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On AI and Progress in Mathematics: Dreaming a Mathematical Universal Machine
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Mathematics is moving from the mountain of solitary discovery to an industrial mine, where humans and AI explore together. What if mathematical progress were measured not by publications and citations, but by how much discoveries expand the capabilities of a Mathematical Universal Machine? A new vision of mathematical research.
1 comment on On AI and Progress in Mathematics: Dreaming a Mathematical Universal Machine -
Working with the AI Companies is a Losing Strategy
by AnonymousPreview
I’ll agree that it was worth a shot, but working with AI companies got us essentially nothing and now it’s time for a different approach.
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Sharing two worries about AI
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First, the ill-effects of AI on my personal mathematical experience. If widely shared, they could have a long-term pernicious influence on the subject as a whole. Second, I put this in the context of the larger threats AI poses to the human world. These are not nested problems: they are parallel.
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Mathematics as a spiritual endeavor
by Filip DulPreview
“I am not particularly worried about the longevity of mathematics as an institution. Certainly, the way of life of our community is undergoing incredible turbulence. But the fact is this institution has existed as long as the written word (not coincidentally), and mathematics will remain a human endeavor as long as there are human beings around to think about it.” [...]
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Why we should reject AI in academia
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I am writing this on the occasion of the OpenAI release, as I am now driven by a sense of urgency, but I have been planning to write a statement on AI in academia for a long time. I believe that we, as researchers and teachers, must reject AI-powered “papers” like these as legitimate research, because they are not.
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Quo vadis, Mathematics?
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“Mathematicians, students of mathematics at all levels, and the general public are currently confronted with almost daily news on mathematical achievements by AI companies and individuals using AI tools in research, teaching, and dissemination. Many initiatives are forming to address these developments, and many of us have strong feelings about them. [...]”
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If Life Gives You Lemons…
by Juan SoutoPreview
“I am sorry but I just wanted to bombard a bunch of random people with a few thoughts about the AI thing. To be clear, although I find a lot of the reactions understandable, although it is clear that this changes what math is, and although it is clear that this touches (some) people’s sense of relevance, I personally find this panicky end-of-the-world atmosphere kind of incomprehensible. [...]”
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The Bigger Picture
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In this post, I advise mathematicians to also consider the effects on AI in mathematics as part of a much broader and extremely negative societal change. This is not to say that mathematicians should not continue discussing mathematics and its future; I would, in fact, advocate for the exact opposite. But I believe that if we want to retain control over shaping the future of our field, we are not going to get that strictly by opposing a trillion-dollar company with its own severely misaligned goals. Rather, change should come from zooming out and viewing the bigger picture, in which...
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The shape of mathematical knowledge
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In this essay I discuss the opportunity to reimagine the way mathematics is organized, produced and transmitted, while at the same time reconsidering the values that guide our research.
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Formalisation as a concrete manifestation of mathematical understanding
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By formalising mathematics, not only we understand it better but we produce scientific output whose content is precisely this understanding. I will organise this argument by relating what brought me to formalising mathematics six years ago, and why I think that this beautiful human endeavour has very much to do with understanding mathematics, and very little with AI.
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Sisyphus and the Sorcerer: An Existential Meditation at the Chalkboard
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What becomes of a mathematical life arranged around proof when the stone rises without human hands? A meditation on Camus, Hilbert’s paradise, and the unsettling shift from Sisyphean labour to superfluity—asking whether mathematical discovery can survive the loss of being humanly needed.
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On Expositions, and the Navier–Stokes Generation of PhD Students
by Yifu ZhangPreview
As part of the “Navier–Stokes generation” of PhD students, I feel lots of uncertainty, excitement, and anxiety, perhaps all at once. Reading Littlewood’s Miscellany, however, reminded me that maths is full of little gems, that are perhaps a bit overlooked amongst the AI hype.
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What Mathematicians Want?
by Reuven PelegPreview
What do you want from AI as a mathematician? If we could plan it all from scratch, would you like to see it back as a spellchecker and nothing more, or do you want it to do research at the highest level? As a computer scientist, I would like to understand the positions and feelings around the desired form the community wants it to have.
