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The Dialectical Theorem: The future of universities, mathematics departments, and training of human mathematicians

  • Thomas Koberda
  • Alex Kontorovich
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Abstract

We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we explore why human mathematical expertise might nevertheless remain valuable, what kinds of expertise universities should cultivate, and how graduate education might adapt. We also discuss the institutional and economic uncertainties that threaten the continued existence of a thriving mathematical profession, even if the value of human mathematical understanding endures.

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Cite

BibTeXRIS
BibTeX
@misc{koberda2026dialectical,
  title = {{The Dialectical Theorem: The future of universities, mathematics departments, and training of human mathematicians}},
  author = {Thomas Koberda and Alex Kontorovich},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14362},
  eprint = {2610.14362},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14362},
}
RIS
TY  - UNPB
TI  - The Dialectical Theorem: The future of universities, mathematics departments, and training of human mathematicians
AU  - Thomas Koberda
AU  - Alex Kontorovich
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.14362
UR  - https://arxiv.org/abs/2610.14362
AB  - We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we explore why human mathematical expertise might nevertheless remain valuable, what kinds of expertise universities should cultivate, and how graduate education might adapt. We also discuss the institutional and economic uncertainties that threaten the continued existence of a thriving mathematical profession, even if the value of human mathematical understanding endures.
ER  -