An AI Model Proved a Quantum Conjecture Open Since 2008 — And It Is Lean-Checked

For eighteen years, the Aaronson-Ambainis conjecture sat open. Now an AI research system running an unreleased Anthropic model says it has closed the proof, and the Lean proof assistant accepted it. The paper and the formalization are public. The peer review is not. What was actually proved The conjecture, posed by Scott Aaronson and Andris Ambainis around 2008 in their paper “The Need for Structure in Quantum Speedups,” asks a narrow but load-bearing question: when can a quantum computer be exponentially faster than a classical one rather than merely polynomially faster? Aaronson and Ambainis had connected that question to a conjecture about polynomials. The proposed statement, in essence, was that bounded polynomials of low degree have influential variables — meaning there is at least one input variable that carries a large share of a function’s influence, rather than the influence being smeared thinly across thousands of variables that each matter a little.

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