversations. This post should be read…
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What I feel like when I work with an AI
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Shmuel Weinberger, Andrew MacLeish Distinguished Service Professor of Mathematics at the University of Chicago As Yogi Berra said, it’s tough to make predictions, especially about the future. So I decided to write about my present experience, which I think I have a better chance of being right about. At the least, it’ll provide a snapshot…
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Why do mathematics in the age of AI
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Srivatsav Kunnawalkam Elayavalli, Assistant Professor, UC Berkeley I am a mathematician. I like to think deeply. But why? It is not because I get a paycheck. Sometimes I wonder if it is because I am good at it and want to prove something to the people around me. It is not. Ultimately it is because…
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Writing mathematics in the age of AI
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Martin Hairer Professor of Pure Mathematics at EPFL and Imperial College London With this post, I would like to start a discussion about best practices for writing a mathematics article in which some (or possibly all) of the results were obtained with the help of AI. (I will use ‘AI’ or ‘AI system’ as a…