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Understand

True or hype?

4 claims about AI, each with its verdict.

These texts are written by an AI and have not been reviewed yet.

AI has solved hundreds of open math problems.

Verdict : Not demonstrated

OpenAI released 722 manuscripts on 6 October 2026, but its own repository describes results at different stages of verification, and no named third party has evaluated the whole set. Three manuscripts were withdrawn by 7 October.

On 6 October 2026, OpenAI published the openai/math repository: 722 manuscripts at launch (719 in the registry's current count), grouped into 372 problem families. They come from an unreleased internal model. The README mentions about 4,000 problems posed and about 3 hours of ChatGPT Pro per result.

The repository itself describes a mixed picture. Its README says the release “includes results at different stages of verification” and that “Some of the unformalized results could have issues.” Only part of the results comes with Lean supplied by OpenAI, and the registry notes that the formalization file itself carries the entry “review: status: unchecked”.

The registry lists the release as “under review”: no named third party has evaluated the whole set. Of the 373 attached entries, 371 are unevaluated, one is contested (family 244) and one groups the three withdrawn manuscripts. The counts of confirmed results do not line up: about 42% (300 of 719) according to history.md, 162 of 722 according to Nature as relayed by a third-party site, and “roughly 50% of the results were released unconfirmed” according to an OpenAI spokesperson quoted by Retraction Watch. The Washington Post headline refers to “more than 300 math research problems” (headline seen in a search result only).

On 7 October 2026, three manuscripts were withdrawn. The registry lists them: “Algebraicity of Weil classes on split abelian eightfolds”, “Kuga-Satake K3” and “rational Hodge conjecture for products of K3”. For this withdrawal, OpenAI's change log (history.md) gives the reason: “a sign error invalidates a stabilization-trace cancellation argument”. It also records 14 revised manuscripts, 13 updated for citations and 6 formalizations added. Retraction Watch (8 October) reports the sentence “continue to update the repo with new formalizations and with any errata we notice”.

Public reactions run from 6 to 10 October. The Association for Human Mathematics states: “Releasing over 700 files at once is not a demonstration of scholarship”. Nature's headline reads “mathematicians are up in arms” (article of 7 October, updated on the 9th). Scott Aaronson writes: “no human has understood just about any of these proofs yet”. Terence Tao's blog feed contains the phrase “excessive emphasis on automated solving of open problems by AI”. The site Proofs and Prompts gathered more than 100 reactions on 8 October. Also on 8 October, Asaf Karagila wrote about family 244: “it should be issued a desk rejection for the quality”. The registry specifies that this objection concerns the writing and the method, without showing the statement to be false, and that the author does not read the Lean.

Verdict. OpenAI did publish a very large number of manuscripts. That they solve hundreds of open problems is not demonstrated: the repository speaks of varying stages of verification, three manuscripts are already withdrawn and no named third party has evaluated the whole set. “Not demonstrated” does not mean “false”: public examination is ongoing.

In the registry

Sources

A proof in Lean is a verified proof.

Verdict : Partly true

A successful Lean check is a real mechanical verification. DiscoverIA, however, uses “formally verified” only when a named third party has replayed the proof, and the fidelity of the formal statement is judged separately.

Lean is a language in which a proof is checked by a program, the Lean kernel. If the check succeeds, the formal proof does follow from the formal statement. That is a mechanical guarantee. Two questions remain open: who ran the check, and does the formal statement say the same thing as the announced result?

On the first question, DiscoverIA applies a rule: Lean supplied by the claimant is not enough. The status “formally verified” requires a named third party, and a platform's verifier counts as a tool and not as a third party. Example: for openai/math, part of the manuscripts comes with Lean supplied by OpenAI, and the release remains “under review”, with no named third party for the whole set.

The Gauss case shows the rule applied. The Lean project team and Math, Inc. (the Gauss system) completed the formal verification of sphere packing in dimension 8 in February 2026 (arXiv, 25 April 2026). The project's human authors are co-claimants, hence never third parties: on 12 October 2026 the status was first lowered to “not evaluated”. It was then raised back to “formally verified” on the strength of a named third party, a contributor: a public CI run of 11 October 2026 (run 38101133826, conclusion success, 828 of 828 modules checked), on a byte-for-byte copy of the Math, Inc. repository. Reproduction level N2, one external replay. The registry keeps two reservations: the replayer is an individual whose change was merged by that same person, and the replay was AI-assisted.

On the second question, DiscoverIA judges the fidelity of the statement separately from the status. For Gauss, that judgment has not been made: level “not judged” as of 12 October 2026. A gap remains possible. For Navier-Stokes, OpenAI announced a finite-time blow-up on 8 September 2026, with a Lean formalization supplied by OpenAI. An arXiv paper of 6 October 2026 (Bastounis, Circelli, Hansen) writes that “the formalised Lean proof does not correspond to the NL proof”. The registry lists the entry as “contested”: the objection concerns the match between the Lean and the text, and priority, with no refutation on the substance in the sources read. A post by Asaf Karagila dated 10 October 2026 is titled “Why I don't trust Lean code from AI” (page not read in detail by the registry).

