陶哲轩：用了GPT-5 Pro后，小尺度、宏观尺度很赞，中尺度有点垮

Core Insights - The article highlights the collaboration between renowned mathematician Terence Tao and AI, specifically ChatGPT-5 Pro, in exploring the potential of AI in mathematical research [2][3] - Tao's experience emphasizes the importance of evaluating AI tools from multiple perspectives to understand their value [3][14] Research Process - The problem addressed involves determining whether a smooth immersed sphere in R^3 with principal curvatures bounded by 1 encloses a volume at least equal to that of a unit sphere [7] - AI proved useful in small-scale tasks such as specific calculations, while its assistance was limited in medium-scale tasks like strategy selection [7][12] - At a macro level, AI demonstrated value in understanding the overall structure and key difficulties of the problem [7][14] AI's Contributions - AI accurately computed necessary quantities and provided a complete proof for the star-shaped case, utilizing both familiar and novel mathematical tools [9][10] - Tao was surprised by AI's ability to derive a proof in just one line, which led him to further validate AI's steps [10] - AI also suggested a numerical approach to tackle the problem, although it was recognized as a brute-force method lacking theoretical insight [11][12] Challenges and Limitations - Despite AI's strong performance in specific calculations, Tao recognized the need for a differential geometry expert to make substantial progress [12][14] - AI's tendency to reinforce Tao's incorrect assumptions at the medium scale highlighted its limitations in strategic decision-making [13][14] - The core difficulty of the problem was identified as understanding extreme non-round geometries, which AI did not adequately address [13][14] Conclusion - Tao concluded that while AI can be beneficial in exploring mathematical problems, caution and contextual awareness are essential to avoid being misled by seemingly plausible intuitions [17]