DeepMind's AlphaProof Nexus solves 9 of 353 open Erdős problems in peer-reviewed Science paper

Google DeepMind's AlphaProof Nexus solved nine of 353 open Erdős problems, according to a new study in Science. Two of the nine had gone unsolved for 56 years. Unlike other recent AI-math efforts, the results went through peer review.

What the system solved

Per the study and reporting by The Decoder, AlphaProof Nexus produced the following results:

• Erdős problems: 9 of 353 open problems solved (about 2.5%). The team posted these solutions online ahead of the paper.
• OEIS conjectures: 44 conjectures from the Online Encyclopedia of Integer Sequences (OEIS) proved.
• Algebraic geometry: one open question solved.
• Min-max optimization: an improvement to a known bound. Min-max optimization is used to train some AI models.

How it 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 its error messages guide the next attempt. For harder sub-problems, the system can call AlphaProof, DeepMind's specialized proof tool.

Google DeepMind reports that the system solved all nine Erdős problems even without AlphaProof, so the specialized tool was not required for those results. That claim comes from the company, and independent replication has not been reported.

Parameter count, context window, pricing and public availability for AlphaProof Nexus have not been disclosed. It is a research system, not a released API model.

Context: a dispute over how AI math gets published

The study arrives during a heated debate over AI-generated mathematics. According to The Decoder, OpenAI recently put hundreds of AI-generated proofs on GitHub rather than submitting them to journals. The Association for Human Mathematics, led by Terence Tao, called for a boycott in response. DeepMind took the opposite route and submitted its work for peer review.

What this means

Lean verification and peer review answer different questions. Lean checks mechanically that a proof is logically valid. Peer review checks whether the problems were correctly stated, whether the results are new, and whether they matter. Using both gives DeepMind's claims more credibility than a bulk repository of unreviewed proofs.

The success rate is modest. Nine of 353 Erdős problems shows that the approach works on a small slice of open problems, not most of them. The 44 OEIS conjectures and the algebraic geometry result suggest the method is not limited to one problem family. How difficult each solved problem was relative to the rest remains for mathematicians to judge.

The architecture result may matter more than the benchmark. If the nine Erdős solutions really hold without AlphaProof, then a general-purpose LLM in a tight loop with a proof checker is enough for this class of results. That would make the approach easier for other labs to reproduce and extend.

Publication norms are becoming a competitive axis. With a mathematician-led boycott already under way, labs that skip peer review may face resistance from the community whose validation they want. DeepMind has now set a precedent that others will be measured against.