Binghui Peng

[1/n] Recent OpenAI research has demonstrated the ability of LLMs to solve frontier problems in mathematics. We design a simple pipeline (using GPT 5.5 Pro and Claude Opus 4.8) that resolves 9 challenging open problems, including open problems from prominent theoretical computer science venues—4 from COLT open problem list and 1 from FOCS —as well as 4 problems from the commutative algebra. Project link: github.com/Pengbinghui/pi…, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory

@jdjncmcmsnf it is some arXiv paper, so I can't believe that is the case. One suspicion is that the query exceeds their token limit so it fails; other suspicion is some internal system error; neither these two suspicions can be answered by GPT, that's my worry

@binghuip Well that was my experience. My point is you can ask gpt why. But the reply you got is for sure hard to believe. Did you ask which paper that was not able to fetch?

Does anyone know why GPT-5.6 Pro keeps ending with “Thinking failed” after hours of reasoning?

@jdjncmcmsnf Not true, it said it tries to fetch some paper but not success, hardly believe this is the reason

@binghuip You can ask gpt itself why. The reply is they have searched all tentative ideas and all boil down to hard issues that can not bypass. They do not how to proceed further, then failed

We also solved Erdős Problem 477 (showing that the set of 13th powers admits a tiling complement in ℤ). Check out the solution here: github.com/Pengbinghui/pi…. Thanks @Diyi1996 for helping us verifying the proof.

And we do not stop at proofs: we also build an agentic pipeline that automatically formalizes all 4 commutative-algebra solutions in Lean 4 with one button click!

📌 4 COLT open-problem-track questions: • Shuffled SGD — the SS–RS–GD inequalities (Yun, Sra, Jadbabaie, COLT 2021) • Robust conditional probability estimation (Langford, COLT 2010) • Learning measured-output quantum circuits (Kun & Reyzin, COLT 2015) — partial solution • Unweighted data selection for linear regression, Problem 3 (Hanneke, Moran, Shlimovich, Yehudayoff, COLT 2025) 📌 4 open problems in commutative algebra (open problems in Commutative Ring Theory by Cahen–Fontana–Frisch–Glaz) 📌 An open question from my own FOCS 2023 paper — On the adversarial robustness of online leverage-score sampling.

[1/n] Recent OpenAI research has demonstrated the ability of LLMs to solve frontier problems in mathematics. We design a simple pipeline (using GPT 5.5 Pro and Claude Opus 4.8) that resolves 9 challenging open problems, including open problems from prominent theoretical computer science venues—4 from COLT open problem list and 1 from FOCS —as well as 4 problems from the commutative algebra. Project link: github.com/Pengbinghui/pi…, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory

🧵(1/8) An @OpenAI internal reasoning LLM achieved an AI Math milestone: solving an open problem central to its mathematical subfield— in this case, the unit distance problem of discrete geometry. We came across it in a side quest to truly push our model on the hardest problems.