Google DeepMind's AlphaProof Nexus solved nine open Erdős problems, according to a peer-reviewed study in Science

Google DeepMind reports in a new peer-reviewed study in Science that its AlphaProof Nexus system solved dozens of open math problems on its own. The system solved nine of 353 open Erdős problems, two of which had gone unsolved for 56 years. The team had shared those solutions online before the paper appeared. AlphaProof Nexus also 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. The system is built around Gemini 3.1 Pro, which writes and revises proofs in the formal language Lean. Lean checks each draft after every edit, and its error messages guide the next attempt. For harder sub-problems, the system can call AlphaProof, a specialized proof tool. DeepMind says it solved the nine Erdős problems even without AlphaProof. The study comes during a heated debate over AI-generated mathematics. OpenAI recently posted hundreds of AI-written proofs to GitHub instead of submitting them to journals, and a mathematicians' group led by Terence Tao called for a boycott. DeepMind's decision to go through peer review offers a contrasting approach to having AI results checked.