AI独立解决三十年数学问题的变体，陶哲轩分享自动化研究经验

Core Viewpoint - The article discusses the recent proof of a weakened version of Erdős Problem 124, which has remained unresolved since its introduction in 1984. The proof was conducted by Princeton University mathematician Boris Alexeev using the AI system Aristotle from Harmonic, which has shown remarkable mathematical reasoning capabilities [2][4]. Summary by Sections Proof and AI Involvement - Boris Alexeev utilized the AI system Aristotle to address Erdős Problem 124, demonstrating its enhanced reasoning abilities and natural language interface [2][4]. - The AI independently proved a simpler version of the problem, showcasing its surprising mathematical proof capabilities [4]. Controversy and Clarifications - There has been controversy regarding claims that AI solved the complete version of the problem, which were clarified by Alexeev. He corrected a spelling error in the formal statement that weakened the claim [3][4]. - The problem's subtlety and the AI's achievement highlight the complexities involved in mathematical proofs [4]. Broader Implications in Mathematics - Terence Tao emphasizes that many unsolved mathematical problems exhibit a "long tail" structure, suggesting that AI can help tackle relatively easier problems that have been overlooked [9]. - Tao's experience with the Equational Theories Project demonstrated the potential of automation in solving a significant number of algebraic implications quickly [10][11]. Ongoing Research and Future Prospects - Researchers are systematically scanning remaining problems on the Erdős Problems website to identify similar misstatements or quick solutions, focusing on the easier "low-hanging fruit" [15]. - The advancements in AI tools are expected to clarify the more challenging problems by resolving simpler issues first, indicating a transformative shift in the mathematical field [15][16].