OpenAI's 722 AI Math Proofs: Only 162 Checked in Lean
We matched OpenAI's 722 published math manuscripts against its own Lean formalization catalogue. Only 162 main results are machine-checked, and none of the 143 manuscripts dated in October.
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On October 6, 2026, OpenAI published a broad release of new mathematical results produced by an unreleased internal frontier model, and dropped the whole corpus into a public GitHub repository under an Apache-2.0 licence. Sam Altman framed it on X the next morning in seven words: "We are entering a new era of discovery now." By the time we read the repository on October 7 it had collected 2,735 stars and 232 forks.
The headline number everyone repeated was 722 manuscripts across 372 result families. That number measures output. It does not measure verification, and verification is the only thing that distinguishes a theorem from a very confident paragraph.
So we counted the verification.
What we counted, and how
The repository ships two files that can be reconciled against each other. CONTENTS.md is the manuscript map: every paper in the collection appears there as a link to its own folder under preprints/. lean/formalization.yaml is the formalization catalogue, described in the repository as the "catalog of papers with a formalized main result", with each entry pointing back at the PDF it certifies.
Extracting every preprints/…/*.pdf link from CONTENTS.md yields 722 unique manuscript folders, matching the stated count exactly. Extracting every id: path from formalization.yaml yields 162 unique manuscript folders. All 162 resolve to folders that exist in the manuscript map, so there are no orphans on either side.
Of the 722 manuscripts OpenAI published, 162 — 22.4% — carry a Lean formalization of their main result. The other 560 are mathematics written by a model and checked by nobody a reader can name.
That is not a hidden fact. The repository README says plainly that "Many, but not all, of the manuscripts have been formalized" and warns that "Some of the unformalized results could have issues." What the README does not do is attach a number to "many", and the number turns out to carry the story.
The October cliff
Each manuscript folder encodes a date in its name — 721 of the 722 do, in the form …-September-23-2026. Grouping the collection by that date, and overlaying which of those manuscripts appear in the formalization catalogue, produces the pattern below.
Manuscripts by folder date, split by whether the formalization catalogue lists their main result. Source: openai/math, read October 7, 2026.
| Date cohort | Manuscripts | With Lean formalization | Share |
|---|---|---|---|
| Sep 10 – Sep 18 | 4 | 0 | 0% |
| Sep 22 – Sep 27 | 567 | 159 | 28.0% |
| Sep 30 – Oct 2 | 7 | 3 | 43% |
| Oct 3 – Oct 6 | 143 | 0 | 0% |
| All dated manuscripts | 721 | 162 | 22.5% |
The late-September burst is the verified part of the collection. Five days, September 23 to 27, account for 567 manuscripts — 79% of everything released — and 159 of the 162 formalizations. Coverage inside that burst runs from 36% on September 23 down to 19% on September 26.
Then there is a second burst. The 143 manuscripts dated October 3 to 6, including 112 on October 5 alone, arrived in the final seventy-two hours before publication. Not one of them appears in the formalization catalogue.
The innocent reading is that formalization lags writing, which is exactly what the README promises to fix: OpenAI says it "will continue to update this repository with Lean formalizations as we obtain them." The uncomfortable reading is that one fifth of the collection was added after the verification pipeline had already finished its pass, and shipped anyway on the publication date. Both readings are consistent with the data. Only the second is consistent with the release being timed.
Either way, a reader who treats the 722 as a single body of work is averaging a 28%-verified corpus together with a 0%-verified one.
A fourth number that does not match
There is a smaller discrepancy worth flagging because it will propagate. Gizmodo's write-up, headlined around 377 new math results, takes that figure from The New York Times. The repository as published catalogues 372 families. Five results separate the reported count from the shipped one, and since OpenAI has committed to "protocols for paper revisions" with a preserved release history, the gap may simply be the difference between a pre-publication briefing and the final tree. Anyone citing a count should say which file and which date they read it from. We read 372 families and 722 manuscripts on October 7, 2026.
