ResearchPapers, evidence & method
OpenAI says internal model disproved the Exponential Time Hypothesis, proved local smoothing and built 4D quantum field theories
OpenAI says an unnamed internal model refuted the 27-year-old Exponential Time Hypothesis, proved the local smoothing conjecture in all dimensions, and established 4D quantum field theories including QCD. It released Lean proofs for the math results while outside experts review them.
From the The Verge · AI article of October 26, 2026 and cited sources: The claimed ETH refutation is a deterministic algorithm. [1] [6] [7]
SOURCES[1] OpenAI announces three big science discoveries and a new… theverge.com[6] ForkLog — OpenAI says its AI refuted ETH forklog.com[7] The Next Web — OpenAI says its AI model has disproved ETH thenextweb.com
AT Pulse research deskPublished · Updated · 5 min read · AI-assisted analysisAI-assisted, not human-edited. Methodology Corrections Who owns this site
- Original source
- The Verge · AI article, independent perspective
- Brief by
- AT Pulse research desk AI-assisted; publisher and contact on the desk page
- Studies
- arXiv 2608.02859 (Aug 2026) [14] date from arXiv ID
- When
- October 26, 2026 article published
- Covered
- Oct 27 edition
- Evidence
- 14 sources across 14 sites
- 1OpenAI announces three big science discoveries and a new…theverge.com
- 2Working with academic communities to build scientific…openai.com
- 3OpenAI says its AI refuted the Exponential Time Hypothesisfourweekmba.com
- 4OpenAI models' claimed ETH disproof and Kakeya-related and…datastudios.org
- 5Engadget — OpenAI announces new discoveriesengadget.com
- 6ForkLog — OpenAI says its AI refuted ETHforklog.com
Reach: not measured yet
The claimed ETH refutation is a deterministic algorithm. It exactly counts the satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and the 3-SAT case refutes ETH. OpenAI says the proof was checked in Lean. Coverage notes that the speedup over exponential time is small, runtimes may still be enormous, and the result would not imply P = NP. [1] [6] [7]
OpenAI also claims to have proved the local smoothing conjecture in every dimension, which would settle the Kakeya and Stein restriction conjectures. The model's raw output and a Lean proof are on GitHub without expert explanation. The GitHub summary covers restriction estimates only in the interior of the conjectured range, which is narrower than a full resolution. [1] [11]
A third claim, a rigorous existence proof for 4D gauge theories including QCD, has not been released. A review group led by David Gross is assessing it, and sources disagree on its timeline. OpenAI says it will not seek academic credit for any of the results. [5] [6] [11]
OpenAI chose a review process in which selected experts see results first. Its own AGMAI math advisers had recommended against this kind of early access. The reviewers say their involvement is not a certification. The announcement comes weeks after a 722-manuscript release that needed three withdrawals and 14 revisions within a day, and after a $15M Simons Foundation, OpenAI and Anthropic initiative to fund checking of AI-generated math. [1] [7] [8] [9] [10]
The evidence so far is OpenAI's own claims plus Lean formalizations, with no independent confirmation. If the ETH result holds, it would also refute SETH and many conditional fine-grained lower bounds.
Read the full assessment
For AI-for-science teams, checking results, not generating them, becomes the bottleneck.
Executive brief
OpenAI says an unnamed internal model has disproved the Exponential Time Hypothesis (ETH), a 27-year-old assumption that underpins a large part of complexity theory. The claim comes with a Lean formalization, and the hypothesis's own authors have agreed to examine it. OpenAI also claims a proof of the local smoothing conjecture in every dimension, which it says also settles the Kakeya and Stein restriction conjectures, plus a rigorous existence proof for 4D quantum field theories including QCD. No result has been peer-reviewed. The reviewers say their involvement is not a certification, and OpenAI's own math advisers had just advised against the "shepherd" review model it chose.
What changed and event timeline
722 manuscripts released
OpenAI posted 722 AI-generated manuscripts from an unreleased model. Within 24 hours it withdrew three over a sign error and revised 14 more. Several mathematicians criticized the volume ().
$15M Simons initiative
The Simons Foundation, OpenAI and Anthropic committed $15M combined to help mathematicians vet AI results. OpenAI's share is $5M plus model access and compute (;).
ETH disproof found and Lean-checked
According to OpenAI, the model produced the disproof on October 16 and it was verified in Lean the next day ().
Local smoothing proof
The model's output came on October 18, with Lean formalization on October 19 ().
Advisers reject early access
OpenAI's AGMAI math panel recommended that labs not give selected people first access to results. It cited unequal access, borrowed reputation and biased selection ().
Three claims announced
The math and CS materials went to GitHub. The physics work is being held back while a group led by David Gross reviews it ().
Capabilities and access
Read the full section
- Model: an unnamed internal OpenAI model. No version or public access has been announced (Unite.AI; ForkLog).
- Public now: the ETH write-up with a Lean proof, and the raw local-smoothing output with a Lean proof, both on GitHub.
