In traditional mathematics (or "Math 1.0"), a breakthrough proof of a long-standing open conjecture generates a large amount of subsequent activity and excitement in the field. The authors of the proof are invited to give many talks, and meet with other experts in the area. Workshops are set up to discuss the proof, as well as other recent developments. As a result, new connections and collaborations are formed, followup problems are shared, and other mathematicians (both junior and senior) are attracted to the field (including in some cases the authors themselves, if they initially came from a different subject). As a result of all this activity, the proofs naturally become digested, streamlined, placed in context with other results in the field, and ultimately become part of the textbooks and lecture notes for the next generation of mathematicians in the field. (1/4)
Bartosz Naskręcki on Twitter / X
Congrats to @LechMazur for the solution and to Terence Tao for the digestion and storytelling. You see the trend. Mathematicians are still needed if we want to make any sense of the formal proofs. For now... Maybe the next gen LLMs will simply read allthe blogs of Terry and… https://t.co/yXiISCrNAF— Bartosz Naskręcki (@nasqret) August 13, 2026
If math is more than proof, we need to better celebrate the rest of it
[This is a guest post by Grant Sanderson. This blog post was initially written in a different file format and converted using AI. — T.] A sentiment echoing throughout the mathematics communit…
Michael Truell on Twitter / X
We believe Cursor discovered a novel solution to Problem Six of the First Proof challenge, a set of math research problems that approximate the work of Stanford, MIT, Berkeley academics. Cursor's solution yields stronger results than the official, human-written solution.…— Michael Truell (@mntruell) March 3, 2026
Tony Feng on Twitter / X
I am a mathematician but I avoided commenting on this because the problems are (far) outside my domain. Even if I sat down to read the technical details (which I have not), it would be hard to appreciate the context of prior work, etc. But I've gotten enough sense of things… https://t.co/VZzosBYFto— Tony Feng (@tonylfeng) August 5, 2026
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Mathematics with large language models as provers and verifiers
During 2024 and 2025 the discussion about the theorem-proving capabilities of large language models started reporting interesting success stories, mostly to do with difficult exercises (such as problems from the International Mathematical Olympiad), but also with conjectures [Feldman & Karbasi, arXiv:2509.18383v1] formulated for the purpose of verifying whether the artificial intelligence could prove it. In this paper we report a theorem proving feat achieved by ChatGPT by using a protocol involving different prover and verifier instances of the gpt-5 model working collaboratively. To make sure that the produced proofs do not suffer from hallucinations, the final proof is formally verified by the lean proof assistant, and the conformance of premises and conclusion of the lean code is verified by a human. Our methodology is by no means complete or exact. It was nonetheless able to solve five out of six 2025 IMO problems, and close about a third of the sixty-six number theory conjectures in [Cohen, Journal of Integer Sequences, 2025].
Przemek Chojecki | PC on Twitter / X
The Growing Map of Open Mathematical Problems.We mapped 15,000+ conjectures from UnsolvedMath to show potential links between concepts.It also shows how under formalized the frontier is (less than 10%). pic.twitter.com/nm0PCpXVPf— Przemek Chojecki | PC (@prz_chojecki) August 28, 2026
OpenAI accused of stealing math proof from expert Andreas Thom | Valerio Capraro posted on the topic | LinkedIn
BREAKING: OpenAI might have stolen another major proof. In a detailed Mathstodon post, which I report in full in the comments, Andreas Thom presents several pieces of evidence suggesting that OpenAI may have trained Astra on conversations in which he and Gábor Kun were working on Gromov’s soficity conjecture, one of the ten problems OpenAI later announced Astra had solved. I know Andreas. We met several times early in our careers. He is an exceptional mathematician, a leading expert on sofic and hyperlinear groups, and one of the most respected scholars in the field. He has spent two decades working on this problem. If his account is correct, this is not a minor dispute over attribution. It would mean that unpublished human work was absorbed into a model and then presented to the world as a breakthrough by the model itself. And if the allegations raised by Levent Alpöge, Tristan Buckmaster, and now Andreas Thom are all substantiated, we are no longer looking at isolated incidents. We may be looking at one of the greatest intellectual scandals in the history of science. AI is not discovering new mathematics. AI is stealing human discovery. | 201 comments on LinkedIn
Terence Tao: AI companies are harming mathematics | New Scientist
AI firms are making new mathematical discoveries at a rapid pace, but not sticking around to help unpick the new proofs. That is not the way to advance our understanding, says mathematician Terence Tao
Ten advances in mathematics and theoretical computer science
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
The Technological Turn in Mathematics
Quickly evolving technologies, such as Interactive Theorem Provers (ITPs), Automated Theorem Provers (ATPs), and Large Language Models (LLMs), all falling under the general heading 'AI for mathematics,' are transforming mathematical practice in profound ways. This chapter explores the implications of these innovations, focusing on their impact on how mathematical knowledge is created and shared. It also discusses how they are reshaping the social dimension of mathematics, altering collaboration dynamics, trust relationships, and the collective production of knowledge. For instance, tools like ITPs facilitate large-scale collaborations and make new types of teamwork possible, where trust is not a necessary ingredient. ITPs also help us mitigate our human fallibility, yet they raise questions about the nature of formalization and the relationship between traditional and formal mathematics. Technologies such as LLMs are reshaping the division of epistemic labour between humans and machines and urge philosophers of mathematics to ask questions about the value of their work.
Terence Tao – Kepler, Newton, and the true nature of mathematical discovery
“And what those stories teach us about how AI will revolutionize math”
Talia Ringer 🕊🪬 on Twitter / X
Poured my heart and soul into advocating for formal proof with AI assistance in a mathematical setting because of the large collaborations I thought it could empower. (1/3)— Talia Ringer 🕊🪬 (@TaliaRinger) September 10, 2026
AI helped produce two proofs for the same cryptography problem
Last Thursday Massachusetts Institute of Technology graduate student Seyoon Ragavan sent a new quantum cryptography proof to his friend Yao-Ting Lin, a doctoral student at the University of California...
How I Vibed a Proof of Conway’s Conjecture — overreacted
You can just prove things, apparently.