OpenAI announced three claimed breakthroughs on October 26, 2026, spanning computer science, mathematics, and physics. The company is using different release arrangements, with external researchers examining and explaining the computer science and physics results.
Its computer science claim would refute the Exponential Time Hypothesis, a widely accepted conjecture underpinning hundreds of papers on computational difficulty. OpenAI says its model produced the result on October 16 and formalized it in Lean, a computerized proof-checking system, the following day. Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will lead an independent examination, emphasizing that their participation is not an endorsement. The materials are publicly available on GitHub.
In a separate mathematics project, OpenAI claims a proof of the local smoothing conjecture, proposed by Christopher Sogge in 1991, across all spatial dimensions. According to the company, the result also resolves the Kakeya and Stein restriction conjectures. OpenAI released the model's explanation and Lean proof for researchers to examine and develop their own accounts.
Separately, the physics work claims rigorous existence proofs for certain interacting quantum field theories in four dimensions, including quantum chromodynamics, which describes the strong force between quarks and gluons. David Gross will lead an external group preparing its own account before the AI-generated materials are released. The work also addresses the existence of pure Yang-Mills theory, part of a Millennium Prize problem.
OpenAI says it seeks no academic credit for the discoveries; researchers should receive recognition for the explanations they produce. The company has also contributed $5 million to the Simons Foundation to support workshops and conferences examining AI-generated results.
