DeepMind’s AlphaProof Nexus solves 9 open Erdős problems, published in Science
Google DeepMind’s AlphaProof Nexus, a Gemini 3.1 Pro-based system that drafts Lean proofs and uses compiler feedback to revise them, solved 9 of 353 open Erdős problems, including two that had stood for 56 years, according to a study published in Science. The system also proved 44 open OEIS conjectures, settled a 15-year-old algebraic geometry question and improved a known bound in min-max optimization, with inference costs of a few hundred dollars per problem. DeepMind says a simpler LLM-plus-Lean loop also solved all nine Erdős problems; an independent audit cited by 36Kr found one solution was already implied by an earlier theorem, which would reduce the count to eight under a stricter definition.
It offers a peer-reviewed example of an AI system contributing to open mathematics, in contrast to OpenAI’s unreviewed GitHub release of hundreds of proofs, which drew a boycott call from the Association for Human Mathematics.
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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