Recent OpenAI research has demonstrated the ability of LLMs to solve frontier problems in mathematics (1 minute read)
Summary
OpenAI research shows LLMs can solve nine open math problems from COLT, FOCS, commutative algebra, and Erdős problems using a simple pipeline with GPT-5.5 Pro and Claude Opus 4.8, with Lean formalizations.
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[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://github.com/Pengbinghui/pipeline-math…, joint work with @runzhou_tao, Steven Wang & @HantaoYu_Theory
Pengbinghui/pipeline-math
Source: https://github.com/Pengbinghui/pipeline-math
This repository collects resolutions of a number of open problems from the COLT open-problem track, commutative ring theory, Erdős problem and an open question from a FOCS 2023 paper by the authors.
Contributor. Binghui Peng, Runzhou Tao, Steven Wang, Hantao Yu, Diyi Liu
Proof discovery. The proofs are generated by GPT-5.5 Pro via a simple prover–verifier pipeline; the papers are assembled with Claude Code, then polished and verified by the authors.
Formalization. We also formalize the commutative ring theory solutions in Lean using our agentic Lean formalization pipeline, fully automated, open source soon!
News
- 2026-06-28: Added write-up for Erdős Problem 477 (tiling complement) — paper.
Open problems answered
Each problem links to its current write-up and, where available, a machine-checked Lean 4 formalization. Write-ups are uploaded gradually and may be merged into a single paper over time.
COLT open-problem track
- Shuffled SGD — the SS–RS–GD inequalities (Yun, Sra, Jadbabaie, COLT 2021) — paper
- Learning measured-output quantum circuits (Kun and Reyzin, COLT 2015) - paper (Partial solution).
- Unweighted data selection for linear regression (Hanneke, Moran, Shlimovich, Yehudayoff, COLT 2025) — paper (Problem 3)
- Robust conditional probability estimation (Langford, COLT 2010) — paper
FOCS 2023 (authors’ own open question)
- Adversarial robustness of online leverage-score sampling (Jiang, Peng, Weinstein, FOCS 2023) — paper
Commutative ring theory — Glaz et al., Open Problems in Commutative Ring Theory
- Problem 4: finite-conductor vs. quasi-coherent rings — paper, Lean
- Problem 20 (Cahen–Fontana–Frisch–Glaz) — paper, Lean
- Problem 27: integer-valued polynomials over algebras (Werner) — paper, Lean (27b)
- Problem 30(c) — paper, Lean
Erdős problems
- Problem 477: tiling complement — paper
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