Google DeepMind's AlphaProof Nexus solved dozens of open math problems, including nine Erdős problems, two of which had been unsolved for 56 years, according to a study in Science. The results were peer-reviewed before publication, contrasting with OpenAI's recent release of AI proofs on GitHub without peer review, which sparked a boycott.
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Google DeepMind's AlphaProof Nexus published research in Science, autonomously solving dozens of open math problems, including nine Erdős problems, and unusually passing peer review. Meanwhile, OpenAI released hundreds of AI proofs directly to GitHub rather than submitting to journals, prompting the Association for Human Mathematics led by Terence Tao to call for a boycott.
According to a study in Science, Google DeepMind's AlphaProof Nexus autonomously solved dozens of open math problems. What makes this result special is not just the quantity, but that it passed peer review—DeepMind submitted its work for peer review, which is uncommon for AI mathematics results.
The study was published amid a fierce debate about AI mathematics. One focus of the debate is how AI-generated proofs should enter the academic record: whether they should go through journal review like traditional mathematical research, or be published directly on code-hosting platforms.
Among the specific results, AlphaProof Nexus solved nine of 353 open Erdős problems. Of these nine, two had been unsolved for as long as 56 years. The team had already shared these solutions online before the paper was published.
Erdős problems are named after their proposer, Paul Erdős, and are usually simple to state but difficult to prove, making them a common touchstone for testing automated mathematical reasoning. Solving two of these 56-year-old open cases means the system reached areas where human mathematicians had long failed to break through.
In addition to the Erdős problems, AlphaProof Nexus also proved 44 conjectures in the OEIS integer sequence database. OEIS is an online database of integer sequences, and its conjectures often involve combinatorics and number theory, are numerous, and vary in difficulty.
It also solved an open problem in algebraic geometry and improved a known bound in min-max optimization, a technique used to train some AI models. The improvement in min-max optimization has potential application value because it is related to the training techniques of some AI models.
AlphaProof Nexus 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 error messages guide the next attempt. This "draft—check—revise" loop enables the system to gradually approach a correct proof under the constraints of formal verification.
For harder subproblems, AlphaProof Nexus can call on the specialized proof tool AlphaProof. According to Google DeepMind's report, it can solve those nine Erdős problems even without AlphaProof. This claim comes from Google DeepMind itself, is a vendor self-declaration, and has not yet been independently verified.
In contrast to DeepMind's choice of peer review, OpenAI recently released hundreds of AI proofs to GitHub rather than submitting them to journals. This approach bypasses the traditional academic review process and places AI-generated proofs directly in a public code repository.
The Association for Human Mathematics led by Terence Tao has called for a boycott. The specific target and scope of the boycott call are not clear in the source, but this reaction shows that the way AI mathematics results are published has itself become a focus of controversy, not just the correctness of the proofs.
This article is based on THE DECODER's report on the Science study. The core facts (solving dozens of open problems, nine Erdős problems, two unsolved for 56 years, 44 OEIS conjectures, an open algebraic geometry problem, improvement of a min-max bound, being built on Gemini 3.1 Pro, the Lean checking mechanism, being able to call AlphaProof, DeepMind submitting for peer review, OpenAI releasing hundreds of proofs to GitHub, and the boycott call led by Terence Tao) all come from that report and are marked as confirmed. Among them, "it can solve the nine Erdős problems even without AlphaProof" is Google DeepMind's self-report and is marked as source_claim. The source does not specify the exact number of "dozens," the specific outcome of peer review, the precise number of proofs OpenAI released, or the specific target and scope of the boycott call; these uncertainties are presented faithfully in the text.
The results of AlphaProof Nexus show that AI mathematics systems can already autonomously solve open problems, including long-standing open cases, and enter the academic record through formal verification and peer review. But OpenAI's practice of releasing hundreds of proofs directly to GitHub, and the boycott call it triggered, show that the real controversy in AI mathematics is not only about capability, but also about how results should be verified, published, and accepted.
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