Binghui Peng

Assistant Professor at UMD CS | prev. Google, Stanford, Berkeley, Columbia University, Tsinghua

[Binghui Peng @binghuip]

[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: https://t.co/YCBzYjfz3N, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory

[Binghui Peng @binghuip]

We also solved Erdős Problem 477 (showing that the set of 13th powers admits a tiling complement in ℤ). Check out the solution here: https://t.co/pqsgfPiOUr.

Thanks @Diyi1996 for helping us verifying the proof.

[Binghui Peng @binghuip]

[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: https://t.co/YCBzYjfz3N, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory

[Binghui Peng @binghuip]

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!

[Binghui Peng @binghuip]

[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: https://t.co/YCBzYjfz3N, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory

[Binghui Peng @binghuip]

📌 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.

[Hongxun Wu @HongxunWu]

🧵(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.