OpenAI Publishes Three Research Results With Expert Shepherds

OpenAI announced three new discoveries in mathematics, computer science and physics on October 26, 2026, releasing the results with external experts acting as shepherds on part of the work, according to The Verge.

For the computer science and physics results, OpenAI had outside specialists guide the work. The company released the computer science write-up and its Lean proof on GitHub. The paper claims the Exponential Time Hypothesis is false, describing a deterministic algorithm that counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space.

A group including Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the computer science proof. On the physics side, the result is a mathematically rigorous existence proof of certain interacting quantum field theories with gauge fields and fermions in four dimensions, including QCD. David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov to shepherd that work.

For the math problem, OpenAI released the model output directly on the advice of its advisers. The output proves the local smoothing conjecture in every dimension and resolves the Kakeya and Stein restriction conjectures in all dimensions. It also gives a proof for the Euclidean wave equation that uses an auxiliary partial differential equation to establish Sogge's local smoothing in every spatial dimension of at least two.

OpenAI also published an open letter asking the community about early access, credit and support for researchers.

Recent context

Less than a month earlier, OpenAI mass-released hundreds of manuscripts it said contained solutions to long-standing mathematics questions, and on October 6 it released model output directly. The Exponential Time Hypothesis was originally proposed in 1999 by a group including Impagliazzo and Paturi, and a few months before this release, NYU professor Hong Wang received a Fields Medal for resolving the Kakeya conjecture in three dimensions. The day before the announcement, OpenAI's AGMAI panel recommended that AI companies not adopt the practice of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection.