Google DeepMind's AlphaProof Nexus Solves Dozens of Open Math Problems

Nine Erdős Problems and 44 Conjectures

Google DeepMind's AI system AlphaProof Nexus has solved dozens of open mathematics problems on its own, according to a peer reviewed study published in Science. The system cracked nine of 353 open Erdős problems, two of which had remained unsolved for 56 years.

The team shared those solutions online ahead of the paper. Beyond the Erdős problems, 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.

How the System Works

AlphaProof Nexus is 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, the system can call on AlphaProof, a specialized proof tool. Google DeepMind reports that even without AlphaProof, the system solved the nine Erdős problems.

Peer Review Amid an AI Math Debate

The study lands amid a heated debate over AI math. OpenAI recently published hundreds of AI generated proofs on GitHub instead of submitting them to journals. The Association for Human Mathematics, led by Terence Tao, called for a boycott of that approach.

DeepMind put its work through peer review instead, with the results appearing in Science.

Sources: The Decoder