ChatGPT and Humans Solve an Erdős Problem

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Recent progress in artificial intelligence has enabled the autonomous solution of Erdős Problem #728, marking a significant milestone in computational mathematics. Using tools like Aristotle and ChatGPT, researchers successfully translated informal mathematical reasoning into Lean, a formal proof assistant that guarantees logical correctness. Beyond merely solving the problem, the AI demonstrated a sophisticated ability to rapidly draft and refine complex research expositions, potentially transforming how mathematicians communicate their findings. While the initial formulation of the problem was flawed, the AI assisted in reconstructing the intended spirit of the question and uncovering links to related unsolved conjectures. This development suggests a shift toward a dynamic, high-multiplicity model of academic writing where AI handles routine proofs and stylistic variations. Ultimately, this synergy between generative language models and rigorous formal verifiers allows for a level of speed and precision previously unattainable by human experts alone.

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