Google DeepMind and Cambridge AI agent cracks new rules for 11 Busy Beaver machines

An AI agent built by Google DeepMind and University of Cambridge researchers has done something math competitions never ask for. It wandered into an unsolved corner of computer science and came back with new, verified results. The Gemini-based agentic system discovered compact mathematical acceleration rules for 11 previously unanalyzed six-state Turing machines. It then proved those rules formally, in a format any skeptic can check line by line. What the agent actually found The work is documented in a preprint posted to arXiv on October 15, 2026, under the identifier 2610.22603. The research team includes Google DeepMind researchers Marco Dos Santos, Tom Zahavy, and Vivek Veeriah, working with ties to the University of Cambridge. The target was the Busy Beaver BB(6) frontier. This is a collection of six-state Turing machines whose long-term behavior nobody has managed to pin down. The central question for each machine is deceptively simple: does it eventually stop, or does it run forever? The Busy Beaver problem is famous for being uncomputable, meaning no general algorithm can answer that question for every machine. The DeepMind system examined 1,094 of these BB(6) holdouts. Fro...