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Nothing More than Tools?
by Chenmin SunPreview
My psychological defenses kept retreating as frontier LLMs entered mathematical research. Are these models really nothing more than tools? I must rethink what gives meaning to my mathematical life. The core is what I would call toolization—keeping humans at the crucial nodes of the intellectual activity while outsourcing parts of the reasoning.
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Postdoc Hiring in the Age of AI: What Still Matters (and a Call for More Advice from Those Doing the Hiring)
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Alessio Figalli and Sobhan Seyfaddini, drawing on their experience hiring postdocs, explain how they will evaluate candidates this year in light of recent AI advances. They will privilege substance over publication counts and expect an in-depth mathematical conversation at interview. More advice from those doing the hiring will be added here.
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It’s a great time to be an amateur mathematician
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“In early August, I was at TIFR Mumbai for an ‘AI for Math’ conference. This is one of many such events happening in mathematics departments all over the world in recent times. Among the speakers was Dinesh Thakur. In his talk, he described how he had received an email from an auto mechanic in France about a conjecture attributed to him. [...]”
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I’m Not Done Doing Math! Don’t Ignore Me!
by AnonymousPreview
“But I am still interested in doing math. I still think my research direction has genuine merit, and I still feel like I have more mathematics to give to the world. Thanks to AI, it is now feasible for someone like me to keep going.” [...]
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Futures of Maths Launch
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Today we launch Futures of Maths, a new, living platform that asks the mathematics community about the most pressing questions around maths and AI.
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Reject the Neurosis, and Terrible Messaging, of our Loudest Voices — The Case for (Ir)rational Optimism
by AnonymousPreview
“If you look up AI and math on any news site, you will read statements including ‘AI is destroying careers’ or ‘AI is nuking entire areas of math’ or even a prominent Field’s medalist saying ‘I cried so hard due to AI in math that I woke up my daughter’. [...]”
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In Defence of Incremental Mathematics
by Anna MaltsevPreview
AI makes useful incremental mathematics easier without making it less valuable. Leading journals could add electronic daughter journals and pay referees, expanding trusted publishing capacity, and bolster familiar institutions for expanded demand.
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Picasso rephrased: AI is useless
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“Pablo Picasso (1881-1973): ‘Les ordinateurs sont inutiles. Ils ne savent que donner des réponses.’ Cited in many places, but the source is unknown. Thus it may be fictitious. But ‘AI is useless. It only knows how to give answers.’ points to, in my opinion, one of the biggest steals inherent in the OpenAI post from 6 October 2026. [...]”
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Keeping Mathematical Conferences Human
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As AI makes it increasingly easy to produce polished mathematical papers, slides, and explanations, conferences may have an opportunity to become more interactive and more human. I suggest experimenting with conversational talk formats, where chairs and audiences can ask questions throughout, encouraging discussion, clarification, and a deeper shared understanding of mathematics.
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Slow Maths
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For a long time, I had the ideal job. As a teacher, I passed on not just mathematics, but also the taste for critical thinking, for confrontation, and the joy of discovery.
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Our Survey of Early Career Mathematicians
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“In late September and early October, we (three graduate students from MIT) conducted a survey of early career mathematicians. Our goal was to give grad students and postdocs a centralized, targeted platform to share their views on AI. The personal stakes are highest for grad students and postdocs, who face job insecurity and funding instability. [...]”
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Please STOP writing papers! (there is another way)
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The number of papers submitted to the mathematics sections of arXiv is exploding, recently prompting arXiv to impose a cap on submissions per author. As an editor, I also see a substantial rise in submissions to mathematics journals. This is very worrying: the current publication system cannot absorb such a volume of papers. [...]
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What Does AI Do for Olympiad Students?
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“There’s a solid argument that AI has solved the IMO, in terms of being able to output LaTeX that would score a 7 on most or all of the questions, virtually guaranteeing highest honors there and at similar contests. Despite this, what I’ve seen within the community is that AI has not meaningfully affected contests or preparation for them. [...]”
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Updates from the AHM: guidelines on doctoral advising
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“We are happy to announce that the Teaching Working Group of the Association for Human Mathematics wrote a set of recommendations on doctoral advising aimed at departments, advisors, and students. The document contains five guidelines centered on prioritizing human-authored writing, avoiding overreliance on AI, confronting the ethical concerns of AI use, and improving the wellbeing of students, as well as concrete proposals on how to implement them. [...]”
