# OpenAI's unreleased model claims 372 math result families, and specialists say most remain unverified

Lean formalizations cover the main result of only 162 of the 722 manuscripts, and a group of mathematicians, in a statement Fields medalist Terence Tao posted to his blog, has urged colleagues to stop working with OpenAI.

- Published: 2026-10-10T06:23:46.359Z
- Canonical: https://polylog.news/ai/2026-10-10/openai-s-unreleased-model-claims-372-math-result-families-an
- Publisher: Polylog (AI desk)
- Section: tech
- Sources: [Polylog editors](https://polylog.news)

On October 6, OpenAI published [722 mathematical manuscripts grouped into 372 result families](https://www.unite.ai/openai-releases-722-math-manuscripts-from-an-unreleased-ai-model/). An internal frontier model that the company has not released produced all of them. The public GitHub repository includes Lean formalizations and abridged summaries of the model's reasoning. OpenAI said the model worked on about 4,000 open problems during an internal evaluation period. The showcased families therefore represent less than 10 percent of what it attempted, and the selection criteria for that subset matter as much as the results.

The catalog claims resolutions of problems that would each be a major result if confirmed: the Mahler conjectures, an exact irrationality exponent for π, the Unique Games Conjecture, the free group factor isomorphism problem, and large-data global regularity for the relativistic Vlasov–Maxwell system, [according to Unite.AI's summary of the repository](https://www.unite.ai/openai-releases-722-math-manuscripts-from-an-unreleased-ai-model/). [Fortune](https://fortune.com/2026/10/07/openai-math-controversy-solutions-370-outstanding-challenges-published-criticisms-celebration/) reported that the field responded with both celebration and criticism.

Verification is the gap. Lean formalizations cover the main result of 162 of the 722 papers. The remaining proofs are informal, and so far only OpenAI's researchers and the model itself have read them in full. Other tallies of machine-checked coverage differ. Even a passing Lean check proves only the formal statement, so a reviewer still has to confirm that the formal statement matches the conjecture as mathematicians state it. Dana Moshkovitz, a theoretical computer scientist who has spent her career on the Unique Games Conjecture, said OpenAI's document states plainly that the conjecture is proven. She also said the proof was written so badly that she could not read it without AI help, [The Decoder reported](https://the-decoder.com/some-mathematicians-call-for-openai-boycott-after-ai-generated-proofs-flood-their-field/).

The professional response has been organized. A group calling itself the Association for Human Mathematics (AHM) accused OpenAI of "total disregard" for the norms of scientific research and urged mathematicians to stop working with the company. Tao, a Fields medalist, posted the statement as a guest post on his blog on October 7, [per The Decoder](https://the-decoder.com/some-mathematicians-call-for-openai-boycott-after-ai-generated-proofs-flood-their-field/). Earlier, OpenAI [withdrew its sponsorship of a Caltech "Mathathon"](https://officechai.com/ai/openai-withdraws-sponsorship-of-caltech-mathathon-after-mathematicians-revolt/) after an open letter against the event drew about 500 signatories.

The release also prompted security warnings. [AI Post](https://t.me/aipost/8430) relayed claims that rapid AI progress in mathematics could threaten internet security, and Ethereum researcher Justin Drake issued what [CryptoSlate called a "bunker mode" warning](https://cryptoslate.com/openais-math-breakthrough-raises-fears-ai-could-break-bitcoin-and-ethereum-security-within-months/) for Bitcoin and Ethereum. [The Week](https://theweek.com/tech/mathspocalypse-now-has-ai-made-maths-pointless) described the argument as a "Mathspocalypse." Coverage of the security case agrees that there is no evidence AI models are close to breaking deployed cryptography. The concern is that faster discovery of new algorithms would shorten the time defenders have to migrate.

Verified so far: the volume of output, and a machine-checked subset whose formal statements still need human audit. Asserted but not verified: the correctness of the informal flagship proofs. No outside party can evaluate the process, because the model is unreleased and the attempts that did not make the cut are unpublished.

## What this means

Generating a proof now costs OpenAI less than refereeing that proof costs the field. The constraint on new mathematics has moved from discovery to verification, and the parties exposed are journals, the Lean and Mathlib formalization community, and OpenAI's academic partnerships. OpenAI gets a capability signal that no benchmark can provide. Mathematicians want to keep control over what counts as a result, and their available tool is withdrawing cooperation, which the Caltech episode shows OpenAI will accommodate. There is a precedent. Appel and Haken's 1976 computer-assisted proof of the four color theorem stayed contested for decades until Gonthier and Werner formalized it in Coq in 2005, and the field ended up accepting machine checking as the standard rather than rejecting the result. The likelier outcome is similar but faster: within months, the Lean-covered subset gains acceptance, specialists confirm or break one or two flagship informal claims such as Unique Games, and journals start requiring formalization for AI-generated submissions. That depends on OpenAI expanding Lean coverage beyond 162 papers. The read is wrong if specialist teams find that formal statements in the verified subset do not match the published conjectures. For crypto assets, the near-term price channel is narrative only. No claimed result bears on the hardness assumptions behind deployed signatures, so expect faster talk of migrating to post-quantum cryptography and switchable algorithms, not breakage.

## What to watch

- Whether Unique Games specialists publish a confirmation or a refutation of the claimed proof. Either one sets how much weight the rest of the informal catalog carries.
- Whether OpenAI adds Lean formalizations beyond the current 162 papers. More coverage would move the dispute from trust to checking.
- Whether major mathematics journals adopt explicit policies on AI-generated submissions. Such policies would show the field absorbing the output rather than boycotting it.