Ascertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics

Abstract

For decades, university mathematics assessed executable procedure, computing and reproducing standard proofs, as a proxy for the understanding it cared about, because procedure was cheap to mark and understanding was not. Generative AI now executes much of this procedure. It does not merely let students bypass the proxy; it exposes how much of what was certified was a proxy. The crisis is not simply cheating but a proxy problem, and resolving it forces a question the discipline has long avoided: what is the irreducible human core of mathematical competence, and how can it be built when some of the executable work can be offloaded? We set out two futures: displacement-and-re-centering, in which AI takes over some execution and education moves toward judgment, formulation and verification; and atrophy, in which premature offloading may erode capacities that depend on prior construction. At the heart of the optimistic future is a verification instability: some forms of oversight are cheap and bounded, while others approach the competence required to construct the work. The outcome is a design choice, not a technological destiny. Rather than add a model, we state the response as two principles: construct before you delegate, and let verification set the ceiling: how far a student can independently verify AI output limits what they may safely delegate. We illustrate with a sequence and two worked problems, and close on the question: whether the construct-before-delegate dependency is a hard constraint or an artefact of how mathematics has been taught.

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BibTeX RIS

BibTeX

@misc{osano2026ascertaining,
  title = {{Ascertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics}},
  author = {Bob Osano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03844},
  eprint = {2610.03844},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03844},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Ascertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics
AU  - Bob Osano
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03844
UR  - https://arxiv.org/abs/2610.03844
AB  - For decades, university mathematics assessed executable procedure, computing and reproducing standard proofs, as a proxy for the understanding it cared about, because procedure was cheap to mark and understanding was not. Generative AI now executes much of this procedure. It does not merely let students bypass the proxy; it exposes how much of what was certified was a proxy. The crisis is not simply cheating but a proxy problem, and resolving it forces a question the discipline has long avoided: what is the irreducible human core of mathematical competence, and how can it be built when some of the executable work can be offloaded? We set out two futures: displacement-and-re-centering, in which AI takes over some execution and education moves toward judgment, formulation and verification; and atrophy, in which premature offloading may erode capacities that depend on prior construction. At the heart of the optimistic future is a verification instability: some forms of oversight are cheap and bounded, while others approach the competence required to construct the work. The outcome is a design choice, not a technological destiny. Rather than add a model, we state the response as two principles: construct before you delegate, and let verification set the ceiling: how far a student can independently verify AI output limits what they may safely delegate. We illustrate with a sequence and two worked problems, and close on the question: whether the construct-before-delegate dependency is a hard constraint or an artefact of how mathematics has been taught.
ER  -

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