Announcing FrontierMath Erdős (A benchmark of 68 significant Erdős problems, open as of August 2026, curated by Thomas Bloom and formalized in Lean). ~ Tom Adamczewski, Greg Burnham. https:// epoch.ai/latest/announcing-fro ntiermath-erdos # LeanProver # ITP # AI4Math
A proof of Conway's refinement conjecture in Lean. ~ Dan Abramov. https:// github.com/gaearon/conway-refi nement # LeanProver # ITP # AI4Math
The θ(p꜀) = 0 conjecture is solved in all dimensions. In 2024 Gady Kozma and Shahaf Nitzan showed how to derive the dying percolation conjecture from a proposed conjecture about percolation on general graphs. (I briefly discussed it in this … Continue reading →
A recent Washington Post article titled "This may be the first academic profession to see its work taken over by AI," ponders if AI can solve mathematical problems, what is left for mathematicians to do?
What do you think? Leave your comments below!
Full story link in comments.
I woke up yesterday with the following thoughts, which are probably either obvious or dumb. A central thesis that many readers, including me, took from Douglas Hofstadter’s Gödel Escher Bach when young was that the secret of intelligence (and therefore, of AI) was going to have a lot to do with self-referentiality and “strange loops.” […]
A Lean formalization of Hamilton's three-manifold theorem. ~ Bennett Chow, Yuan Liao, Ziyang Qin. https:// arxiv.org/abs/2608.21502v1 # LeanProver # ITP # Math
I can't help finding that a rather stylish way to rip off your customers, right down to the phrase "this once".
Just discovered this very interesting blog post by @davidbau.bsky.social. davidbau.com/archives/202... It is an interesting formulation of the idea that it is up to humans to decide what world is worth building (and to take responsibility for the results)
Jeremy Horpedahl tells the story: Nicholas Polson has, by my count using his SSRN page, already written 258 working papers in 2026 alone. He’s already written (or at least published to SSRN), six papers today, August 26, 2026. OK, but … Continue reading →
Luke Ford writes: [Regarding] the replication crisis, researcher degrees of freedom, and the gap between what statistical methods claim to establish and what they can actually support . . . Looking at the current state of the social sciences, do … Continue reading →
"not right to call proving one conjecture made by a mathematician, using theory developed by over a century of work by mathematicians, with an AI built by mathematicians and trained by reading everything ever written by all mathematicians as 'replacing mathematicians'." Thomas Bloom via Cal Newport.
I wonder if we can apply LLMs to trace the development and provenance of ideas and use that, rather than citations, as the signal?
Just send me your goddamn prompt.
Mathematical Discourse is a new online, peer-reviewed mathematics journal, publishing videos of mathematics research talks of the highest quality. Our inaugural scientific and editorial boards are listed at the end of this message. Our goal is to promote and nourish a culture which values communication as an essential part of the research process. Giving a […]
A frequent commenter pointed me to this paper, “Sport and longevity: an observational study of international athletes.” All I can say is . . . Wow! This paper is an absolute clinic in bad quantitative social science research. I’ll leave … Continue reading →
Ben Krause, Hamed Mousavi, Joni Teräiväinen, and I have just uploaded to the arXiv our paper Quantitative bounds for sets lacking polynomial progressions with shifted prime difference. The purpose of this paper is to obtain quantitative versions of this theorem of Wooley and Ziegler: Theorem 1 Let be polynomials of one variable with integer coefficients […]
Lew Ludwig leads AI workshops and wrote a book on AI in higher ed, yet his gut resists AI-based assignments.
A reflection on Gloucester Cathedral’s stonework helped him understand why.
Read more: https://maa.org/math-values/there-and-back-again-why-i-dont-ask-my-students-to-use-ai/
https:// proofsandprompts.com/2026/08/0 9/why-do-mathematics-in-the-age-of-ai/
For example, if the models are jumping around quite a lot, making guesses until they get lucky, then there will be less to be learned from failed attempts than if they are arriving at proofs by a gradual process of modification of an initially proposed argument.
I was thinking more of the mathematical literature when I wrote that. I don't think the answer to your question is obvious. Clearly they will have some kind of data, but I don't know whether it is similar enough to the kind of data that humans generate to be as useful for learning to do research.
