# Google DeepMind AI mathematical and computational research > Live situation record from CLSTR: https://clstr.news/situations/google-deepmind-ai-mathematical-and-computational-research > Updated: 2026-10-22T11:37:59.000Z. Sources: 8. Developments: 2. Google DeepMind has achieved significant milestones in applying artificial intelligence to complex mathematical and computational problems. Initially, the development of the AlphaProof Nexus system demonstrated the ability to solve long-standing mathematical research problems, including two Erdős problems that had remained unsolved for 56 years. This system utilizes a formal verification process with the Lean language to ensure logical accuracy through self-correction. Subsequent research expanded these capabilities into the analysis of Turing machines. In collaboration with the University of Cambridge, a Gemini-based AI agent identified mathematical acceleration rules for 11 previously unanalyzed six-state Turing machines, provisionally named ‘Cryptids’. These findings were also supported by formal proofs generated via the Lean 4 theorem prover. Additionally, researchers demonstrated the efficacy of simulated AI prompt auctions, which showed the potential to preserve 99.2% of modeled welfare when routing requests among competing models. ## Timeline ### 2026-10-22: Google DeepMind researchers achieve breakthroughs in AI auctions and Turing machine analysis Google DeepMind researchers have developed AI auction simulations that preserve 99.2% of modeled welfare and an AI agent that discovered new mathematical acceleration rules for 11 Turing machines. 2 sources. https://clstr.news/cluster/google-deepmind-researchers-achieve-breakthroughs-in-ai-auctions-and-turing-machine-analysis ### 2026-10-12: Google DeepMind AI solves long-standing mathematical problems Google DeepMind’s AlphaProof Nexus AI has solved nine long-standing mathematical problems, including two Erdős problems unsolved for 56 years, using a formal verification system via Lean. 6 sources. https://clstr.news/cluster/google-deepmind-ai-solves-long-standing-mathematical-problems --- Cite as: Google DeepMind AI mathematical and computational research. CLSTR, https://clstr.news/situations/google-deepmind-ai-mathematical-and-computational-research