OpenAI says its models produced results in three fields and is working with academic groups to examine, explain and independently assess them.
On October 26, 2026, OpenAI described three AI-generated research results—in mathematics, theoretical computer science and physics—and outlined separate plans for academic groups to examine them. The company says it is treating the outputs as starting points for scrutiny and explanation, rather than as finished scientific accounts.
In mathematics, OpenAI says its models produced a proof of the local smoothing conjecture in every dimension, which the company says also resolves the Kakeya and Stein restriction conjectures in all dimensions. OpenAI reports that it formalized the result in Lean, a proof-assistant language, and published the natural-language write-up and formal proof. The company says the result was generated on October 18 and formalized the following day.
A second claim concerns the Exponential Time Hypothesis, a longstanding conjecture used to establish conditional limits on the efficiency of algorithms. OpenAI says its system produced a counterexample and that the result was formalized in Lean. Russell Impagliazzo and Ramamohan Paturi of UC San Diego, and Ryan Williams of MIT, will lead a group examining the claim. OpenAI says the natural-language proof, Lean formalization and raw data are being made public to support review; it also committed to fund a conference on the result’s implications.
For physics, OpenAI says its models produced mathematical existence proofs involving quantum chromodynamics and related four-dimensional quantum field theories, including a subproblem concerning pure Yang–Mills theory. A group led by David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, will shepherd the work. Unlike the other materials, the AI-produced physics artifacts are being held back while the group works on an explanation.
The different release plans reflect the distinct stages of review, and the claims should not be read as settled results: the collaborations are intended to help experts inspect and explain them. OpenAI says participation is voluntary and unpaid, and that collaborators’ conclusions are independent. The company also says it will fund researchers’ work to assess and build on the results.