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OpenAI says its AI cracked three famous problems in maths, computer science and physics. Here is what was claimed, what experts are saying, and what nobody has checked yet. Every claim below is OpenAI's or the named outlet's.
On Monday, October 26, 2026, OpenAI published "Working with academic communities to build scientific understanding". It announced three results from its internal models and a new release approach: outside experts acting as "shepherds" who organise groups to understand each result.
Maths: OpenAI says its models proved Sogge's local smoothing conjecture (proposed in 1991) in every dimension, which would also resolve the Kakeya conjecture and Stein's restriction conjecture in all dimensions. OpenAI says the AI output came on October 18 and was formalised in Lean on October 19. The write-up and Lean proof are on GitHub.
Computer science: OpenAI says its system proved the Exponential Time Hypothesis (ETH) is false, found on October 16 and checked in Lean on October 17. A group led by Russell Impagliazzo and Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT) will examine it. In an open letter quoted by The Next Web, they wrote that their involvement "should not be taken as certification of the claim". OpenAI itself says practical speedups will need significant further research.
Physics: OpenAI says its models produced a rigorous existence proof for certain four-dimensional quantum field theories, including QCD and pure Yang-Mills theory, which OpenAI calls part of a Clay Millennium Prize problem. A group led by Nobel laureate David Gross will shepherd it and has not released the AI material yet.
Criticism: The Verge reports that the AGMAI panel of maths advisers OpenAI put together recommended against hand-picking who gets results first. Hindustan Times notes OpenAI was criticised last month for bypassing peer review. OpenAI calls these manuscripts "raw research data"; they are not peer-reviewed papers.
Chapters:
0:00 Three claims, one big "if"
0:19 OpenAI's Oct 26 announcement and the shepherds
0:49 Maths: waves, local smoothing and Kakeya
1:55 Computer science: is the Exponential Time Hypothesis false?
2:55 Who is checking the ETH claim
3:30 Physics: QCD and Yang-Mills existence
4:29 OpenAI's four principles
5:05 What critics and reporters say
5:42 What's still unverified
6:23 What it means for you
Would you trust a proof that no human has fully read yet? Tell us in the comments.
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Sources:
OpenAI: https://openai.com/index/building-scientific-understanding-with-academic-communities/
The Verge: https://www.theverge.com/ai-artificial-intelligence/1019143/openai-eth-kaseya-science-math-physics
