About 162 of OpenAI's 722 math manuscripts have computer-verified main results according to one count of the release's contents file. The other 560, a little under three quarters, arrive as unreviewed claims. The gap between those two numbers is the real story behind the headlines about AI ending mathematics.
What OpenAI Actually Released on 6 October 2026
OpenAI released 722 mathematical manuscripts across 372 result families on the evening of 6 October 2026, according to the repository the company published with the release. The scale is real, but the unit matters: a result family groups related manuscripts, so 372 families is not the same as 372 independent results, and 722 manuscripts is not the same as 722 proven theorems.
The OpenAI README accompanying the release gives the process numbers. The company says it posed roughly 4,000 problems to the model, and that each result consumed about 3 hours of ChatGPT Pro thinking compute on average. A spokesperson said almost every result came from a single prompt handed to a single AI agent. That is a vendor claim about its own process, and outsiders cannot check it because OpenAI has not named the model or released the prompts.
Press counts differ from the repository. Scientific American reported 372 results, while the repo says 722 manuscripts in 372 families. Using the repo's own wording is the safer path, and treating the two counts as different units rather than as a contradiction.
How Many Manuscripts Have Computer-Verified Results?
Only a minority of the manuscripts carry full formal verification. One count reported after the release says Lean formalizations confirm the main results of about 162 manuscripts, a little under a quarter of the 722. Roughly 560 manuscripts lack a fully Lean-checked main result, though some are partly formalized. Sources count in different units, so these figures are approximate.
OpenAI's own README is direct about the limitation. It states that not all results have accompanying Lean formalizations, and that some of the unformalized results could have issues. That caveat comes from OpenAI, not from a critic. As of 7 October 2026, no independent peer review or replication of the release existed, so nobody could say how many manuscripts are actually correct.
The reading burden is the practical consequence. One manuscript per working day means 722 manuscripts take nearly two years of one mathematician's time. That is an illustrative calculation, not a measured figure, but it shows why verification, not generation, is the slow step.
Does the Quasi-Riemann Paper Prove the Riemann Hypothesis?
No. The biggest headline in the release, the Quasi-Riemann Hypothesis, is much narrower than its name suggests. The Riemann Hypothesis concerns where the zeros of the Riemann zeta function sit. The OpenAI entry covers a related family of functions, Hecke L-functions, over a single number field: the rationals extended by the square root of minus three.
The entry claims these Hecke L-functions have no zeros where the real part of s is above 7/8. The full Riemann Hypothesis would push that boundary from 7/8 down to 1/2, and would apply to the zeta function itself, which this claim does not cover. So a headline saying OpenAI proved the Riemann Hypothesis is wrong, and the entry's Lean-checked mark in OpenAI's contents file still awaits independent confirmation.
Which Headline Results Carry a Lean Check?
Four headline entries carry a Lean-checked mark in OpenAI's contents Firebase on what the file itself reports. Lean is a proof checker that accepts or rejects every logical step of a proof written in a formal language, so a Lean pass does not depend on trusting the author. The four marked entries, per OpenAI's file and secondary reporting, are:
Headline Results and Their Verification Status
The table below compares the four Lean-marked headline entries against major entries listed without a formal check, using OpenAI's contents file as the source of each status.
| Result | Status in OpenAI's file | What it actually claims |
|---|---|---|
| Catalan's constant is irrational | Lean checked | No fraction of two whole numbers equals the constant |
| Quasi-Riemann Hypothesis | Lean checked | Zero-free line at Re(s) > 7/8 for Hecke L-functions over Q(√-3), not the zeta function |
| Two-point Chowla result | Lean checked | A restricted case of the Chowla conjecture |
| Zariski cancellation in dimension 4 | Lean checked | A counterexample, disproving the property in dimension four |
| Hilbert's 10th problem over the rationals | Not Lean checked | Undecidability claim, pending human verification |
| Birch and Swinnerton-Dyer formula entry | Not Lean checked | Claim about the BSD conjecture, pending human verification |
Sources disagree on a few entries, and one report lists a claim about how well pi can be approximated by fractions as not yet formalized. The only reliable move is to read the contents file yourself and check the exact statement typed into the checker, not the headline attached to it.
