Google DeepMind publishes peer-reviewed Science study on AlphaProof Nexus, which solved nine open Erdős problems and proved 44 OEIS conjectures

Google DeepMind has published a peer-reviewed Science paper on AlphaProof Nexus. The system uses Gemini 3.1 Pro to draft and revise proofs in Lean, a proof checker that verifies each edit, and it can call the separate AlphaProof tool for harder sub-problems. Reported results are nine of 353 open Erdős problems solved (two of them open for 56 years and solved even without AlphaProof), 44 OEIS conjectures proved, one open algebraic geometry question solved, and an improved bound in min-max optimisation. The Erdős solutions were shared online before the paper appeared. Our only source is The Decoder's secondary report, with no links to the paper itself.

The main audience is mathematicians and AI research labs. Because Lean checks every proof, the results do not depend on trusting the model, and that makes them more credible than unverified AI maths claims. Peer review also sets a higher standard for competitors, notably OpenAI, whose bulk proof release drew criticism. Practical impact outside research maths is limited for now. There are no products or deployments to act on, and the results cover a small slice of the problems attempted.

"Dozens of open problems" and "autonomously" flatter the result: nine of 353 Erdős problems is about 2.5 per cent, and many OEIS conjectures are likely to be far easier than famous open problems. The contrast with OpenAI is editorial framing, and we have not seen the paper's own account of how much human setup, problem selection and compute went in. The Erdős results were already public, so the news is the peer review, not the mathematics.

1. 01Independent mathematician assessments of the nine Erdős solutions and the 44 OEIS proofs, including how significant or easy they were, over the next few weeks.
2. 02Whether DeepMind releases the Lean proofs, code or tool access, so outside researchers can reproduce results and measure the failure rate on the other 344 Erdős problems.
3. 03Whether other labs, especially OpenAI, submit similar work to peer review, and whether the Association for Human Mathematics boycott call leads to any change in how AI maths results are published.