The paper “Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis” by Thomas Koberda examines how powerful AI systems are changing what it means to train as a mathematician. The central problem is that producing an original theorem, solving difficult problems, or even writing a polished PhD dissertation is increasingly possible with substantial AI assistance, so these outputs can no longer by themselves demonstrate that a student has developed genuine mathematical expertise.
Koberda therefore argues that graduate education should place greater emphasis on intellectual agency: the ability to understand mathematics deeply, exercise mathematical judgment, develop technical competence, and participate responsibly in the mathematical community.
A major concept is the distinction between productive and premature cognitive offloading. AI can legitimately accelerate routine work, exploration, computation, and verification, but excessive dependence on it may prevent students from developing the internal mathematical abilities that AI is supposed to support.
The paper consequently proposes maintaining both independent, AI-free training and AI-augmented modes of research, while reconsidering the role of the PhD thesis and oral defense as demonstrations of mathematical understanding rather than simply production of novel results. More broadly, Koberda argues that universities should increasingly see mathematics education as a way of preserving and reproducing human mathematical expertise, rather than merely as a system for generating new theorems.
ARTICLE [PDF]
Koberda therefore argues that graduate education should place greater emphasis on intellectual agency: the ability to understand mathematics deeply, exercise mathematical judgment, develop technical competence, and participate responsibly in the mathematical community.
A major concept is the distinction between productive and premature cognitive offloading. AI can legitimately accelerate routine work, exploration, computation, and verification, but excessive dependence on it may prevent students from developing the internal mathematical abilities that AI is supposed to support.
The paper consequently proposes maintaining both independent, AI-free training and AI-augmented modes of research, while reconsidering the role of the PhD thesis and oral defense as demonstrations of mathematical understanding rather than simply production of novel results. More broadly, Koberda argues that universities should increasingly see mathematics education as a way of preserving and reproducing human mathematical expertise, rather than merely as a system for generating new theorems.
ARTICLE [PDF]
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