OpenAI says it has solved the Kakeya conjecture, ETH and quantum field theory

OpenAI announced that its internal models produced three AI-assisted research results, covering mathematics, theoretical computer science and physics, all of which are currently research claims awaiting expert verification. In mathematics, OpenAI says the model proved the local smoothing conjecture in all spatial dimensions and would simultaneously resolve the Kakeya and Stein restriction conjectures in each dimension, with the output produced on October 18 and Lean formalization completed the next day, and the natural-language argument and Lean proof have been made public. In computer science, the system found a deterministic subexponential-time exact counting method for satisfying assignments of fixed-width Boolean formulas, which, if the 3-SAT case holds, would refute the exponential time hypothesis (ETH); a working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will review the proof.