A proof of Conway's refinement conjecture in Lean. ~ Dan Abramov. https:// github.com/gaearon/conway-refi nement # LeanProver # ITP # AI4Math
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!
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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)
"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?
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...
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. 🤯
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/...
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.
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.
The Mathlib Initative is hiring! www.renaissancephilanthropy.org/careers/math... (part-time contractor, helping to solve the "2000 PRs" issue, note the required qualifications) and www.renaissancephilanthropy.org/careers/devo... (full-time, solving distributed systems challenges). 14 Sept deadline.
Mathematics is also incomplete (assuming it's consistent) and that hasn't stopped lean from engaging with it at research level
@sciam.bsky.social gave me the opportunity to share some personal thoughts about the recently reported AI results from the #imo2025:
NSF announces funding for ICARM: the Institute for Computer-Aided Reasoning in Mathematics, based in Carnegie-Mellon . Amazing! Carnegie-Mellon press release here: www.cmu.edu/news/stories...
Accept submissions of explicitly unfinished ideas, theories, or speculative models to start discussion. Gets more finished with feedback from reviewers and/or readers.