OpenAI Details New Discoveries and Academic Collaborations

OpenAI has announced three new discoveries in mathematics, computer science, and physics concerning harmonic analysis, complexity theory, and quantum field theory.

To evaluate how to share raw AI research data with experts, OpenAI is testing three distinct release approaches advised by external shepherds. For the mathematics result, OpenAI released the AI output directly to let researchers organize their own explanations. For the computer science result, an external collaborator group was formed to explain the output while making it publicly available. For the physics result, OpenAI formed an external collaboration and deferred to them regarding when to release materials.

According to OpenAI, the external collaborations operate under four principles: transparency, no academic credit for OpenAI, recognition for the working groups, and independence.

In mathematics, OpenAI says its models produced a proof of the local smoothing conjecture in all dimensions, resolving the Kakeya conjecture and Stein's restriction conjecture in all dimensions. According to the company, the proof relies on a new auxiliary partial differential equation. Sogge proposed the local smoothing conjecture in 1991. Guth, Wang, and Zhang proved it in two spatial dimensions in 2019, and Wang and Zahl proved the Kakeya conjecture in three dimensions in 2025. OpenAI says it obtained its AI output on October 18th, 2026, formalized it in Lean the next day, and released the AI output and Lean proof to its GitHub repository, following a release model used on October 6th, 2026.

In computer science, OpenAI says its models produced a disproof of the Exponential Time Hypothesis (ETH), a conjecture about the computational complexity of Boolean formula satisfiability. OpenAI states it obtained the natural language disproof on October 16th, 2026, and formalized it in Lean on October 17th, 2026. A group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will verify and shepherd the work. Impagliazzo, Paturi, and Francis Zane originally proposed the hypothesis, authoring papers on the topic over the last 30 years. The group opted to make the natural language proof and Lean formalization public immediately on GitHub.

OpenAI also agreed to fund a conference to explore how the refutation of the ETH affects the field.