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OpenAI Hands ETH, Kakeya, Yang-Mills Proofs to Reviewers

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TL;DR

  • The ETH disproof algorithm solves 3SAT in roughly 2^(n/sqrt(log n)) time — subexponential but not polynomial, leaving P vs. NP intact.
  • The Kakeya claim covers all dimensions, extending Hong Wang and Joshua Zahl's 2025 Fields-Medal result, which proved only the three-dimensional case.
  • Yang-Mills reviewers — Nobel laureate David Gross plus Douglas, Jaffe, Klebanov, and Nekrasov — chose to keep OpenAI's artifacts private and write up the work themselves, separating their names from the AI output.

OpenAI says one of its internal models disproved the Exponential Time Hypothesis on October 16 and formalized that disproof in Lean the next day, according to The Next Web. The company has published both the model's write-up and the formal proof on GitHub, alongside two more claims it is handing to the research community: a proof of Christopher Sogge's 1991 local smoothing conjecture in all dimensions, which would also settle the Kakeya conjecture and Stein's restriction conjecture, and a proof that pure Yang-Mills theory exists in four dimensions, part of a Clay Mathematics Institute Millennium Prize problem.

The verification is where the real work still has to happen.

The computer-science claim has been handed to Russell Impagliazzo and Ramamohan Paturi at UC San Diego and Ryan Williams at MIT. In an open letter the three wrote that "Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny," adding that "If the claim is correct, it will change an important part of theoretical computer science." Williams said the group "signed no non-disclosure agreements and will not be paid."

The physics piece is being handled differently. A group led by Nobel laureate David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, "chose not to release the AI-produced material for now and will write up the work itself." Where OpenAI pushed the ETH disproof straight to GitHub as a Lean file plus a model write-up, the Yang-Mills claim is being filtered through its human authors before anything public lands.

OpenAI says it does not seek academic credit for the three results and "has also given $5m to the Simons Foundation for workshops and conferences on AI-produced results." Mathematicians raised adjacent concerns about AI attribution in the Leiden declaration in June. A handful of the researchers we track on our OpenAI page started circulating the three announcements within hours of publication; whether they still matter three months from now depends on three names in San Diego and Cambridge.

What others are reporting

Coverage cluster as of 2h after publish

  1. OpenAI Read →

    First-party post detailing the timeline, Lean formalization dates, reviewer selection process, and the three-track dissemination strategy across math, CS, and physics.

  2. arXiv Read →

    Independent academic audit by Sienicki and Sienicki using formal verification and human reconstruction; the only systematic third-party check on all three claims published to date.

    No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked.
  3. Runtime Wire Read →

    Focuses on OpenAI's transparency architecture: publishing both the natural-language argument and Lean formalization on GitHub alongside organized independent review, treating verification as part of the announcement.

    A disproof of ETH would affect hundreds of results built on computational-hardness assumptions.
  4. Unite.AI Read →

    Details the shepherd model — OpenAI enlisted domain experts to guide community understanding field by field — and frames AI-generated proofs as raw data requiring human conversion into science.

    AI-generated manuscripts amount to raw research data that must still be converted into scientific understanding.
  5. Hacker News Read →

    Community reaction thread captures practitioner-level surprise at the ETH result and skepticism about verification timelines; top comment with 404 points reflects the field's disbelief.

    ETH is false! I really would not have believed it.

Originally reported by thenextweb.com

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Original headline: OpenAI Says Its Models Disproved the Exponential Time Hypothesis, Produced Yang-Mills and Kakeya Proofs