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arXiv · 2609.28140

Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis

Thomas Koberda
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Abstract

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.

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Thomas Koberda. 2026-09-23. Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis. https://arxiv.org/abs/2609.28140

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