722 manuscripts in 372 result families from an unreleased OpenAI model
OpenAI published 722 manuscripts grouped into 372 claimed results across number theory, algebraic geometry, analysis, combinatorics, theoretical computer science and mathematical physics, all produced by an unreleased internal model, with Lean formalizations attached to 235 of the families and none yet checked by anyone outside the company.
- Lab
- OpenAI
- Model
- Unreleased internal OpenAI model, not named in the release
- Field
- Mathematics
- Date
- 2026-10-06
Sources
Original work
Announcement
Media coverage
Independent commentary
What was found
The repository's README says the model was posed about 4,000 open problems during an evaluation, that each result used on average three hours of ChatGPT Pro thinking compute, and that the output was aggregated into families and filtered for significance; a family groups a principal result with companions, consequences or alternative proofs. The families claimed include the full Birch-Swinnerton-Dyer formula in Selmer corank at most one, the quasi-Riemann hypothesis, a negative answer to Hilbert's tenth problem over the rationals, the Unique Games Conjecture, , matrix multiplication with exponent at most , Kakeya in three and four dimensions, nonamenability of Thompson's group F, isomorphism of the free group factors and Kadison's similarity conjecture, alongside dozens of counterexamples to named conjectures. Lean 4 formalizations are linked from 235 families; the formalization catalogue lists 162 papers whose main result is formalized and Comparator challenge files for checking the statements against permitted axioms. Ten families also come with abridged summaries of the model's reasoning. The README names two exceptions to the fixed procedure, the work on a zero-free region for the Riemann zeta function and the Hodge conjecture for CM abelian varieties, and says the write-up of the zero-free region was edited by humans for readability.
Novelty check
Read the README, the manuscript map CONTENTS.md and the Lean catalogue lean/formalization.yaml at commit adc7f1241b42e322a6451854ab7e4b4c146bf78a on 2026-10-07. Novelty was not checked family by family, which at this scale is beyond one entry; the families split out as their own entries carry their own checks, starting with the quasi-Riemann hypothesis and Kakeya. A Hacker News commenter cross-referenced the list against ProofAtlas's ranking of 500 open problems and counted about 90 claimed full resolutions, among them Hilbert's tenth problem over the rationals, Unique Games, Landau-Siegel zeros, Baum-Connes and Hadwiger's conjecture; that count was not reproduced here. OpenAI said on 2026-09-21, when the Advisory Group on Mathematics and AI was announced, that an internal model had resolved more than 100 open problems; the registry carries no entry for that statement, which came without manuscripts.
Caveats and known objections
Graded claimed throughout, because nothing in the release has been read by a mathematician outside OpenAI on the record, and the Lean catalogue records its own review status as unchecked, the same self-assessment that kept the Navier-Stokes entry at claimed. The README says plainly that some of the unformalized results could have issues. Where Lean exists it covers the main result of a paper rather than every claim in it, and the Comparator statements were written by OpenAI alongside the proofs, so whether each one says what the literature means by the named conjecture is a separate question for each family. A text search of the Lean library found no sorry and no axiom declarations, which is not a build and not a statement audit. The account of provenance is not checkable: the model is unreleased, a spokesperson told Scientific American that almost every result came from a single prompt to a single agent and then that some may have taken multiple attempts, and Andrew Sutherland told the magazine that one-shot claims should be treated as unverified until the model is released and the results replicated. The Advisory Group on Mathematics and AI, hosted at the Institute for Advanced Study, recommended on 2026-09-29 that labs publish the model name, prompts, a summarized chain of thought, the time taken and the estimated compute cost, and asked labs to stop testing advanced problems on proprietary models; the release gives average compute and ten reasoning summaries, not per-result prompts or costs, and Scientific American reports OpenAI saying it is not bound by the recommendations. Terence Tao has criticized the pace of releases of this kind, while Daniel Litt argued in the same article that withholding results would harm mathematics. Autonomy is graded ai-led rather than autonomous because humans chose the 4,000 problems, aggregated the output and applied the significance filter, and because the README names exceptions to the fixed procedure without describing them. This entry is a container for the release; individual families will diverge from its grades as checks land.
Nobody outside the lab has checked this yet.
Reading the primary source closely enough to say whether it supports the claim counts as a check, and you are credited on the entry.
Or on GitHub: submit a check challenge the grade send a correction or send a pull request
Flag this for triage
Signals order the review queue and nothing else. They are never published, and they never move a grade: that takes a citation.
Entry history (1 event)
- AddedEntered the registry graded Claimed and AI-led.
Entries are never deleted. A grade that does not hold up is downgraded on the record, with the reason beside it.
Community discussion
Graded claimed for verification and ai-led for autonomy. What these mean.
Cite this entry
whataifound.org. (2026). 722 manuscripts in 372 result families from an unreleased OpenAI model. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-10-06-openai-math-collectionBibTeX
@misc{whataifound-openai-2026-collection,
title = {722 manuscripts in 372 result families from an unreleased OpenAI model},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by OpenAI. Verification: Claimed. Autonomy: AI-led.},
url = {https://whataifound.org/finding/2026-10-06-openai-math-collection}
}