OpenAI claims to have disproved the exponential time hypothesis and solved the Kakeya conjecture in all dimensions

On October 26, OpenAI announced that its internal model achieved three results: proving the local smoothing conjecture in all dimensions, disproving the exponential time hypothesis (ETH), and establishing a rigorous existence proof for certain four-dimensional quantum field theories including quantum chromodynamics. ETH holds that no subexponential-time algorithm exists for solving all 3-SAT problems; OpenAI presented an algorithm with runtime 2^{O(n/√log n)}, which, if the proof holds, disproves this foundational hypothesis that has been used for nearly 30 years. The original proposers Impagliazzo and Paturi are organizing an independent review together with Ryan Williams of MIT. On the mathematics side, the model, with the help of a new auxiliary partial differential equation, advanced the local smoothing proof to all dimensions, and according to OpenAI's account thereby resolved the Kakeya conjecture and the Stein restriction conjecture in all dimensions; the Lean formalized proof has been made public. The physics part includes an existence proof for pure Yang–Mills theory; no resolution of the mass gap was announced, a working group led by David Gross is organizing it first, and the AI's original proof is not being made public for now.