AI时代的数学家培养：智力主体性、认知外包与博士论文
Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis
AI总结：
本文主张在AI时代，研究生数学教育应围绕智力主体性培养，区分生产性与过早认知外包，提出独立与AI增强互补的训练模式，并重新定义博士论文与答辩的角色，使学术数学成为人类数学专业知识的再生产与管理机构。
AI中文摘要：
强大的人工智能正在削弱数学产出与数学专业知识证据之间的传统关系。特别是，原创定理的产出或一篇精雕细琢的学位论文，本身已不再能证明其名义作者的智力素养。我认为，研究生数学教育因此应围绕智力主体性的培养来组织：即内部技术能力、数学判断力、理解力以及对共享智力文化的负责任参与。我区分了生产性认知外包与过早认知外包，提出了互补的独立训练模式和AI增强训练模式，并建议对博士论文和论文答辩的角色进行相应的重新定义。更广泛地说，我认为学术数学应日益将自身理解为一种用于再生产和管理人类数学专业知识的机构，而非主要作为产生定理的机制。
英文摘要：
Powerful artificial intelligence is weakening the traditional relationship between mathematical output and evidence of mathematical expertise. In particular, the production of an original theorem or a polished dissertation can no longer, by itself, certify the intellectual formation of its nominal author. I argue that graduate mathematical education should therefore be organized around the formation of intellectual agency: internal technical competence, mathematical judgment, understanding, and responsible participation in a shared intellectual culture. I distinguish productive from premature cognitive offloading, propose complementary independent and AI-augmented modes of training, and suggest a corresponding reformulation of the role of the PhD thesis and dissertation defense. More broadly, I argue that academic mathematics should understand itself increasingly as an institution for the reproduction and stewardship of human mathematical expertise rather than primarily as a mechanism for producing theorems.