That’s an important question and will become very important if/when the volume of AI-generated mathematics greatly increases. But for these recent results, I think it’s safe to trust the experts (just as I trust people who say that Wiles and Taylor-Wiles really did prove FLT).
I think their proofs have been formalized.
I've just written a blog post about whether current LLMs are better at some kinds of mathematics than others, with an emphasis on "current", given how quickly the situation is developing.
gowers.wordpress.com/2026/08/12/w...
For the sake of anyone who might read this blog post in the distant future (a month from now, say), let me mention that I am writing it a few days after OpenAI announced that it had solved ten major problems in mathematics and theoretical computer science, including the first construction of a non-sofic group, […]
Whatever you’ve been writing to me to ask if I’m aware of: yeah, I’m aware of it. In particular: Anyway, about the AI stuff. I don’t know whether this is literally our last year alive—I doubt it—but it’s pretty clearly the last year of math and theoretical computer science research in the style we’ve known […]
Last September I went to a workshop at the Lorentz Centre in Leiden to discuss mathematics and AI with historians, philosophers, computer scientists, AI researchers, and mathematicians of several different flavours (though there was a surprising preponderance of algebraic geometers). The whole event was extremely stimulating, with some talks but also a lot of time […]
I continue to wonder about utility of #genAI. I gave Claude some text I wrote and asked it to find and add suitable references. In the response it gave some warnings that straight-up assumed I am a student cheating on an assignment. 🤯
The Ramanujan challenge Ido Kaminer shared with me the following information about The Ramanujan Challenge for AI, and I am happy to share it with the readers of this blog. The challenge page is at ramanujanmachine.com/ramanujan-challenge; Here is the The … Continue reading →
An AI ChatBot solves a long standing Erdős problem. New "Devlin's Angle" post for the MAA. https:// maa.org/math-values/ai-solves- an-80-year-old-erdos-problem/
An AI ChatBot solves a long standing Erdős problem. New "Devlin's Angle" post for the MAA. maa.org/math-values/...
We are all having to keep revising upwards our assessments of the mathematical capabilities of large language models. I have just made a fairly large revision as a result of ChatGPT 5.5 Pro, to which I am fortunate to have been given access, producing a piece of PhD-level research in an hour or so, with […]
Quadratic functions are the workhorse of the analysis of iterative algorithms such as gradient-based optimization. They lead, in discrete and continuous time, to closed-form dynamics that treat all eigensubspaces of the Hessian matrix independently. This leads to simple math for understanding convergence behaviors (maximal step-size, condition number, acceleration, scaling laws for gradient descen…
Boris Alexeev writes on how he's been experimenting with AI to solve Erdos Problems: xenaproject.wordpress.com/2025/12/05/f...
Congratulations to Floris van Doorn and Christian Thiele for their new ERC grant for formalization of analysis in Lean www.mathematics.uni-bonn.de/en/news/will...
Here's the statement in Lean. How little can one get away with importing in order to prove this? Can it be proved by induction on max(l)-min(l) for example, avoiding the reals completely?
xenaproject.wordpress.com/2025/10/22/f...
A chat around what's been happening in the world of AI and Erdos problems, and what it highlights.
My talk at the Simons Foundation last week is now up on YouTube youtube.com/watch?v=K5w7VS2sxD0 . It is a hopefully-comprehensible general audience talk about what I think is a big decision which mathematicians will have to decide whether to back or not.
It’s been over three years since my last post on this blog and I have sometimes been asked, understandably, whether the project I announced in my previous post was actually happening. The answer is yes — the grant I received from the Astera Institute has funded several PhD students and a couple of postdocs, and […]
Amongst the projects funded is my project www.renaissancephilanthropy.org/a-dataset-of... to create what in 2025 is a super-hard dataset of pairs (informal hard proof, formal statement) of recent results from top journals. The challenge for machine is to formalise the rest of the paper.
Renaissance Philanthropy have announced the first 29 grants they've given from their AI For Math fund www.renaissancephilanthropy.org/ai-for-math-... . Interesting to see that around half of the funded proposals mention Lean.