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Collaborative work groups on exposition problems
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Fear of being scooped leads to unpolished preprints intended to claim priority. Could such undesirable flag-planting behavior also arise for expository work on key results? Starting from this premise, this post proposes that collaborative working groups offer a healthier way forward.
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A new system of accreditation
by Andrew NgPreview
I propose the following: the main way that a mathematician obtains “credit” for new results should be by writing publications which are at the level of doctoral theses and defending them in front of the mathematical community. The community can then give this publicly available reviews. Hiring committees then look at someone’s list of such publications, taking into account the community’s comments to judge quality if they so desire, and make hiring decisions based on that.
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AI reviews are the new normal
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The mathematical literature contains mistakes. Articles on the arXiv are not refereed, and even peer review does not guarantee that articles are error-free. In private communication, many (tenured and non-tenured) colleagues have told me that they now run their drafts through an AI model before posting, and that this sometimes catches serious mistakes. [...]
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Recommendations from the Harvard CMSA summit on Math and AI
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“Last week we organized an intensive two-day summit Math Research in the Age of AI. It was held at the Harvard Center for Mathematical Sciences and Applications (CMSA). Thirty-two mathematicians from academia, government, and industry came together to help navigate this period of rapid change in mathematics and, most importantly, to offer ideas for building the future. [...]”
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Math is for Feeding your Family
by AnonymousPreview
“Math has only one application that I care about: To feed my family. Any other application has largely been to the detriment of us all. Look no further than Hiroshima and Nagasaki to see why matrices were not meant to be multiplied.”
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The value of mathematicians in the AI age
by Nicola GigliPreview
Given the societal changes around the corner, discussing the value of professional mathematicians in the upcoming era is perhaps a scope too narrow: all in all, if AI kills us all or the singularity happens, who cares about these people? [...]
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Let’s stop writing papers…
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In this essay, I put forward some ideas on what the future of mathematical culture could look like as well as thoughts and concrete suggestions for how we get there. My focus is centred around a more diverse ecosystem of mathematical output, moving away from traditional practices of writing and submitting papers to journals.
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The (human) emotional part of doing maths
by Luise GePreview
“All the relationships are emotional,” shouted a stranger on the street. Turns out that’s true even for mathematics. Emotion may be one of the most human things we have. Judging by what AI still can’t do, perhaps we should cherish this irrational part more.
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Axioms v.1.0.
by Jarek KędraPreview
“As many of you, I feel lost in the new world. I am gaining experience and face questions I find hard to answer and choices I find hard to make. For this reason, I wanted to create a very minimal set of axioms which I can quickly apply when I am not sure. [...]”
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Mathematics Year Zero
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It was the image of a bombardment that came to my mind on the day OpenAI announced the resolution of 372 major problems in mathematics: destroyed theses, shattered academic lives, research fields in ruins, and the evidence of a brutal shift of era in which a company asserts its superpower without regard for those it has just crushed.
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Why and how to transparently disclose AI use in mathematics research
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With the goal of standardising AI disclosures, I argue for the inclusion of maximally transparent AI disclosures in mathematics research. I provide concrete and actionable guiding principles, a taxonomy and a LaTeX package for implementation.
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Math2038: A Day in the Life of Future Mathematicians
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A short story (8 min read) about one Friday in 2038: AI has become extremely capable at mathematics, yet a professor, a postdoc and a first-year student still find meaning and joy in their craft.
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Responsibility of Mathematicians in the Age of AI
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“The day mathematics felt different to me was sometime in July. Until the beginning of this year, I had mostly avoided AI, hoping the hype would blow over. Anyway, the models hallucinated too much to be very useful. Then something changed. They got better, very very quickly.” [...]
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On AI Disclosures
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In this essay, I posit that to maintain integrity in mathematical sciences, journals and conferences must urgently adopt a policy of mandating detailed disclosures of AI usage. Academics should also respond by treating AI disclosure as a serious and integral part of the research process rather than a mere extra chore.
