Google DeepMind’s AlphaProof Nexus, an advanced AI system designed to generate machine-verified mathematical proofs, has successfully solved nine open Erdős problems. This achievement includes two problems that had remained unsolved for 56 years, marking a significant milestone in AI-driven mathematical discovery.
This breakthrough closely follows OpenAI's recent announcement of its AI disproving an 80-year-old Erdős conjecture. However, Google DeepMind's AlphaProof Nexus went further by tackling nine problems across combinatorics and graph theory, demonstrating a broader scope of capability.
The AlphaProof Nexus system operates by pairing a large language model (LLM) with Lean, a powerful interactive theorem prover and proof assistant. This combination allows the AI to autonomously generate and rigorously verify mathematical proofs. Each problem was solved at an approximate cost of a few hundred dollars. Beyond the Erdős problems, the AI also proved 44 open conjectures from the Online Encyclopedia of Integer Sequences.
Interestingly, a simpler version of the AlphaProof Nexus agent managed to achieve similar results, albeit at a higher computational cost. The researchers noted that problems requiring entirely new mathematical constructions currently remain beyond the system's capabilities.
Google DeepMind's rapid progress in solving long-standing mathematical problems underscores the accelerating pace at which AI is moving towards generating original solutions. The system's ability to generate proofs, verify them in Lean, and iteratively refine them until they pass formal verification, is a game-changer. This methodology is expected to significantly assist researchers in making novel discoveries at machine speed, fundamentally transforming the landscape of mathematical research.
