OpenAI claims AI refuted the Exponential Time Hypothesis; Impagliazzo, Paturi and Williams lead open review

On 26–27 October 2026 OpenAI announced that internal models had produced three claimed scientific results: a refutation of the Exponential Time Hypothesis (ETH) in complexity theory, a local-smoothing proof with implications for the Kakeya and Stein restriction conjectures, and existence results for certain four-dimensional quantum field theories including quantum chromodynamics. The company posted a process note on working with academic communities; TechCrunch covered the ETH claim and the outside response.

What OpenAI says about ETH

ETH, proposed by Impagliazzo, Paturi and Zane, has long been used to argue that many hard problems (related to SAT) need roughly exponential time. OpenAI says its system found a deterministic subexponential algorithm that would make ETH false, produced a natural-language write-up on 16 October and a Lean formalisation on 17 October, and released both on a public GitHub repository. The company stresses that a refutation of ETH would not settle P vs NP.

Independent review, not endorsement

A group led by Russell Impagliazzo and Ramamohan Paturi (UC San Diego) — originators of ETH — and Ryan Williams (MIT) agreed to help organise an open, independent examination. Williams said they signed no NDAs and receive no compensation, asked OpenAI to release raw data, and invited the community to help set norms for AI-generated breakthroughs. Their participation is a review process, not a stamp of approval; TechCrunch notes that Anthropic later also released its own claimed ETH refutation.

Limits

OpenAI calls the manuscripts “raw research data” and has asked outside experts to act as “shepherds”. None of the three claims is peer-reviewed. Past AI proof drops have sparked debate about whether Lean checked the full advertised statement. Readers should treat the announcements as claims under scrutiny, not settled theorems.