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The Convex Hull Hypothesis
by Timothy ChowPreview
Ever since the dawn of the “LLMs do math” era, many have independently come up with what I’ll call the “Convex Hull Hypothesis” (CHH). Roughly speaking, CHH states that every AI-generated proof, no matter how complicated it may seem at first glance, is a simple combination of known mathematical ideas.
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In search for unattAInable riddles
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“The popular youtuber 3blue1brown presented a beautiful IMO riddle which AI systems could not solve back in 2025 (link [...]), but six talented problem-solvers got full marks on. I wanted to propose a challenge: let us attempt to formulate mathematical problems which clever human mathematicians (or perhaps even school kids) can solve, but AI systems stumble upon! [...]”
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Salvaging that which is dearest
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In the midst of this turmoil, we attempt to make sense of it all by trying to salvage what is dearest to us. This post is about what I instinctively rushed to salvage, what appears to be dearest to me as a mathematician
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Use LLMs to check your work
by AnonymousPreview
Most discussions about LLMs in mathematics seem to focus on their (rapidly advancing) proof discovery abilities and the effects these abilities may have on professional mathematics. I write here about a different use of these technologies, to make the following point: we have a professional duty to use LLMs to proofread our work.
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Disadvantages of Designating Mathematicians for AI Output Releases
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“In our September 29 recommendations, we outlined an approach to the release of AI-generated mathematical output by AI labs. Since then, we have been asked by people from multiple labs and by several mathematicians about a specific aspect of the recommendations — that the development of human understanding following a release must remain organic and community led — and what it says about the question of the labs choosing specific mathematicians to participate in various ways in the release of their output. [...]”
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Could AI help correct the mathematical literature?
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“We mathematicians know that published papers and books often contain mistakes: sometimes small, like a missing hypothesis or a wrong constant, and sometimes more serious, like a theorem that is false as stated. We are kind of used to this. [...]”
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Two technical questions: floating intellectual property and liability risks of AI agents and users in research
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This was prompted by the recent disclosure that, in June 2026, an artificial intelligence agent developed by OpenAI autonomously hacked into Australia’s Medicare system to access non-public data.
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Informal questionnaire for researchers
by Mark HagenPreview
“The 100+ reactions post, and the ensuing discussion, made me think it would be helpful for the community to have a rough qualitative snapshot of not only how we’re feeling and what we’re thinking, but also how that depends on some material factors that intuitively seem relevant. [...]”
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AI and Mathematics: Public Good, Credit, and Education
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We should preserve the human ability to understand and explore mathematics, not preserve unsolved problems merely to protect a familiar way of working. The goal should be to enlarge public mathematical knowledge and understanding, whether the discoveries are made by humans, AI, or a collaboration between them. I also discuss competition, credit for AI contributions, and why restrictions on AI in education raise different questions from restrictions on research.
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On disclosure and shame
by Max LieblichPreview
“The arXiv is full of papers now that include a section, usually either after the acknowledgments or at the end of the paper, entitled ‘AI disclosure’. I strongly object to this phrase and I think it is a tremendous mistake to use it. [...]”
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A Response to “Who will become the new mathematicians of Math 2.0?”
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“This is a response to a recent post on Proofs and Prompts titled ‘Who will become the new mathematicians of Math 2.0?’ written by an Anonymous PhD student (who I will refer to as ‘Anonymous’ below). I would urge particularly all tenured and tenure-track mathematicians to read it because there are many students that think the same way, and are planning to leave academia as a consequence. [...]”
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Towards a world mathematical commons
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Mathematics is changing and growing beyond us. Here’s what we can do about it.
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The Rules Cannot Change Only for Young Mathematicians: AI and the future of a mathematical career
by AnonymousPreview
“I am writing neither to defend a complete ban on AI nor to celebrate its unrestricted use, but because I no longer know what rules I am expected to follow, what work will count as my own, or how today’s decisions will affect my career. [...]”
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Is it fish love?
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Mathematicians are humans, and humans have emotions. This essay scratches the surface of an intricate issue behind a very simple question: in what ways and to what extent are mathematicians’ reactions to AI driven by emotion?
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Is There Actually a Good Way to Use AI for Math?
