An AI system just proved an 18-year-old quantum conjecture — and Lean checked every step
Physical Superintelligence (PSI) announced on November 6 that an internal research system running instances of a non-public Anthropic model produced a complete proof of the Aaronson–Ambainis conjecture — a quantum-computing…
By Emma Clarke
Physical Superintelligence (PSI) announced on November 6 that an internal research system running instances of a non-public Anthropic model produced a complete proof of the Aaronson–Ambainis conjecture — a quantum-computing question open since 2008 — on the third day of a run. The Lean proof assistant accepted the proof, and the system then improved the result twice, with Lean re-checking each version. The paper and the Lean 4 formalization are public. The conjecture is about the limits of quantum speedups: roughly, whether a quantum computer can be exponentially faster than a classical one on unstructured problems. PSI's repo audit says the formalization contains 648 machine-checked theorems with no placeholders and no added axioms, and the declarations were replayed through Lean's kernel and lean4lean, an independent checker. The caveats matter: human mathematicians still nee…
It is part of a fast-moving week in AI, as researchers, builders, and enterprises keep adjusting to what the latest capabilities mean for them.
