---
title: 'OpenAI says its models produced three proofs in math, computer science and physics, all pending independent review'
url: 'https://securteksecurity.com/news/openai-says-models-produced-three-proofs-math-computer-science-physics'
markdown: 'https://securteksecurity.com/news/openai-says-models-produced-three-proofs-math-computer-science-physics.md'
date: '2026-10-26'
description: "OpenAI said on October 26, 2026 that its internal models produced three research results: a disproof of the Exponential Time Hypothesis, produced October 16 and formalized in Lean October 17; a proof of Sogge's 1991 local smoothing conjecture in every dimension, produced October 18 and formalized O…"
taxonomy:
  category:
    - AI
---

# [OpenAI says its models produced three proofs in math, computer science and physics, all pending independent review](https://securteksecurity.com/news/openai-says-models-produced-three-proofs-math-computer-science-physics)

   26th Oct 2026  

OpenAI said on October 26, 2026 that its internal models produced three research results: a disproof of the Exponential Time Hypothesis, produced October 16 and formalized in Lean October 17; a proof of Sogge's 1991 local smoothing conjecture in every dimension, produced October 18 and formalized October 19, which the company says also resolves the Kakeya and Stein restriction conjectures; and existence proofs for four dimensional quantum field theories including quantum chromodynamics and pure Yang-Mills theory, part of a Clay Millennium Prize problem, with the physics artifacts held back for write up by a group led by Nobel laureate David Gross. The math and computer science writeups and Lean files are public on GitHub. The Exponential Time Hypothesis review is led by its original proposers, Russell Impagliazzo and Ramamohan Paturi, with MIT's Ryan Williams, and OpenAI linked the work to a $5 million Simons Foundation contribution.

This item rests on a single reporting chain: OpenAI's own October 26 announcement and summaries of it. None of the three claims has been independently confirmed. The named reviewers stress that their involvement is not certification of the claims, and Lean checks the formal argument, not its interpretation. This item will be updated when confirmation or denial appears.

Update, October 28: Anthropic has published its own independent refutation of the Exponential Time Hypothesis. Its paper, posted October 26 at 11:07 PM ET and credited to "Claude (Anthropic)," presents a deterministic algorithm that solves and counts 3-SAT in subexponential time, with a Lean 4 formalization checked by a second, independently written kernel. Anthropic says an internal Claude research model found the core algorithm on October 16, the same date OpenAI reports, using 14 million output tokens with no human input in the discovery; Claude's version also refutes the stronger SETH, and Anthropic counts more than 800 papers whose results rest on ETH. Both labs are explicit that the result is purely asymptotic and changes nothing for real solvers or cryptography, and no human has yet checked either proof by hand.

Sources: [Unite.AI](https://www.unite.ai/openai-says-its-models-produced-three-proofs-in-math-cs-and-physics/); [Dealroom](https://dealroom.co/news/167089-openai-says-its-ai-disproved-a-core-computer-science-assumption-gives-5m/); [TechTimes](https://www.techtimes.com/articles/329569/20261027/two-ai-systems-disproved-same-complexity-conjecture-independently-same-day-800-papers-risk.htm); [SiliconNoon](https://siliconnoon.com/exponential-time-hypothesis-is-false-openai-and-anthropic-say/)

---

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