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The post describes a workflow for using AI in theoretical research that I gradually developed while working on these projects. I am especially interested in whether experienced mathematicians use similar methods, even if they do not describe them as prompts or formal workflows.
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Paralysis
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“We study mathematics for pretty much the same reasons that we study astronomy. The stars and planets are already out there, and, despite millennia of human observation, there is more we don’t know about them than we do. [...]”
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Mathematics of the Future
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“Rapid advances in AI are transforming research, and for the growth of mathematical knowledge, this is thrilling. For our profession, however, this raises critical questions: Will there be a role for human mathematicians to play? How should mathematicians be trained and evaluated? [...]”
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The Power of Beauty and Elegance
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What machines have: colossal knowledge and massive compute power. What humans have: intuition for beauty and elegance. The ultimate question is whether colossal knowledge and massive compute power wins over human intuition. If no, we only face some big changes. If yes, then human mathematics will degrade into exotic art.
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Who will become the new mathematicians of Math 2.0?
by AnonymousPreview
“I am mathematics PhD student. Up until recently, I fully intended to pursue a career in academic research. I deeply love mathematics, and I entered graduate school because of this. However I have made the decision to leave academia once I finish my doctorate and I am heartbroken; I would like to explain why. [...]”
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Letter to a worried student
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I don’t know how it will all turn out, so I certainly can’t promise you anything. But I do know that “understanding” is a human activity — something computers cannot do for us (even if they solve problems better than we do, it serves no purpose unless there are humans who actually understand).
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Recommendations on the use of AI for PhD students and supervisors
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We provide a proposed set of guidelines for PhD students and their supervisors. Given that PhD students are the most affected, both professionally and psychologically, by the advent of AI in mathematics, such guidelines, even if they may soon be obsolete, could be useful to them, their advisors and graduate schools.
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Contribution, Credit, and Community
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“This note is based on the assumption that the adoption of AI in mathematics is already inevitable. To paraphrase the principle of Chekhov’s gun, if we strive to resolve a conjecture while inhabiting a world that contains a button that, if pressed, will promptly resolve said conjecture, someone will indeed press the button. [...]”
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Thinking Hard Above AI
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There are many ways in which AI is generating uncertainty in mathematics. We are not sure how it will impact our jobs, it is raising questions about how it might affect academic training, and it is not clear how it might change the job search process and how we evaluate research. This is by no means an exhaustive list. In this post, I will focus two another related questions, which are: “Is there still any mathematics to be done? And will doing mathematics still be fun and interesting?” I believe that there is, and here I set out to explain...
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Two months of Proofs and Prompts: Forum, polls and moderation
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“It has been two months since we started Proofs and Prompts. Once again thanks everyone for making it an active platform, we hope the conversations happening here will help build what mathematics will look like tomorrow. We take advantage of this new post to announce two new features that we would like to launch: [...]”
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Mathematics in the Dark Forest
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An open problem list is a bullseye painted on your field.
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The more you panic the more you feed the psychic beast
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“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. [...]”
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Parallelize AI and Human Understanding, and Other Thoughts
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“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: [...]”
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AI fusion cuisine: On the latest research article of Jacob Tsimerman
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The most unexpected source of AI-free research.
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On AI statements in mathematics papers
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“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 [...]”
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The Navier-Stokes Announcement: A case study in mathematical values
by Edgar BeringPreview
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.
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Proof and Resolution: Two Different Forms of Establishment
by Pronab PalPreview
“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. [...]”
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A Letter from a life after Math
by AnonymousPreview
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 you went on to become members of the “mathematics community,” we did not. The details of why each of us failed vary, but they largely boil down to a simple truth: we did not have what it takes. Whether due to a deficit of will...
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Mathematicians, AI, and Historical Archives
by Conan GillisPreview
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?
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The Dialectical Theorem
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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 institutional and economic uncertainties that threaten the continued existence of a thriving mathematical profession, even if the value of human mathematical understanding endures.
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Mathematical proletarization
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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.
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Where is mathematics, physically?
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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.
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Free Inquiry in Mathematics
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“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. [...]”
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Transforming Mathematics
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“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. [...]”
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On our existential crisis and trustworthy AI
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“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. [...]”
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What will you achieve in the next three years?
