AlphaProof Nexus解9道Erdős难题
据《Science》发表的一项研究，Google DeepMind 的 AlphaProof Nexus 用 Gemini 3.1 Pro 起草 Lean 证明，并借助编译器报错反复修改，在 353 道开放的 Erdős 问题中解出 9 道，其中两道已悬置 56 年。该系统还证明了 OEIS 的 44 个开放猜想、解决一个悬置 15 年的代数几何问题，并改进了 min-max 优化中的一个已知上界，单题推理成本约数百美元。DeepMind 表示，去掉 AlphaProof 和进化搜索、只保留大模型加 Lean 反馈的简版也能解出这 9 道题；36氪援引的独立审计则指出，其中第 846 题的答案其实已被早先定理蕴含，按更严格定义应计为 8 道。
它提供了一个经同行评审的 AI 参与开放数学问题的案例，与 OpenAI 将大量未审稿证明直接发布到 GitHub、并招致人类数学协会抵制呼吁的做法形成对照。
Google Deepmind's AlphaProof Nexus solved dozens of open math problems and actually got peer reviewed
Oct 12, 2026
Google Deepmind's AI solved dozens of open math problems on its own, per a new study in Science. AlphaProof Nexus cracked nine of 353 open Erdős problems, two unsolved for 56 years. The team shared those solutions online ahead of the paper.
Beyond that, AlphaProof Nexus proved 44 conjectures from the OEIS integer sequence database, solved an open question in algebraic geometry, and improved a known bound in min-max optimization, a technique used to train some AI models. It's built around Gemini 3.1 Pro, which drafts and revises proofs in the formal language Lean. Lean checks each draft after every edit, and error messages guide the next attempt. For harder sub-problems, it can call on AlphaProof, a specialized proof tool. Even without AlphaProof, it solved the nine Erdős problems, Google Deepmind reports.
The study lands amid a heated debate over AI math. OpenAI recently dumped hundreds of AI proofs on GitHub instead of submitting them to journals. The Association for Human Mathematics, led by Terence Tao, called for a boycott. Deepmind put its work through peer review.
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