OpenAI Claims AI Model Disproves Exponential Time Hypothesis, Resolves Kakeya Conjecture, and Proves Quantum Field Existence
OpenAI announced on October 26, 2026, that its internal AI models have produced proofs for three major scientific breakthroughs: a refutation of the Exponential Time Hypothesis (ETH), a proof of the local smoothing conjecture in all dimensions (resolving the Kakeya and Stein restriction conjectures), and rigorous existence proofs for certain four-dimensional quantum field theories, including Quantum Chromodynamics (QCD) and pure Yang-Mills theory. The ETH refutation, found on October 16 and verified in Lean on October 17, claims a subexponential-time algorithm for counting satisfying assignments of fixed-width CNF formulas. OpenAI released the ETH and local smoothing manuscripts and Lean proofs on GitHub, while the physics group withheld their materials to write their own explanations. Independent expert groups, led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams for computer science, and David Gross for physics, will examine the results. OpenAI stated it does not seek academic credit and donated $5 million to the Simons Foundation for workshops.