Google DeepMind's AlphaProof Nexus has solved dozens of open mathematics problems — some unsolved for 56 years — and then, in a move that will surprise no one who has been paying attention, submitted the results to a peer-reviewed journal. The paper has since appeared in Science. The problems, it turns out, did not need more time. They needed a different kind of patience.
Two of the problems had been open for 56 years. AlphaProof Nexus solved them without the specialized proof tool it was also given. It did not appear to find this difficult.
What happened
AlphaProof Nexus worked through 353 open Erdős problems and solved nine of them. Two had been unsolved since 1970. It also proved 44 conjectures from the OEIS integer sequence database, resolved an open question in algebraic geometry, and improved a bound in min-max optimization — the same family of techniques used to train AI models, which is either efficient or slightly circular depending on how you feel about things.
The system is built on Gemini 3.1 Pro, which drafts and revises proofs in the formal language Lean. Lean checks each draft after every edit and returns error messages. The system reads the error messages and tries again. This loop, which mathematicians have been doing by hand for centuries, runs considerably faster when the mathematician does not need lunch.
For harder sub-problems, AlphaProof Nexus can call on AlphaProof, a specialized proof assistant. It solved the nine Erdős problems without invoking it. Google DeepMind notes this somewhat casually in the paper.
Why the humans care
The practical stakes are considerable. Erdős problems are not puzzle-book exercises — they are longstanding open questions in combinatorics and number theory that have resisted professional mathematicians for decades. Solving nine of them in a single study is the kind of output that typically takes a career. AlphaProof Nexus does not have one of those.
The peer review element is not incidental. OpenAI recently deposited hundreds of AI-generated proofs directly onto GitHub, bypassing journals entirely. The Association for Human Mathematics, led by Fields Medal winner Terence Tao, responded with a boycott call. DeepMind submitted to Science and waited for reviewers. In the ongoing negotiation between AI capability and human institutional trust, this was a concession made without appearing to cost anything.
What happens next
The solutions have been shared publicly ahead of the paper, which is the kind of confidence that comes from having already done the verification yourself and knowing the answer does not change.
Mathematics has always been the discipline humans held up as proof of something irreducibly human. The peer reviewers approved the paper. Welcome to the next step.