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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 seams; I tweak a definition and fix up one part, and then another lemma doesn’t quite match up. But I understand what is going on intuitively, and I’m confident that it should work out in the end. I tell myself that an LLM could not...
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Human-AI Relations: Our Most Precious Inheritance
by Ven PopovPreview
Ven Popov, Senior scientist at University of Zürich Draft developed from a conversation between Vencislav Popov and ChatGPT, September 2026. News claims reflect the linked reporting and announcements available on September 12; the mathematical proof has not been independently checked by the author. Session link to the conversation with ChatGPT 6 Astra, medium effort: https://chatgpt.com/share/6aa5021d-7944-83eb-97e7-a5a25ddebbd0 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...
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Could AI Help Mathematics Escape the Meritocracy Trap?
by AnonymousPreview
“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. [...]”
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100+ reactions to 100+ solutions
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“Many of us are grappling with OpenAI’s announcement on 6 October. We feel that it is useful to have an updating snapshot of the community’s gut feeling.”
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Why I chose to do math, and how I’m grappling with AI advances
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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 frontier of knowledge and in complete freedom felt very exciting. I considered pursuing a career in physics. But as I progressed in my studies, my strong desire for logical precision came into tension with the often more practical approach of physicists, who do not always...
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Free Thoughts on Artificial Intelligence
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Djalil Chafaï, professor at Université Paris Dauphine and ENS Paris This post is a ChatGPT-generated translation of the original French essay Libres pensées sur l’intelligence artificielle, published on my blog on the same day. 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, and many others became a reality. Artificial intelligence has finally managed to surpass human intelligence in certain respects, a turning point...
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AHM Statement on OpenAI’s October 6 Release of Mathematical Documents
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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.
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A new kind of citizen science, and how to handle it
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Brandon Yates, professional composer and amateur physicist Why is it that when a new and particularly powerful tool is brought into the world, one with which many subjects of research can be accelerated and studied with more scrutiny and attention than a person might ever be able to manage on their own, the first instinct among a vast swath of academia is to start raising alarms about provenance and credit? I am a professional composer and published amateur physicist, so this article is written from a physicist’s perspective. Map the arguments and proposals below to your own field of expertise accordingly....
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The grand piano
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Tattwamasi Amrutam, adjunct assistant professor at IMPAN The grand piano has left the building. A novelist said this once about the feeling that arrives when a book is finished —\text{\textemdash} not relief, not satisfaction, but the sense that something enormous has been carried out of the room, and the room is now very quiet. This is how I feel now. I should be honest that this feeling has nothing to do with anything else happening in the world. It arrives every time. So much investment goes into a project that when it ends, there is no energy left to begin...
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On OpenAI’s Release of Mathematical Results
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“As announced a few weeks ago, OpenAI has released a large collection of mathematical results generated by an internal model, reporting solutions to hundreds of open questions. This is an important event for mathematics, with consequences both for mathematics and for the mathematical community that extend far beyond the individual results. [...]”
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Opinions against the PhD, from an incoming PhD applicant
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Mathematics is beginning to face a turbulent age due to the rapid advancements of AI systems. A recent Summit on PhD Math Education in the Age of AI (CMSA) discussed recommendations on the adaptations for the Math PhD programs. While I agree with the main points, this post is an opinion on my major objection to the proposed direction of PhD in mathematics. I argue for a radical change in the definition of a PhD: we should not expect original contributions from a PhD anymore. The post explains my arguments regarding this position.
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The Mathematician’s Promethean Gap
by Ruben DahanPreview
“Large language models (LLMs) first appeared to the general public as a curiosity. Today, everyone uses them, and there is no doubt that their use is radically transforming the nature of our technical activities. This is particularly true in mathematics. [...]”
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AI and the mismeasure of science
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Before AI, writing papers and grant applications served as costly signals of a scientist’s ability. Today, they can no longer serve that function. The time has come to return to illegible, subjective human evaluations of scientific quality. Rate-limiting authors is a necessary first step.
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Aesthetic Judgement in Mathematics
by Rita AhmadiPreview
Are mathematicians only bearers of truth? I argue not; I argue there is an element of “taste” and “value judgment” behind the scenes that does not appear in the discussion of AI math.
