Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis
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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BibTeX
@misc{koberda2026training,
title = {{Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis}},
author = {Thomas Koberda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28140},
eprint = {2609.28140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28140},
}
RIS
TY - UNPB
TI - Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis
AU - Thomas Koberda
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28140
UR - https://arxiv.org/abs/2609.28140
AB - 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.
ER -