陶哲轩 Caltech 演讲 Math 2.0：只追求解题会损害数学长期健康
Terence Tao's slide from the lecture he gave yesterday evening at Caltech “Math 2.0”
陶哲轩在 Caltech 的 Math 2.0 演讲中表示，AI 已能攻克过去难以触及的问题，但仅以解题为目标对数学长期健康有害。他认为纯数学中的开放问题更像灯塔，用于指引探索周边数学图景，而非终点；尝试解题过程中成功、失败或部分进展所获得的经验，往往比最终答案更有价值。他警告自动化工具过早抵达这些灯塔，会扰乱对未走路径的探索并让周边领域失去活力，不加区分地用 AI 以不可再生的方式解题，会损害学科长期进步及向更复杂的现实应用的迁移。
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Terence Tao's slide from the lecture he gave yesterday evening at Caltech “Math 2.0”
AI can now crack open problems that were once out of reach, and he says that is the wrong thing to celebrate on its own. Basically he says chasing problem-solving alone is hurting math.
> “Further blind optimization of problem-solving alone is now actively harmful to the long-term health of mathematics.”
> “Contrary to popular opinion (or some of our own marketing), mathematicians are not singularly focused on solving open problems.”
> “Particularly in pure mathematics, open problems serve as “lighthouses”: not destinations to be reached in and of themselves, but as useful guides to explore the mathematical landscape around these problems.”
> “The lessons learned while attempting to solve these problems — whether they succeed, fail, or achieve partial progress — are often more valuable than the final solution to the problem itself.”
> “Reaching these lighthouses prematurely by automated tools can disrupt the exploration of the paths not taken, and sterilize the surrounding field.”
“Indiscriminate use of AI to solve problems in a non-renewable fashion damages the long-term health and progress of the field, as well as safe transfer to messier, real-world applications.”