{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28140",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Koberda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fze3kn6hc5bfb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28140",
  "fulltext_url": null,
  "id": "fze3kn6hc5bfb",
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  "landing_url": "https://arxiv.org/abs/2609.28140",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ],
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      "openalex",
      "3600|Doctoral Education Challenges and Solutions"
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  "openalex": "W7214177392",
  "pdf_url": "https://arxiv.org/pdf/2609.28140",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fze3kn6hc5bfb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28140",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28140"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.HO",
      "subfield": "general"
    }
  ],
  "title": "Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis",
  "title_text": "Training Mathematicians in the Age of AI: Intellectual Agency, Cognitive Offloading, and the PhD Thesis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/fze3kn6hc5bfb",
  "venue": "arXiv",
  "versions": []
}