An AI model just closed a quantum optimization problem that human mathematicians left open for more than a decade.
Researchers used Claude Fable 5 to construct a formal proof of the Farhi, Goldstone and Gutmann (FGG) conjecture, which states that depth-p Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees achieves an approximation ratio of exactly (2p+1)/(2p+2). The proof was then verified end-to-end by Lean 4, a mechanical proof assistant, meaning no human had to trust the model's reasoning on faith. The team first formalized known parts of the problem in Lean, reduced the conjecture to a single open mathematical statement, and handed that to the model along with an agentic toolkit to fill the gap.
What makes this more than a benchmark stunt is the methodology. The model did not brute-force a solution — it identified a hidden dynamical symmetry in the problem and borrowed tools from an adjacent field to convert an existence problem into an explicit construction. That kind of cross-domain transfer is exactly what mathematicians spend careers developing, and the Lean verifier confirms the logic holds without requiring anyone to take the AI's word for it.
The result sits in a line of recent work using formal verification to backstop AI-generated mathematics, but resolving a named open conjecture in quantum information raises the stakes. The relevant question now is whether this methodology scales to harder problems — or whether the decade-long gap on this particular conjecture happened to align unusually well with what large language models are good at.