Source reported
Hundreds of papers assume ETH. OpenAI says its model disproved it; checks have just begun
What happened
OpenAI's model found a claimed disproof of the Exponential Time Hypothesis (ETH) on 16 October, and the company checked it in the Lean proof language the next day, per The Next Web. OpenAI published the write-up and Lean proof on GitHub on 26 October, alongside claimed results in harmonic analysis and quantum field theory. The scientists who proposed ETH, with MIT's Ryan Williams, are now organizing an independent review, and they state that their involvement is not a certification of the claim. TechCrunch reports that Anthropic also released its own refutation of ETH hours after OpenAI's announcement.
What we know
- OpenAI says its model found the ETH disproof on 16 October and verified it in Lean the next day; the write-up and Lean proof are on GitHub, per The Next Web and Engadget.
- Russell Impagliazzo, Ramamohan Paturi and Ryan Williams wrote in an open letter that their involvement "should not be taken as certification of the claim," per The Next Web.
- The review group says it signed no non-disclosure agreements and will not be paid; OpenAI agreed to release raw data and fund a conference, per The Next Web.
- Williams told TechCrunch that parts of the proof are "routine" but two or three are "alien-looking," and that OpenAI's algorithm is probably not the best possible.
- Williams said OpenAI told him it had checked whether the result breaks any cryptographic systems and was reasonably confident it implies no breaks, per TechCrunch.
- Per Engadget and The Next Web, ETH underpins hundreds of papers in fields including databases, computational biology and geometry, which would need revisiting if the refutation holds.
What we don't know yet
- Whether the refutation survives independent human scrutiny; the review group has only just begun and has not endorsed it.
- Whether OpenAI's algorithm builds on pre-existing work: TechCrunch reports Anthropic mathematician Levent Alpöge suggested it did, and OpenAI has not been shown responding in these sources.
- Whether the result bears on P versus NP; Williams said computer scientists should give P = NP somewhat more weight, but that is his opinion, not a proof.
- Whether the cryptography assurance holds; it is OpenAI's own account relayed by Williams, and no independent analysis has been published.
- How credit will be assigned for AI-originated results; the reviewers raised the question in their letter without answering it.
Why it matters
If the refutation holds, researchers in complexity theory, databases and computational biology would need to re-examine hundreds of papers that took ETH as given, and cryptographers would need to confirm that no key-size assumptions are affected.
Claims
- ConfirmedOpenAI says its model found a disproof of the Exponential Time Hypothesis on 16 October 2026.
- ConfirmedOpenAI published the ETH write-up and a Lean proof on GitHub.
- ConfirmedThe scientists who proposed ETH, together with Ryan Williams, are organizing an independent examination and say their role is not a certification of the claim.
- UnconfirmedAnthropic released its own refutation of ETH hours after OpenAI's announcement.
- UnconfirmedThe ETH refutation is independently verified as correct.
- ConfirmedOpenAI told Ryan Williams it was reasonably confident the result implies no breaks in cryptographic systems.
Related coverage
Why you can trust this story
85%Source map · 4 outlets / 4 articles
- TechCrunch
- Article 1techcrunch.comreport
- Engadget
- Article 1engadget.comreport
- The Next Web
- Article 1thenextweb.comreport
- OpenAI
- Article 1openai.comofficial
How this credibility score is calculated
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- Claims checked against the source
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Checked claims were verified against the cited source text. Weights are fixed and explainable.
Human accountability
- 4 independent origins / 4 sources
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Verification ledger · 6
- Claim: OpenAI says its model found a disproof of the Exponential Time Hypothesis on 16 October 2026.Status: ConfirmedVerification trailVerifiedChecked by verification engine
At least one checkable detail was matched against the full text of the cited source.
- Claim: OpenAI published the ETH write-up and a Lean proof on GitHub.Status: ConfirmedVerification trailVerifiedChecked by verification engine
At least one checkable detail was matched against the full text of the cited source.
- Claim: The scientists who proposed ETH, together with Ryan Williams, are organizing an independent examination and say their role is not a certification of the claim.Status: ConfirmedVerification trailVerifiedChecked by verification engine
At least one checkable detail was matched against the full text of the cited source.
- Claim: Anthropic released its own refutation of ETH hours after OpenAI's announcement.Status: UnconfirmedVerification trailUnverifiedChecked by verification engine
No automated check against the source text is available.
- Claim: The ETH refutation is independently verified as correct.Status: UnconfirmedVerification trailUnverifiedChecked by verification engine
No automated check against the source text is available.
- Claim: OpenAI told Ryan Williams it was reasonably confident the result implies no breaks in cryptographic systems.Status: ConfirmedVerification trailVerifiedChecked by verification engine
At least one checkable detail was matched against the full text of the cited source.
Update log · 0
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