Deepmind’s AlphaProof Nexus Solves Decades-Old Math Problems Via Peer Review

Google Deepmind’s AI system solved nine Erdős problems and dozens of other conjectures, with results published in Science after formal peer review.

Threat Times Systems DeskOctober 13, 20262 min read

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Illustration: A sleek white tablet rests on a clean wooden desk beside a scattered stack of yellow legal pads covered in dense mathematical formulas. — AI-generated illustration: Threat Times

Key points

AlphaProof Nexus solved nine Erdős problems, two unsolved for 56 years, according to a study in Science.
The system proved 44 OEIS conjectures and improved bounds in min-max optimization techniques.
Deepmind submitted work for peer review, contrasting with OpenAI’s unreviewed GitHub releases that sparked a boycott.

Google Deepmind announced that its AlphaProof Nexus AI system solved dozens of open mathematical problems, including nine Erdős problems, according to a new study published in Science. The research team shared these solutions online prior to the formal publication of the paper, marking a significant milestone in automated theorem proving capabilities.

The system successfully cracked nine of 353 open Erdős problems, two of which had remained unsolved for 56 years, as reported by The Decoder. Beyond these specific challenges, AlphaProof Nexus proved 44 conjectures from the OEIS integer sequence database and solved an open question in algebraic geometry. It also improved a known bound in min-max optimization, a technique frequently used to train certain AI models.

Technical Approach and Verification

AlphaProof Nexus relies on Gemini 3.1 Pro to draft and revise proofs using the formal language Lean, according to Google Deepmind. Lean checks each draft after every edit, providing error messages that guide the system’s next attempt. For more difficult sub-problems, the system can call upon AlphaProof, a specialized proof tool. Google Deepmind reports that the system solved the nine Erdős problems even without utilizing AlphaProof.

The publication of this study arrives amid a heated debate regarding AI-generated mathematics, per The Decoder. OpenAI recently released hundreds of AI proofs on GitHub without submitting them to academic journals. This action prompted the Association for Human Mathematics, led by Terence Tao, to call for a boycott of unreviewed AI mathematical outputs.

Peer Review Standards

Unlike the OpenAI approach, Google Deepmind submitted its AlphaProof Nexus results for formal peer review before publishing, according to The Decoder. This distinction highlights a growing divide in how researchers handle AI-generated scientific and mathematical discoveries. The peer-review process ensures that the proofs meet established academic standards for validity and rigor, addressing concerns about the reliability of automated theorem proving.

What should you do?

Researchers and mathematicians should verify AI-generated proofs through independent peer review before citing them in academic work. Institutions should establish clear guidelines for the publication of AI-assisted mathematical discoveries to maintain academic integrity. Technical teams should monitor developments in automated theorem proving tools for potential impacts on software verification and security protocols.

What to do and how to stay safe

Verify any AI-generated mathematical proofs through independent peer review before using them in research or development.
Establish institutional guidelines for the publication and validation of AI-assisted scientific and mathematical discoveries.
Monitor advancements in automated theorem proving tools for implications on software verification and security practices.
Encourage collaboration between AI developers and mathematicians to ensure rigorous validation of automated results.

General security guidance from the Threat Times newsroom. It is not confirmed advice from the organisations named in this story.