Google DeepMind reported that AlphaProof Nexus, an agent framework combining LLMs with formal proof search, autonomously solved 9 of 353 unsolved problems left by Paul Erdős. The results were disclosed in a paper published to arXiv on May 21, 2026, and include two problems that had remained open for 56 years. Every proof was machine-verified in the formal proof assistant Lean, with Lean proofs and natural-language summaries released via the paper (HTML version) and a GitHub results repository.
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