OpenAI says its models produced proofs in math, computing and physics; experts will now review them
Redacción IvokaOct 27, 12:00 PM 3 min
OpenAI presents three results as proofs produced by its models. The math and computing ones were published so the community can examine them; the physics one will first be explained by an outside group.
OpenAI announced three findings in mathematics, computer science and physics. It is worth reading calmly: these are claims by the company that specialists must now review.
The three results, according to OpenAI
- Mathematics (harmonic analysis): its models proved the local smoothing conjecture, proposed by Christopher Sogge in 1991, in every spatial dimension. The company says the result also resolves the Kakeya and Stein restriction conjectures. In earlier work, Larry Guth, Hong Wang and Ruixiang Zhang had proved the local smoothing conjecture in two spatial dimensions in 2019.
- Computing: its models disproved the Exponential Time Hypothesis (ETH), a longstanding conjecture in computational complexity about the difficulty of solving Boolean satisfiability problems. It is used in hundreds of papers in areas such as graph theory, computational biology, databases and computational geometry. Refuting it does not automatically deliver faster algorithms: researchers must still determine what the result means for practical computation.
- Physics: existence proofs, according to the company, for interacting theories involving gauge fields and fermions in four dimensions, including quantum chromodynamics (QCD). The work also addresses pure Yang-Mills theory, a component of one of the Clay Mathematics Institute's Millennium Prize problems.
How it was published. According to OpenAI, the math proof was generated on Oct. 18, 2026 and formalized in Lean (a proof assistant that helps verify arguments with computer-based checks) the following day; the ETH disproof was produced on Oct. 16 and formalized in Lean a day later. The natural-language and formal Lean proofs for the math and computing results are in a public GitHub repository. For the ETH, the review will be led by Russell Impagliazzo and Ramamohan Paturi (UC San Diego) alongside Ryan Williams (MIT), and OpenAI agreed to fund a conference examining the claim. For physics, an outside group led by David Gross and including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov will prepare its own account before the model-generated physics materials are released. OpenAI says all three collaborations will operate independently, with participants free to publish their findings, and that it will support review workshops and conferences through a previously announced $5 million contribution to the Simons Foundation.
What does it mean for you? It does not change your work today. It is a signal of what AI companies want to show: that their models can reason about very hard problems. What independent reviewers say remains to be seen.
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