Why AI Formal Proofs Are Incomplete
On 26 October 2026, OpenAI announced three candidate results from an internal model: a proof of the local smoothing conjecture for the Euclidean wave equation (which would resolve the Kakeya and Stein restriction conjectures), a deterministic subexponential algorithm refuting the Exponential Time Hypothesis, and a constructive existence proof for four-dimensional Yang–Mills theory. They were announced with Lean formalizations, in varying degrees, and remain under independent review. This deep dive discusses the essay "Incompleteness Exhibited Twice", which argues that the episode shows…
The skinny
The skinny isn't ready yet — notes appear once the transcript is processed.