What the AlphaProof Nexus count actually includes

What happened

A Science summary released through EurekAlert on October 8, 2026 describes AlphaProof Nexus, by Tsoukalas and colleagues, as a system of multiple agents that uses feedback from the Lean compiler. The summary says it solved 9 of 353 Erdős problems it attempted, two of them unsolved for more than 50 years, and 44 of 492 open OEIS conjectures, plus problems in algebraic geometry, optimization, quantum optics, and graph theory. The denominators are the finding. A headline that says dozens, without them, is a different sentence. The page filing the summary is Futureweb.

What the repository adds

The DeepMind results repository says it contains mechanically formalized Lean proofs for the successful problems only, and that the repository is not an official Google product. The license line is Apache-2.0. There is no downloadable product API in that README. A reader who wants the proofs can read the files. A reader who wants a service cannot order one from the page. The desk is Artificial Intelligence.

What the commentary is

The summary names Tsoukalas and colleagues and describes multiple agents using Lean compiler feedback. Two of the nine Erdős problems had been unsolved for more than 50 years, which is the summary's historical clause, not a ranking of difficulty this page computed. The other fields it names are algebraic geometry, optimization, quantum optics, and graph theory. The repository's Apache-2.0 line is the license on the successful proofs, not a product grant. A failed attempt is absent from that tree because the README limits the files to successes, and the summary is where the attempt counts live. SMC Spain can repeat 9 of 353 without becoming the paper. A headline that says dozens has dropped 353 and 492, which are the numbers that make the result checkable. There is no public API in the README this page is using. A second lab can rerun a Lean file in the repository. It cannot rerun a headline that dropped the denominators. The summary remains the count, and the disclaimer remains on the README. SMC Spain's note is a commentary on the Science publication. It repeats the 9-of-353 figure. It is not the paper, and a judgment it offers about the method is the commentator's, not a sentence this page will move into the summary. On-device inference, a different bound, is what on-device inference keeps.

Why it matters on this desk

The dependency is a peer-reviewed count with a denominator, plus a repository that formalizes only the successes and disclaims product status. That is a narrower claim than a model that solved open mathematics. The 9 and the 44 are successes. The 353 and the 492 are the attempts the summary names. Dropping the second number changes the result. A training cutoff, a different limit, is what a training cutoff does not mean.

What this page will not import

A social-media thread by a researcher is context, not a source this brief needs. An outlet sentence that says dozens, without 353 or 492, does not replace the summary. This page also does not describe the agent loop, the prompts, or how Lean was called. The impact is the count and the formalized proofs of the successes. The software desk, for a version rather than a proof, is Software.

Where the accounts overlap

The Science summary and the Spanish commentary agree on the publication and on 9 of 353. The repository agrees that the successful proofs are formalized in Lean and adds that the tree is not an official product. They do not, in the texts used here, agree on a public API, because none offers one. The overlap is the count. The extra sentence is the disclaimer.

What to watch next

A correction to the 9 or the 44, or a repository that adds the failed attempts, would change the record. A product announcement with an API would be a new document, not this one. Another headline that says dozens would not. The October 8 summary is the count. The repository is the file of successes and the disclaimer.

What would change the record

If Science issues a correction, the fractions move. If the repository drops the not-a-product line, the disclaimer sentence has to go. If a later paper reports a larger solved set, that paper is a new brief. The Lean files for the successes can stay as they are while any of those happens. This page will not treat a missing failure file as evidence the attempt did not occur. The summary already counted the attempts.

What stays a fraction

What stays specific is an October 8, 2026 Science summary of AlphaProof Nexus: 9 of 353 Erdős problems attempted, two of them open more than 50 years, and 44 of 492 open OEIS conjectures, with further problems in four named fields. The results repository holds Lean proofs of the successes, says it is not an official Google product, and is under Apache-2.0. The commentary is a second account of the publication, not a substitute for the summary. A reader who remembers only dozens has dropped the number that makes the result checkable. The checkable numbers are 9, 353, 44, and 492. They are the brief.