OpenAI Claims Three Proofs in Math, Physics, and Computer Science

Less than a month after its October 6 release of hundreds of AI-generated mathematics manuscripts, OpenAI announced three claimed discoveries across mathematics, theoretical computer science, and theoretical physics on Monday, pairing the computer science and physics claims with external academic working groups it calls “shepherds,” according to The Verge.

The Three Claimed Proofs Added to GitHub

1. Mathematics — Local Smoothing for the Euclidean Wave Equation: OpenAI released model output directly on GitHub claiming to use an auxiliary partial differential equation to prove Sogge’s local smoothing conjecture for waves in every spatial dimension $n \ge 2$, which would also resolve the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates across all dimensions (following NYU professor Hong Wang’s recent Fields Medal for resolving the 3D Kakeya conjecture).
2. Computer Science — Refuting the Exponential Time Hypothesis (ETH): OpenAI released a paper and Lean formalization presenting a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space—a result that, in the case of 3-SAT, would refute the 1999 Exponential Time Hypothesis. An independent working group comprising ETH co-authors Russell Impagliazzo and Ramamohan Paturi of UC San Diego alongside MIT professor Ryan Williams requested immediate public release on GitHub while they examine the proof.
3. Physics — Four-Dimensional Interacting Quantum Field Theories: OpenAI described a not-yet-fully-released “mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics,” to be shepherded by a panel led by David Gross alongside Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov.

Debate Over Academic ‘Shepherds’ vs. Open Repositories

The announcement comes one day after OpenAI’s own Advisory Group on Mathematics and AI (AGMAI) recommended that AI labs avoid designating handpicked researchers for exclusive early access—citing unequal access, borrowed reputation, and selection bias—and instead publish AI outputs directly to scholarly repositories with Lean-formalized proofs and problem-selection disclosures.