Google DeepMind 用 LLM 智能体解决 9 个 Erdős 开放问题
Google DeepMind solves 9 Erdős problems
Google DeepMind 团队在 arXiv 发布论文，对用 LLM 生成 Lean 形式化证明来求解开放问题做了首次大规模评测。其最强智能体自主解决了 353 个 Erdős 开放问题中的 9 个，单题成本为几百美元，并证明了 492 个 OEIS 猜想中的 44 个，正被用于组合数学、优化、图论、代数几何和量子光学研究。
Authors:George Tsoukalas, Anton Kovsharov, Sergey Shirobokov, Anja Surina, Moritz Firsching, Gergely Bérczi, Francisco J. R. Ruiz, Arun Suggala, Adam Zsolt Wagner, Eric Wieser, Lei Yu, Aja Huang, Miklós Z. Horváth, Andrew Ferraiuolo, Henryk Michalewski, Edward Lockhart, Codrut Grosu, Thomas Hubert, Matej Balog, Pushmeet Kohli, Swarat Chaudhuri
Abstract:Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the first large-scale evaluation of this method's ability to solve open problems. Our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars, proved 44/492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. A basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes but proved costlier on the hardest problems. These findings demonstrate the power of AI-aided formal proof search and shed light on the agent designs that enable it.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.22763 [cs.AI] |
| (or arXiv:2605.22763v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2605.22763 arXiv-issued DOI via DataCite |
Submission history
From: Swarat Chaudhuri [view email]
[v1]
Thu, 21 May 2026 17:24:57 UTC (1,291 KB)
[v2]
Mon, 8 Jun 2026 12:23:48 UTC (1,301 KB)
来源：Hacker News · arxiv.org