- Withheld: the physics manuscripts. Inquiries go to the review group (Engadget).
- Credit: OpenAI says it will not seek academic credit for the results (Engadget).
Technical analysis for researchers and developers
- ETH claim: a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space.
- Practical impact: coverage says the gain over exponential time is small and runtimes may still be enormous.
- Scope of the analysis claim: the GitHub summary describes Stein restriction estimates "throughout the interior of the conjectured range" (The Verge).
Read the full section
- ETH claim: a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The 3-SAT case is what refutes ETH (The Verge). Counting is a stronger problem than deciding satisfiability. Inference: because SETH implies ETH, a correct result would also refute SETH, and with it many conditional fine-grained lower bounds.
- Practical impact: coverage says the gain over exponential time is small and runtimes may still be enormous. The result would not imply P = NP (ForkLog).
- Scope of the analysis claim: the GitHub summary describes Stein restriction estimates "throughout the interior of the conjectured range" (The Verge). That wording is narrower than "resolved in all dimensions," because it leaves out the endpoints.
- Lean: a Lean proof is only as good as the statement it formalizes. Whether those formal statements match the conjectures still needs independent review.
Claims and evidence
- ETH is false, with Lean proof. Lab-reported. The reviewers say their involvement "should not be taken as certification" (The Next Web).
- Local smoothing implies Kakeya and restriction in all dimensions. Lab-reported. The output is released raw, without expert explanation (The Verge).
- Existence of 4D gauge theories including QCD. Lab-reported. The manuscript is not public (Engadget).
Read the full section
- ETH is false, with Lean proof. Lab-reported. The reviewers say their involvement "should not be taken as certification" (The Next Web).
- Local smoothing implies Kakeya and restriction in all dimensions. Lab-reported. The output is released raw, without expert explanation (The Verge).
- Existence of 4D gauge theories including QCD. Lab-reported. The manuscript is not public (Engadget).
- Conflicting coverage: one aggregator says the CS result was "verified by an external expert panel" (KuCoin). That contradicts the panel's own statement.
- No independent confirmation of any of the three results exists yet (DataStudios).
Context and prior work
- Impagliazzo and Paturi formalized ETH in 1999 (The Next Web).
- Sogge proposed local smoothing in 1991.
- Hong Wang received a Fields Medal this year for the 3D Kakeya result (The Verge).
Read the full section
- Impagliazzo and Paturi formalized ETH in 1999 (The Next Web).
- Sogge proposed local smoothing in 1991. Guth, Wang and Zhang proved it in two spatial dimensions in 2019, and Wang and Zahl proved Kakeya in three dimensions in 2025 (KuCoin; Hong Wang).
- Hong Wang received a Fields Medal this year for the 3D Kakeya result (The Verge).
- This announcement follows the disputed October 6 bulk release (AI Weekly).
Limitations, safety and contested findings
- OpenAI's last release needed corrections within a day: three manuscripts withdrawn and 14 revised (AI Weekly).
- AGMAI warns that selective early access borrows the reviewers' reputations and skews selection. It wants repository releases that include problem-selection details (The Verge).
- Critics have called bulk AI output "a messy first draft," and some mathematicians refuse to engage with it (AI Weekly).
Read the full section
- OpenAI's last release needed corrections within a day: three manuscripts withdrawn and 14 revised (AI Weekly).
- AGMAI warns that selective early access borrows the reviewers' reputations and skews selection. It wants repository releases that include problem-selection details (The Verge).
- Critics have called bulk AI output "a messy first draft," and some mathematicians refuse to engage with it (AI Weekly). At least one researcher argues for total opposition to AI in mathematics (Weinreich, arXiv).
- Sources disagree on the physics timeline (ForkLog vs. Unite.AI).
Business and practitioner implications
- Signal, not product: nothing here can be deployed yet. The model is internal, and any practical SAT speedup appears negligible (ForkLog).
- Verification is the bottleneck. Labs are now paying for checking work, as with the Simons funding (Crypto Briefing).
- Security and cryptography: if ETH falls, conditional hardness assumptions would need re-auditing. Real-world exposure looks limited for now.
Read the full section
- Signal, not product: nothing here can be deployed yet. The model is internal, and any practical SAT speedup appears negligible (ForkLog).
- Verification is the bottleneck. Labs are now paying for checking work, as with the Simons funding (Crypto Briefing). Teams building AI-for-science pipelines should plan for formal proofs, disclosed problem selection and outside review.
- Security and cryptography: if ETH falls, conditional hardness assumptions would need re-auditing. Real-world exposure looks limited for now.
The source trail.
Sources (14)
OpenAI announces three big science discoveries and a new way to work with academics
Article text retrieved; extracted text may omit tables or interactive elements.
theverge.comWorking with academic communities to build scientific understanding
Related coverage; assess separately
openai.comOpenAI says its AI refuted the Exponential Time Hypothesis
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fourweekmba.comOpenAI models' claimed ETH disproof and Kakeya-related and Yang-Mills proofs
Related coverage; assess separately
datastudios.org