Google DeepMind Solves 9 Erdős Problems
Google DeepMind has unveiled AlphaProof Nexus, a Gemini-powered agent framework that has solved nine open Erdős problems, including a 56-year-old puzzle, proving 44 conjectures and cracking a 15-year-old algebraic geometry problem — all at a few hundred dollars per problem. The breakthrough, which aligns with Fields medalist Terence Tao's earlier 1-2% success rate prediction, highlights how combining a powerful LLM with a strict validator like Lean could become the mainstream approach for automated theorem proving, potentially reducing the need for sophisticated multi-agent systems.
At the core of AlphaProof Nexus is a simple feedback loop: the LLM generates candidate proofs, which are then checked by the Lean theorem prover, with errors fed back for refinement. This mechanism requires no complex multi-tool integration, yet it achieved striking results. The framework uses four distinct agent architectures (A, B, C, D), and notably, the simplest Agent A independently solved all nine Erdős problems, suggesting that raw model reasoning paired with a rigorous validator can outperform more elaborate setups.
Among the solved problems are Erdős #12 (unsolved for 56 years), #125 (30 years), and #846 (34 years). The system also proved 44 conjectures from the OEIS integer sequence encyclopedia, cracked a 15-year-old algebraic geometry problem, and improved a convex optimization bound. Each problem cost roughly a few hundred dollars in compute, and all code has been open-sourced on GitHub. The paper lists 20 authors, including Aja Huang, a core researcher of the AlphaGo project, underscoring DeepMind's long-term investment in reasoning AI.
