OpenAI says its internal models produced three major results spanning mathematics, computer science, and physics, and it has handed the write-ups to outside researchers to check. In mathematics, the models claim a proof of the local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures. In computer science, they claim the Exponential Time Hypothesis is false, a result OpenAI says was verified in Lean. In physics, they claim a rigorous existence proof for interacting quantum field theories in four dimensions, including quantum chromodynamics and a completion of the Standard Model.
OpenAI is not presenting the work as finished science. It calls the manuscripts raw research data and has recruited external experts as shepherds to organise verification. Russell Impagliazzo and Ramamohan Paturi, who proposed the ETH three decades ago, lead the complexity review with Ryan Williams of MIT. Nobel laureate David Gross leads the physics group, while the mathematics result is being released publicly for the community to dissect. The groups asked for all underlying data to be published, and OpenAI says it will claim no academic credit for the discoveries.
Independent verification is still pending. Complexity theorists are organising an open examination of the ETH claim, which underpins hundreds of conditional hardness results across graph theory, computational biology, and geometry. If it holds, a large body of published work has to be revisited and the hunt for faster algorithms gets a new map. It is not a polynomial time result, so P versus NP remains open.