Why the ratio is the number that matters
Lean is the point of the exercise. A formalization is a proof rewritten so a computer can check every inference against a fixed kernel, and when it compiles, the result is true in a way that does not depend on trusting the author, the referee, or the model. For a corpus this size, produced faster than any referee pool on earth can read it, machine-checking is not a nice supplement to peer review. It is the only review that can run at the speed of production.
Which is why the 22.4% is the honest headline. The formalized portion is a genuine contribution: 162 machine-checked results, with build configurations and a comparator harness, is a larger single release of verified new mathematics than any lab has shipped before. The unformalized 560 are a to-do list addressed to the mathematical community, written in a form that is expensive to read and expensive to check, and arriving in a week when that community had already said it did not want to receive work this way.
The release is best read as a corpus of claims, not a corpus of theorems; machine-checked status, not manuscript count, is the number that should move a mathematician.
What a formalization does and does not certify
It is worth being exact about what the 162 buys, because the number is easy to over-read in the other direction too.
A Lean formalization certifies that the proof of a stated theorem is valid — every inference checked mechanically against a small trusted kernel. It does not certify that the stated theorem is the theorem the prose paper claims. The translation from a natural-language statement into a formal one is itself human-or-model work, and a formalization of a subtly weakened hypothesis compiles exactly as cleanly as a formalization of the real thing. This is the standard failure mode in formalized mathematics and it predates AI by decades: the kernel is trustworthy, the statement is where the risk lives.
OpenAI has at least made that checkable. The repository ships build configurations and a comparator harness alongside the formal proofs, which means a reader who doubts a given entry can run it rather than argue about it. For the 560 manuscripts with no formalization, there is no equivalent move available — the only way to check them is to read them.
Two results also sit outside the standard pipeline, and the README says so. The writeup covering a zero-free region for the Riemann zeta function was human-edited for readability, and the proof of the Hodge Conjecture for CM abelian varieties departed from the fixed procedure used for everything else. Neither is a defect. Both are the kind of disclosure that makes the rest of the corpus easier to trust, and both are reminders that "produced by a model" describes a spectrum rather than a binary.
The community had already drawn the line
On September 11, twenty-five Fields Medalists — among them Terence Tao, Peter Scholze, Maryna Viazovska, Pierre Deligne and Manjul Bhargava — signed a declaration titled "A Severe Misalignment of AI in Mathematics", which has since gathered thousands of co-signatures. Their argument was not that the proofs were wrong. It was that solving is a proxy for understanding, and that optimising the proxy inverts the goal while creating attribution problems nobody has a protocol for.
The Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study followed on September 29 with public recommendations drawn from more than 600 replies, and asked frontier labs, in terms, to stop testing advanced mathematical problems on proprietary models that the rest of the field cannot access.
OpenAI's post says it drew on that advice. It also says the results came from an internal model it is still "working to responsibly release". Both sentences are in the same announcement.
The bottleneck has moved to explanation
The practical consequence of all this is that 722 PDFs of frontier mathematics now exist and almost nobody can read them at the rate they appeared. OpenAI's own remedy is social rather than technical: it says it will fund workshops, conferences and special programmes to build understanding around the major results, and it shipped ten abridged reasoning summaries as a first gesture in that direction.
That is the same shape of problem every research group now has in miniature. A result lands, and the expensive part is no longer producing it but turning it into something a seminar room, a funder, or a collaborator in another subfield can follow. It is why a slide deck is quietly becoming part of the proof's distribution layer, and why an AI presentation maker like ChatSlide, which turns a paper or a set of findings into a talk, is showing up in research workflows rather than only in sales teams. None of them verify anything. They address the other half of the gap the Fields Medalists named: a result nobody can explain is, for the field's purposes, a result nobody has.
The verification half still belongs to Lean. On the evidence of this release, it currently covers a little over a fifth of what OpenAI has published.
Figures in this article were derived by the author from the public openai/math repository on October 7, 2026, and can be reproduced by matching the preprints/ paths in CONTENTS.md against the id: fields in lean/formalization.yaml.
Disclosure: ChatSlide is operated by a company that also publishes Stanford Tech Review.