What happened

On 26 October 2026 OpenAI published a post announcing three results that it says its models produced in mathematics, theoretical computer science and physics. The post refers only to “our models” and “our system” and does not name a specific model. OpenAI calls the manuscripts “raw research data” that need expert interpretation, and the post reports no peer review or independent confirmation of any claim.

Key details

  • Mathematics: OpenAI says its models proved the local smoothing conjecture in every dimension, which it says also resolves the Kakeya and Stein restriction conjectures in all dimensions. For context, the post cites Guth, Wang and Zhang for two dimensions (2019) and Wang and Zahl for Kakeya in three dimensions (2025). OpenAI says the output was obtained on 18 October and formalized in Lean the next day, and it released a natural-language write-up and a Lean proof on GitHub.
  • Computer science: OpenAI says its system proved that the Exponential Time Hypothesis (ETH) is false, and that a Lean formalization verified the result. A group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will verify and shepherd the work, and that process is not complete. OpenAI says it will make all raw data public and fund a conference on the implications.
  • Physics: OpenAI says its models produced a mathematically rigorous existence proof for certain interacting four-dimensional quantum field theories with gauge fields and fermions, including QCD and a unified completion of the Standard Model, building on Balaban’s constructive approach. It says this includes a proof of pure Yang-Mills existence, a subproblem of a Clay Millennium Prize problem. OpenAI reports a Lean formalization of Yang-Mills existence (16 October) but does not mention one for QCD. A group led by David Gross will shepherd the work and chose to withhold the AI artifacts and write up the results itself.
  • Release approach and funding: external experts recommended a different release strategy for each field. OpenAI says the collaborations are unpaid and independent, that it seeks no academic credit, and that it is contributing $5 million to the Simons Foundation to fund workshops and programs on understanding AI-produced results.
  • What is not shown: the post gives no peer review, no named model, and no independent confirmation. A Lean proof checks that a formal statement follows from its axioms, but experts must still confirm that the formal statement matches the conjecture.

Why it matters

If the results hold, they would be among the largest AI contributions to research mathematics and physics to date, and a disproof of ETH would change assumptions used throughout complexity theory. That is a large “if”. The announcement is OpenAI’s own, the expert groups are still working, and the physics group is deliberately keeping the raw AI output private.

For readers, the useful way to follow this is by what gets confirmed: independent verification from the named expert groups, whether the Lean statements match the problems, and whether the models are released so others can test them. Until then these are claims, not established results.

Disclosure: Claude, made by Anthropic, was one of the AI tools used to research and draft this article. Anthropic is a competitor of OpenAI. All claims are OpenAI’s own.

Sources

  1. Building scientific understanding with academic communities Primary source , OpenAI
  2. Everything That Happened in AI Today, Tuesday, October 27 The Neuron