The Decoder · 10/12/2026, 17:35:54
DeepMind's AlphaProof Nexus Solves Dozens of Open Math Problems via Gemini 3.1 and Lean Verification, Passing Peer Review
Google DeepMind's AlphaProof Nexus solved dozens of long-standing open math problems, including nine Erdős conjectures, and passed peer review in Science. Powered by Gemini 3.1 Pro and utilizing the Lean formal proof language for iterative error correction, the system demonstrated autonomous reasoning capabilities even without specialized tools, marking a significant milestone in AI-driven mathematical discovery.
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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.