AI Tackles Erdős Conjecture: Claude Completes Lean 4 Formalization
ctjlewis · x · 2026-08-02
A GitHub repository named EvolvingPrograms demonstrates a major AI breakthrough in advanced mathematics. Using Anthropic's Claude Fable 5 and Claude Opus 5 models, the project provides a complete Lean 4 formalization of the Erdős–Simonovits degeneracy conjecture (Erdős problem #146).
- Core Finding: The formalization proves that the conjecture actually fails at every level, establishing the sharp asymptotic law at Gibbs weight $e$.
- Technical Details: The entire proof is built on Lean 4 and mathlib. It is notably labeled as "zero" human commits, indicating that the formalization was entirely driven by the AI models.
This achievement highlights the rapidly advancing capability of large language models in complex logical reasoning and automated theorem proving, offering a compelling benchmark for AI-assisted mathematical research.
Related event: Claude and Lean 4 Disprove Erdős Conjecture(4 posts)→
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