What a Lean Pass Does and Does Not Prove
A Lean pass answers only the first of three questions. Lean, the proof checker maintained by the Lean project, verifies that each step follows from the ones before it. If step 112 of a 200-step proof does not follow, Lean rejects the proof, something a tired human reviewer could miss.
But Lean checks only the statement someone typed into it. A model can target a famous open problem while the formal statement proves a weaker version, and the checker will happily pass a true proof of a different question. Reviewers of the release warned that a formally verified theorem might claim something weaker than the actual open problem. Matching the formal statement to the open problem requires a human.
The third question is understanding. Terence Tao warned of proof indigestion at Caltech on 11 September 2026: Lean can pass a proof that no human has read. Yet Tao still backs formal verification. In January 2025 he wrote that in mathematics outputs can be completely checked, which filters out much of the rubbish. The filter checks correctness, never comprehension, so every passing proof still goes to a person.
Why Mathematicians Are Angry About Credit and Secrecy
The conflict in the mathematical community is about how the work arrived, not about any single proof. Quanta Magazine reported on 5 October 2026, the day before the release, that OpenAI was keeping more than 100 results secret, and that mathematicians were preprinting early to avoid being scooped by AI. A preprint timestamps a claim, so publication order matters when a model can produce results faster than a human.
Process transparency is the sharpest complaint. Andrew Sutherland of MIT said that until the model is released and results can be replicated, claims about one-shotting problems with a single agent should be treated as unverified. An independent advisory group on mathematics and AI formed in September 2026, hosted at the Institute for Advanced Study, with members including Gowers, Hörer, and Witten. It recommended that OpenAI disclose model names, prompts, and compute, and deposit the papers in academic repositories. The release included average compute time and 10 reasoning summaries, but no model name and no prompts, skipping at least two of the group's recommendations.
Credit is a second fight. One secondary report says mathematicians credited two humans, Diego Córdoba and Luis Martínez Zoroa, with the key insight in OpenAI's earlier Navier-Stokes claim; it is a single source and remains unconfirmed. Tao said the pace is insane and there is no reason to be this fast. Quanta also reported declining Math Overflow activity and arXiv limiting submissions, with one researcher saying the pace breaks a system built for human-speed papers. Both excitement and fear fit the evidence: some results carry Lean checks in OpenAI's file, and the rest rest on OpenAI's word alone.
Turning a Video Breakdown Into a Written Piece Worth Checking
The lesson of this release is that output is cheap and verification is expensive, and the same holds for content. A 12-minute video breakdown, like the one this article is based on, contains a careful argument about reading the primary source before repeating a headline. If you have that kind of explanation, interview, or lesson sitting inside a YouTube video, Skala Blog turns it into a written article: paste the URL, the video is transcribed, and you get a draft you can check line by line, the same way a Lean pass still ends at a human reader.
This draft follows the video's core discipline: every number traces back to the repository's own counts or is labeled as secondary reporting. That standard is what makes written content retrievable and trustworthy.
More writing from Dev doido and the Crazystack TypeScript team lives at crazystack.com.br.
Frequently Asked Questions
- Did OpenAI prove the Riemann Hypothesis? No. The Quasi-Riemann entry establishes a zero-free line for Hecke L-functions over Q(√-3) where the real part of s exceeds 7/8. The Riemann Hypothesis concerns the zeta function's zeros on the 1/2 line, which this entry does not address.
- How many of the 722 math manuscripts are verified? One count says Lean formalizations confirm the main results of about 162 manuscripts, roughly a quarter. OpenAI's own README says not all results have Lean formalizations and that some unformalized results could have issues.
- Can anyone reproduce OpenAI's math results? Not yet. OpenAI has not named the model or released the prompts. Andrew Sutherland of MIT said replication claims should be treated as unverified until the model is available.
- Why are mathematicians posting preprints earlier? Quanta reported on 5 October 2026 that researchers preprint early to timestamp claims before an AI system publishes the same result first. If a company can hold more than 100 results privately, a mathematician cannot know whether a problem is already solved.
- Is classical mathematics dead after this release? No. The evidence shows a minority of verified results, no independent review as of 7 October 2026, and human mathematicians still deciding what counts as proved. What is failing is the assumption that humans can read everything machines produce.
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