Skip to content
DraconiticResearch
Search Sources API
201,683 studies31 sourcesUpdated 54 min ago
PreprintarXiv licencearXiv

Mathematics Graduate Training in the Age of AI

  • David Glickenstein
Open at sourcePDFDOICite

Abstract

Generative AI changes the conditions under which graduate mathematics is learned, assessed, written, and defended. The central claim of this paper is that mathematics graduate programs should respond to the moment by clarifying what graduate mathematics education is trying to teach and assess. In most ways, the goals of mathematics education have not changed. Rather, with changing tools it has become more essential than ever to make clear the goals of mathematical training. We use the term mathematical judgment to refer to the capacity to evaluate mathematics (e.g., claims, definitions, examples, proofs, analogies, computations, uses of tools, research directions) as mathematically sound, useful, well-posed, and appropriately justified. The recommendation is to center training on mathematical judgment, and we examine possible policies for graduate programs in Mathematics to this end.

Related

  1. Graduate Mathematics in the Age of AI: Forming Mathematicians for Original, Independent, and Responsible Inquiry
    Bacim Alali
    arXivPreprintCC BY-NC-ND 4.0Full textGeneral mathematicsarXiv
  2. The Dialectical Theorem: The future of universities, mathematics departments, and training of human mathematicians
    Thomas Koberda, Alex Kontorovich
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  3. Reorganizing Graduate Statistical Inference for Modern Biostatistical Practice
    Raphael C Kim, Michele Santacatterina
    arXivPreprintCC BY 4.0Full textStatisticsarXiv
  4. What professional knowledge of mathematics do CLIS teachers need?
    Teresa Assude, Jeannette Tambone, Aliette Vérillon
    La nouvelle revue de l'adaptation et de la scolarisationPeer-reviewedLicence not statedFull text7 citedGeneral mathematicsHAL
  5. Domain-Specific Mathematics Performance of Grade 8 Students: Evidence from a K to 12 Achievement Test
    Raymart Gorosin, Laila Teressa Bersoto, Febraida Mendiola +3
    Psychology and Education: A Multidisciplinary JournalPeer-reviewedLicence not statedFull textGeneral mathematicsHAL

Cite

BibTeXRIS
BibTeX
@misc{glickenstein2026mathematics,
  title = {{Mathematics Graduate Training in the Age of AI}},
  author = {David Glickenstein},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21132},
  eprint = {2609.21132},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21132},
}
RIS
TY  - UNPB
TI  - Mathematics Graduate Training in the Age of AI
AU  - David Glickenstein
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.21132
UR  - https://arxiv.org/abs/2609.21132
AB  - Generative AI changes the conditions under which graduate mathematics is learned, assessed, written, and defended. The central claim of this paper is that mathematics graduate programs should respond to the moment by clarifying what graduate mathematics education is trying to teach and assess. In most ways, the goals of mathematics education have not changed. Rather, with changing tools it has become more essential than ever to make clear the goals of mathematical training. We use the term mathematical judgment to refer to the capacity to evaluate mathematics (e.g., claims, definitions, examples, proofs, analogies, computations, uses of tools, research directions) as mathematically sound, useful, well-posed, and appropriately justified. The recommendation is to center training on mathematical judgment, and we examine possible policies for graduate programs in Mathematics to this end.
ER  -