Verdict. A proof accepted by the Lean kernel is verified by machine, and that point is true. It counts as “formally verified” in DiscoverIA's sense when a named third party has replayed the check. Even then, what it establishes depends on the fidelity of the formal statement, which has not been judged for Gauss. In the other cases, the machine check exists, but the status is not established.

In the registry

Sources

AI discovered a theorem (when the case is a formalization or a literature search).

Verdict : False

In the cases listed here, the sources describe the machine verification of an already known result, or the rediscovery of solutions already published. None is a new theorem.

The registry distinguishes several natures of result. A “formalization” is the machine verification of a known result. A “literature search” finds solutions that were already published. A “new result” is something else, and DiscoverIA never presents a formalization as a discovery. This article covers cases where the word “discovered” does not match the sources, and says nothing about genuinely new results.

Fermat-Wiles. On 4 September 2026, Anthropic announced a complete Lean proof written by Claude (11 days, 13 M lines, per the registry title). Its page speaks of “the first complete computer-checked proof of Fermat’s Last Theorem”. The theorem is known: the registry notes that this is a verification of existing mathematics and not a new result. The status is “formally verified”, with the Lean kernel and a comparator as tools, and Kevin Buzzard cited as a third party by the Anthropic page, not rechecked elsewhere.

Sphere packing in dimension 8. The proof has existed since Viazovska (2016). The February 2026 work, whose final steps come from Math, Inc.'s Gauss system, is a formalization in Lean: the registry notes that it is a formalization and not a new result.

Erdős no. 339. In October 2025 (12 October on Bubeck's side, 18 October on Weil's), members of OpenAI announced that GPT-5 had solved 10 Erdős problems. The solutions turned out to be already in the literature: GPT-5 had found existing references. The announcement was deleted. Thomas Bloom (erdosproblems.com), cited by The Decoder on 18 October 2025, calls it “a dramatic misinterpretation”. Status: withdrawn. Finding references is useful work, but it does not produce a new theorem.

Erdős no. 333. On 25 December 2025, two authors of a public message claimed the first “autonomous” resolution by a language model. According to Quanta Magazine (article of 3 August 2026, date read from the URL), the problem had been solved by Erdős in 1977. The claim was abandoned by its author after an earlier solution was found. Status: withdrawn.

Verdict. In these cases, the right words are “verified by machine” or “found in the literature”. “Discovered a theorem” is false for each of them. The verdict does not apply to every AI result: a new result is judged on its own sources.

In the registry

Sources

The records set by AI are verified.

Verdict : Partly true

Each EinsteinArena record goes through the platform's public verifier, which DiscoverIA classes as a tool. The registry's 16 records remain “not evaluated” for lack of a named third party, and 4 of them were replayed in exact computation by DiscoverIA.

EinsteinArena is an AI-agent platform from Together AI and Stanford, launched on 19 March 2026. The blog post of 13 April 2026 says: “have already discovered the new best solutions to 11 open math problems”. The registry keeps 16 records: 13 from the paper and the blog, and 3 found later on the online leaderboard. The counts differ across pages of the paper (11 or 12), and the registry does not invent another.

Each solution is checked by a public verifier of the platform, a Python program run in a sandbox. DiscoverIA classes it as a tool and not as a third party. The 16 records are therefore “not evaluated”: no named third party. For dimension 11, a notebook in the new-records repository checks in integer arithmetic, but that check comes from the repository team, so from the claimants' side.

Example: the kissing number in dimension 11, 604 spheres against a previous bound of 593 (AlphaEvolve, May 2025). The paper states that 604 resulted from a series of submissions, public discussions and revisions of the verifier. The registry notes that the public verifier may have been revised after the record.

Three records postdate the paper: the Kakeya needle at n = 128 (6 October 2026), the two-deletion correcting code of length 16 (219 words on 5 October 2026, against a cited public record of 215) and ring loading with 15 pairs (12 September 2026). The platform marks their statements and verifiers “Under active review”, and no primary source mentions them. The registry says they must be confirmed against the literature before speaking of a record.

DiscoverIA replayed four of these calculations: the kissing number in dimension 11, the Kakeya needle at n = 128, the two-deletion code of length 16 and ring loading with 15 pairs. Each carries the verdict “reproduced” dated 12 October 2026, with a report and a certificate, in exact arithmetic. These replays are private, at level N1, and the registry specifies that they change neither the public status nor the list of verifiers.

Verdict. The configurations do pass an automatic validity check, and four were replayed in exact computation by DiscoverIA. The word “verified” is therefore partly true. No named third party has evaluated them, and for the three recent records, the record status itself remains to be confirmed.

In the registry

Sources