RESEARCH · RESEARCH · #2652
OpenAI asks outside experts to vet AI-produced proofs that claim to disprove the Exponential Time Hypothesis
OpenAI says internal models produced manuscripts including a claimed disproof of the Exponential Time Hypothesis (ETH) and a partial result related to a Millennium Prize Problem. The company published the raw writeups and Lean formalizations, is funding independent review, and has asked outside experts (including a Nobel laureate) to act as "shepherds" to check and interpret the proofs.
KEY POINTS
- OpenAI says internal models produced manuscripts including a claimed disproof of the Exponential Time Hypothesis (ETH) and a partial result related to a Millennium Prize Problem.
- The company published the raw writeups and Lean formalizations, is funding independent review, and has asked outside experts (including a Nobel laureate) to act as "shepherds" to check and interpret the proofs.
- If the proofs hold up, they would reshape complexity theory and affect many results that assume ETH; regardless, this is a notable instance of AI producing advanced mathematical arguments that still require human verification.
DECISION BRIEF
CONFIDENCE
WHAT CHANGED
OpenAI says its internal models produced manuscripts that include a claimed disproof of the Exponential Time Hypothesis (ETH) and a claimed partial result related to a Millennium Prize Problem. The lab published raw writeups and translated the math and computer-science proofs into Lean, and it has asked outside experts to act as "shepherds" to check and interpret the proofs (coverage says these experts include a Nobel laureate).
WHY NOW
The claim directly targets ETH, a central, widely used assumption in complexity theory; if validated, the result would have immediate relevance to many papers and lines of research that rely on ETH. Irrespective of correctness, the episode is notable as another instance where frontier AI systems produced advanced mathematical arguments that require human expert verification.
WHO IS AFFECTED
Directly affected: researchers in theoretical computer science (complexity theory) and mathematics working on ETH, SAT, and P vs NP; related fields that base results on ETH (sources cite e.g., graph theory and computational biology); working groups and named researchers organizing responses (TechCrunch names MIT professor Ryan Williams and UC San Diego’s Russell Impagliazzo and Ramamohan Paturi).
CONFIRMED
- OpenAI says its internal models produced proofs including a claimed disproof of the Exponential Time Hypothesis (ETH) and a claimed partial result related to a Millennium Prize Problem. - OpenAI published the raw writeups and translated the math and computer science proofs into Lean. - OpenAI asked outside experts to act as "shepherds" to check and interpret the proofs; reporting states these invited experts include a Nobel laureate. - TechCrunch reports OpenAI released solutions to three major problems and structured the releases differently by discipline; computer scientists formed a working group and asked for the proofs to be shared publicly and for OpenAI to fund a conference to discuss them. - TechCrunch reports MIT Professor Ryan Williams is organizing the computer-science response and that Williams, Russell Impagliazzo, and Ramamohan Paturi were asked to help interpret the solution; Williams characterized some parts as "alien-looking." - TechCrunch reports that Anthropic’s team (Levent Alpöge) suggested OpenAI may be basing solutions on pre-existing work and that Anthropic subsequently released its own refutation of ETH.
UNCERTAIN
- Whether the claimed proofs (including the ETH disproof and the Millennium-related partial result) are correct and accepted by the research community — sources report they are claimed by OpenAI but require external verification. - Whether the Lean formalizations fully capture the intended mathematical statements and whether Lean checks suffice to establish the intended claims — the sources note Lean verifies proofs only relative to the formal statement, and experts still must judge adequacy. - The identity and role details of the referenced Nobel laureate (source 3119 title mentions one, but the excerpt does not name them). - Extent to which the new submissions depend on or reuse prior published work — TechCrunch cites Anthropic’s suggestion but provides no definitive attribution. - Precise arrangements and scope of any funded independent review or conference: TechCrunch notes the working group asked OpenAI to fund a conference; sources do not confirm OpenAI’s commitments. - Conflicting signals: Anthropic published its own refutation of ETH shortly after OpenAI’s release, indicating disagreement in early community reactions. Note: where the excerpts report claims, they are currently claims pending external expert validation per the same excerpts.
WHAT TO WATCH
Concrete observable signals to watch next, based on the reported actions and open questions: - Public reports or technical notes from the named "shepherds" or working-group organizers (e.g., Ryan Williams, Impagliazzo, Paturi) assessing the proofs. - Formal audit results or commentary on the Lean formalizations clarifying whether the formal statements match the intended mathematical claims. - Community responses: open letters, working-group minutes, or coordinated reviews calling out errors, confirmations, or replication attempts. - Any peer-reviewed publications or independently reproducible formal-verification artifacts that confirm or refute the claimed results. - Public clarification about the role or identity of the referenced Nobel laureate and the scope of their involvement. - Announcements about whether OpenAI will fund or host the conference/workshop requested by the computer-science working group and its reported outcomes.
WHY IT MATTERS
If the proofs hold up, they would reshape complexity theory and affect many results that assume ETH; regardless, this is a notable instance of AI producing advanced mathematical arguments that still require human verification.
EVIDENCE MAP
4Editorial claims linked to specific sources, with support, contradiction and context shown separately.
OpenAI's internal models produced manuscripts that include a claimed disproof of the Exponential Time Hypothesis (ETH).
SUPPORTEDChecked 2026-10-27 · 2 supporting
The Decoder: reports OpenAI says its internal models "disproved a central assumption in computer science" and that the computer science result centers on ETH.
SUPPORTS TechCrunch AIMEDIA · 2026-10-27TechCrunch: "OpenAI released solutions... One was a surprise rejection of the Exponential Time Hypothesis (ETH)."
OpenAI asked outside experts to act as "shepherds" to check and interpret the AI-produced proofs; the company’s outreach included named complexity researchers and (per reporting) a Nobel laureate among invited experts.
SUPPORTEDChecked 2026-10-27 · 2 supporting
The Decoder: "OpenAI asked outside experts to act as 'shepherds'..." and the article title mentions inclusion of a Nobel laureate.
SUPPORTS TechCrunch AIMEDIA · 2026-10-27TechCrunch: describes naming of Ryan Williams, Russell Impagliazzo, and Ramamohan Paturi as people the lab asked to help interpret the solution.
OpenAI published the raw writeups and (for math and computer science) translated the proofs into Lean; the company engaged with working groups and was asked to fund a conference and other independent review activities.
SUPPORTEDChecked 2026-10-27 · 2 supporting
The Decoder: OpenAI "laid out three results" and says it "translated the math and computer science proofs into Lean" and calls the manuscripts raw research data.
SUPPORTS TechCrunch AIMEDIA · 2026-10-27TechCrunch: describes field-specific handling (e.g., mathematicians got GitHub drops; computer scientists formed a working group and asked for proofs to be shared publicly and OpenAI to fund a conference).
Lean formalization does not by itself guarantee correctness: Lean checks the proof relative to the formal statement as written, and experts must decide whether that formal statement matches the intended mathematical claim.
SUPPORTEDChecked 2026-10-27 · 1 supporting
SOURCES & TIMELINE
2OpenAI released solutions to three blockbuster math problems that have long vexed researchers yesterday. One was a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how we understand what is difficult to compute. As with previous proof-drops from the frontier lab, scientific communities responded with a mixture of thrill and dismay. Anthr…
OpenAI says its internal models have disproved a central assumption in computer science and proved part of one of the Millennium Prize Problems, among other results. Outside experts will now decide whether the proofs hold up. OpenAI laid out three results from math, computer science, and physics in a blog post . The company says its internal AI models produced the proofs. OpenAI calls the manuscripts a kind of raw r…