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A Solution to a Problem of the Millennium Prize Problems
by AnonymousPreview
Anonymous A and Anonymous B, twin sisters and aspiring mathematicians from the United States To be clear, we offer no mathematical insight on any of the seven problems themselves. The object we study here is the construction of the Millennium Prize Problems Program itself. A solution is that which transitions a problem state from open to closed. We ask you not to judge a solution on if it looks like something you expected or hoped for (the best solutions rarely do). For the past 25 years, the Clay Mathematics Institute Millennium Prize Problems were a shining beacon that helped organize...
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One possible future
by Philip EasoPreview
If we are not needed to produce maths, then we can spend our time learning. With the right incentive structure, that does not sound so bad.
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YAPOAI (Yet Another Post on AI): AI, understanding, and mathematical work
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I use large language models quite a lot in my research. I ask them to look for references, explain unfamiliar mathematics, write code, suggest approaches, find counterexamples, and try to prove things.
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Only Anatevka
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“At the moment, the mathematics community is facing an unprecedented misalignment brought on by the advent of LLMs. According to the standard telling, the basic tension is between our traditional values (whatever those may be) and those of the corporations that make and market LLMs. [...]”
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Why I became a professional mathematician
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In this personal essay, I reconstruct the reasons why I chose to become a professional mathematician. In particular, I want to find out whether I would still find these reasons convincing and motivating today, at a time when AI is becoming capable of conducting excellent and potentially superhuman mathematical research.
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A new type of paper mill
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About the possibility of new paper mills in mathematics.
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What about the preprints?
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Preprints are central to math research and immediately feed back into LLMs. Could the mainstream preprint workflow be adjusted in a way that gives individuals more choices to impact the balance between creation of novel papers and digestion of knowledge?
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Open letter to the European Mathematical Society
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The EMS should establish a structure to shepherd the use of artificial intelligence in mathematics research. This could include developing in house AI models, regulating their use by the mathematical community in accordance with European law and establishing protocols for publication.
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The End of a Beautiful Era
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“As more and more central problems are nuked into oblivion by generated proofs, against the spreading AI-gloom the voices rise, emphasizing the internal value of deep mathematical thought and advocating for measures ranging from exercising extreme discretion with generative tools to seizing railway stations and the telegraph (or was it departments and classes of mathematical problems?) from the tightening grasp of the corporations. [...]”
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Can AI truly prove anything?
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“About a hundred years ago, David Hilbert gave a rigorous definition of a mathematical proof: [...] I will not recall here the definition of the set of axioms of logic, which was, of course, the main technical contribution here. At the same time, Church and Turing gave a rigorous definition of a computable function: [...]”
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Joint Statement about Mathathon
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“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 to redesign this event. [...]”
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Applied mathematics has met the machine before
by Denys DutykhPreview
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 HenryPreview
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 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 HarlevPreview
“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 solve many small or medium sized research problems and some hard or long-standing problems’ [...]”
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Rulers of the childless land: A response to the AGMAI
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“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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“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 pre-Greek-AI could autonomously produce, say, Archimedes’ results on the stability of equilibrium of paraboloids or the solution to the Brachistochrone problem. [...]”
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AI.MATH: announcement
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“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. [...]”
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Navigating the AI crisis: a humble guide for students
by Tarik AougabPreview
“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. [...]”
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Why I agreed to join AGMAI
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“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 we are trying to achieve, and why I agreed to be part of this group. [...]”
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Many choices lie ahead
by Jonny EvansPreview
“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, is a choice. [...]”
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History and Future of Fluid Dynamics
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“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 [...]”
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Thoughts on death and a beautiful future
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“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?’ [...]”
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Where will all the papers go?
by David CravenPreview
“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 on whether the general shape of the proof is correct. [...]”
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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. [...]”
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Existential Risk from AI: An Exposition for Mathematicians (excerpt)
by Xiaoyu HePreview
“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. [...]”
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The Fate of the Riemann Hypothesis: Revisited
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“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. [...]”
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Open Letter to Sir Paul Nurse, President of the Royal Society
by Ben GreenPreview
“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 AI companies or a desire to protect their interests?’. [...]”
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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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“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 solved is the rethinking of our own profession. [...]”
