solving a 40-year-old problem of Gyárfás from 1985... (probably my 2nd shortest paper)

6월 24일 2시에 대전 IBS 과학도서관에서 북토크 행사가 있습니다. 인하대 수학과 송용진 명예교수님께서 이번에 쓰신 “문명의 뼈대”라는 수학사 책에 대하여 말씀하신다고 합니다. 신청한 기초과학연구원 ibs.re.kr/scc/libGuidance/no…

One of the most interesting aspects of @leanprover's rise, as I came to understand it writing The Proof in the Code, is the degree to which chance events and small encounters changed its course: *Johan Commelin walking along the side of the road in Princeton *Kevin Buzzard tuning into Tom Hales's lecture from his backyard shed *Patrick Massot needing to check a student's calculation. Another story which I didn't get to include in the book is @TaliaRinger emailing Terry Tao, which turned into meeting for coffee in the summer of 2023, which turned into a multi-hour chat about the potential for Lean and other systems to facilitate large-scale collaborations—the kind that are common in other fields but rare in math (and would later be realized with the equational theories project). As Talia wrote later in the Notices of the @amermathsoc, "In the futuristic world we live in, when you submit a pull request to Terry Tao’s GitHub repository, you do not need to worry much about accidentally breaking his proofs—no matter who you are."

The US government, citing national security authorities, has issued an export control directive to suspend all access to Fable 5 and Mythos 5 by any foreign national, whether inside or outside the United States, including foreign national Anthropic employees. The net effect of this order is that we must abruptly disable Fable 5 and Mythos 5 for all our customers to ensure compliance. Access to all other Claude models is not affected. We apologize for this disruption to our customers. We believe this is a misunderstanding and are working to restore access as soon as possible. Read our full statement: anthropic.com/news/fable-myt…

My prediction from last summer was that the number of frontier AI models getting a gold medal at this summer’s IMO will be… zero! The reason is that they won’t bother to compete, it’ll simply be beneath them. If anyone can now push a button on Codex / Claude Code and get a perfect score, what’s the point? No, they’ll just leave the 17 year olds to take the test on their own. (The open source models will still compete for another year or so. That’s my guess!) Similarly, I think the labs pushing “research math” is also a fad that will expire soon enough. Think about it. GPT solved a major problem (Erdos unit distance); what they’re not reporting is the 1000 other problems they attacked and failed to make progress. [That’s not exactly deception; I also don’t report the dozens of things I tried to prove and failed…] They’re also not reporting the millions of dollars all of this cost them, and for what? Right now the “for what” is advertising: they’re signaling that they’re the best model for math, so you should use them for whatever your reasoning task is. Math departments also spend millions of dollars and produce theorems, but that is their actual end goal. A tech company is happy with a million-dollar theorem only if it predicts a billion-dollar application somewhere else. Once the bubble bursts, investors will want “real” applications from AI, new drugs, self driving / flying cars, etc etc. Nobody will care that the systems are also useful at proving theorems. Nobody but us mathematicians. So like the IMO, I think the frontier labs will get bored of theorems, and will leave us humans alone to keep doing math (and they’ll give us an amazing tool with which to do it!). Does that make sense? What do you think?

Firstproof results are out. My main takeaway: GPT5.5pro is a very strong model. 3/4 teams used it. Our Princeton team used Gemini 3.1 with our fall'25 style harness (original version performed very well on IMO problems). But it is clear vanilla prompting of 5.5pro gives very strong --and token-efficient-- results on research level math problems 1stproof.org/assets/docs/rep…

[단독]AI 안경, 韓시험장까지 침투…토익시험서 첫 컨닝 시도 적발 #뉴스1 news1.kr/society/education/6…

전국 수만 개 개표 단위에서 동점이 여러 건 나오는 건 생일 문제와 같은 구조로, 확률적으로 당연히 기대되는 결과, 이상이 아님. "23명만 모이면 그중 누군가 둘이 생일이 겹칠" 확률은 50%를 넘는 것이 생일문제, 대부분 사람들에겐 직관적으로 쉽지 않음. 시제에 대한 끌로드와 재민이의 설명.

이번 대한수학회 논문상 수상하시는 KAIST 박정환 교수님, KAIST 임보해 교수님 축하드려요... 그리고 대한수학회 노유미 학위논문상 수상하게 되신 4분 모두 축하드립니다. 그중 KAIST 박사학위자: 김재훈 교수님 제자인 임성혁 박사, 권순식 교수님 제자인 김태규 박사 kms.or.kr/board/list.html?co…

RT @snujournal: 공대위의 주장에 따르면, A교수는 ‘학위논문 전달’을 명분 삼아 B씨를 연구실로 불러내 성희롱을 가했다. 이후 연구실 등에서 반복적인 추행과 성적 접근이 이어졌으며, 2025년 5월 B씨가 임신한 사실을 인지한 뒤엔 임신…

Introducing ErdosBench: A Research-Mathematics Benchmark Built from Synthetic Erdős-Style Problems Standard math benchmarks became too saturated for frontier models evaluations. This is why we've built a list of 226 problems based on open Erdos problems. Completely new, 14 public (see below), most private, to test models' capabilities on research-level reasoning. Models get judged not only on yes/no solving, but also on finding obstructions, partial results, computational heuristics and more.

Glad to see this story getting attention. @SidharthHariha1 is extraordinary, and it is great seeing him get the recognition he deserves. He's teaching me so much this summer at @axiommathai . nytimes.com/2026/06/08/scien…

Introducing Goedel-Architect: an open-source framework for formal theorem proving in Lean 4. Using the open-weight DeepSeek-V4-Flash (284B-A13B), it reaches state-of-the-art results, rivaling proprietary systems at a fraction of the cost. It solves 4/6 on IMO 2025, 11/12 on Putnam 2025, and 3/6 on USAMO 2026. On PutnamBench it solves 88.8% (597/672) at just ~$1.65 per problem. Paper: arxiv.org/abs/2606.06468 Project page: goedelarchitect.github.io/

#New_accepted_paper Matthew Baker, Changxin Ding, and *Donggyu Kim*, The Jacobian of a regular orthogonal matroid and torsor structures on spanning quasi-trees of ribbon graphs, Adv. Math., accepted, 2026. arxiv.org/abs/2501.08796

I have started a collection of essays, blog posts, etc discussing AI in mathematics. I do not agree with everything written, but all are valuable to read - the more different views the better! Please reply with your own suggestions. thomasbloom.org/AIlinks.html

This week I joined @kevinroose and @CaseyNewton on Hard Fork to talk about how AI is shaking math, including the big recent @OpenAI proof, and the new Leiden Declaration in which mathematicians express their growing concerns for how AI could degrade the field.

Official OpenAI Academy workshop: Codex for Faculty and Researchers. Free. 1 hour live workshop. Link to sign up in reply.

1/n Today I am releasing Lean Pool - the result of 100 human hours and 1000 agent hours. Lean Pool is a repo for preserving substantial sorry-free formalizations that are valuable but do not fit naturally into mathlib’s scope.

What happened when one of our models found a counterexample to an 80-year-old Erdős conjecture? Researchers @alexwei_, @HongxunWu, and @wjmzbmr1 shared the story on the OpenAI Podcast with @AndrewMayne and explained how mathematicians and models can work together to make new discoveries.

Honoured that our 2016 paper, Robust Estimators in High Dimensions without the Computational Intractability, w/ Ilias Diakonikolas, Daniel Kane, Jerry Li, Ankur Moitra, Alistair Stewart, was awarded the 2026 Gödel Prize This is the highest award for papers in theoretical CS. 1/7