DeepMind AI Agent Autonomously Discovers and Lean-Verifies Rules for 11 Unsolved Turing Machines
rohanpaul_ai · x · 2026-10-22
A Google DeepMind–Cambridge paper, 'At the Limits of Computability,' shows AI moving from answering human-posed math questions to open-ended autonomous discovery.
- The team built a Gemini-based agentic pipeline targeting the uncomputable Busy Beaver frontier, automatically discovering 'accelerations' of Turing machines — compact mathematical rules summarizing many execution steps
- The system integrates pattern recognition, automated conjecturing, informal reasoning, and formal proving in Lean: it tests edge cases in a simulator, drafts informal proofs, then verifies rules with the Lean proof checker
- It autonomously discovered and formally verified novel Collatz-like accelerations for 11 BB(6) machines with no prior documented analysis; these are provisionally classed as 'Cryptids' — machines with exact compact execution descriptions but unresolved halting behavior
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