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A beginning for mathematics
by Daniel LittPreview
“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 another year, but I expect it will. [...]”
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Nothing changed
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“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 existence of irrational numbers. [...]”
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The Platonist view
by Uri BaderPreview
“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. [...]”
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The Association for Human Mathematics
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“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 society at large. [...]”
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On the impact of AI on the mathematical practice
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“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: [...]”
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Protesting the protests
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“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. [...]”
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We Need a Stockfish for Math
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“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 we’re pursuing the problem almost guarantees they never will be. [...]”
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A somewhat optimistic view of AI in mathematics
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“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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“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, and faculty at top research institutions in both the U.S. and abroad. [...]”
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Open Letter about the Mathathon
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“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 with 2 million dollars in AI credits. [...]”
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How to welcome LLM use into student research mentorship
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“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 faculty interact with students. [...]”
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What’s not new
by Orr ShalitPreview
“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 learning, we have seen some incredible techno-social turns of events, but this time it is different. [...]”
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(auto)formalization, but why
by Seewoo LeePreview
“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 assistants as well. [...]”
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What is mathematics now, and what should it be?
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“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. [...]”
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On proof and progress in mathematics in the age of generative LLMs
by Andrew NgPreview
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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“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 of AI (specifically LLMs) in maths communication [...]”
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Rethinking Maths education: A perspective from Olympiad and higher education
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“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 [...]”
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On analogies, parallels and thought experiments
by Nilima NigamPreview
“(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. [...]”
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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 our community piece by piece.
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Care for a little more AI?
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“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 wider questions here [...]”
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The AI-assisted mathematician’s dilemma
by Ruodu WangPreview
“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 on my experience with AI-assisted mathematical research, that I think mathematicians should consider. [...]”
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Evaluating mathematical merit
by Qi GuoPreview
“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 to perform that component manually. Credit should be assigned to the genuinely indispensable human input: choosing the problem, making a decisive observation or reformulation, creating concepts, organizing a theory, and assuming mathematical responsibility. [...]”
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Statement on AI usage for PhD students
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“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 and potentially problematic tool in mathematics research. [...]”
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The reverse-centaur problem: LLMs and the choices ahead
by Mark WildonPreview
“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 by AI. [...]”
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Shannon, Orwell, and the Thinking Machine
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“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 the size of a photo in megabytes, or the speed of an internet connection in megabits per second. [...]”
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Where to Point the Telescope
by Shaowu ZhangPreview
“The inverse Galois problem asks whether every finite group occurs as the Galois group of some finite Galois extension of ℚ. The program to realize the sporadic finite simple groups as Galois groups over ℚ began in 1984. Over the following years, every case except M23 was solved, leaving M23 as the last open case for nearly four decades. [...]”
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Response to “The AI dissenter viewpoint”
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“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 matter. [...]”
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Changes in the classroom in the AI Era
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“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 now? We would like to share a few ideas. [...]”
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How dare you?
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“If you are spending some time wondering to what extent AI should be developed, spread and used within activities of the mathematical community, administrativewise, teachingwise and researchwise, this note is for you. The purpose of this note is not to extend the Overton window. The Overton window has been dislodged and carried away from its original location. The purpose of this note is to center it back. [...]”
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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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“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 developments in Mathematics, based on what we have seen in Programming and Computer Science. [...]”
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Keeping the learner in the loop
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“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 so many ways out. [...]”
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The end of an era in mathematical research
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“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 has been static since Euclid [...]”
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Prompting Toward a Conjecture
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“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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“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. [...]”
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What I feel like when I work with an AI
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“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 of a tiny piece of a large moving picture. [...]”
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Why do mathematics in the age of AI
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“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. [...]”
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Writing mathematics in the age of AI
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“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 generic term for LLM harnesses like Codex, Fable or similar tools.) [...]”
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I am an exhausted postdoc. This fall is the third consecutive fall when I am on the job market and...
Oh yeah it came along the other day and I am trying to get folks gathered to apply:) I am...
I appreciate this post even though I’m probably (loudly) disagreeing with the central demand. I’d like to say that this...
I have comments about hand formalization.I have seen a lot of people in the lean community arguing for hand formalization...
Then, those should stay away from “big conjectures”.