Research profiles and the mathematical landscape: A grassroots proposal for mathematics with AI
Abstract
Repeated mathematical work with AI leaves behind corrections, failed arguments, and sometimes useful ways of asking questions. I propose keeping these in a research profile that the mathematician develops and controls. The profile marks parts of the mathematical landscape according to the researcher's understanding and makes those markings available to later work with AI. This suggests experiments with individual profiles, shared readings of papers, and graduate education. It also raises mathematical questions about the landscape itself: its connections, distances, and changes under discovery. I describe two examples, searching for branches of mathematics with a common base and recovering useful questions from the history of Floer theory. The aim is to give mathematicians something to try and a part in deciding how mathematical AI develops.
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BibTeX
@misc{hofer2026research,
title = {{Research profiles and the mathematical landscape: A grassroots proposal for mathematics with AI}},
author = {Helmut H. W. Hofer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31804},
eprint = {2610.31804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31804},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Research profiles and the mathematical landscape: A grassroots proposal for mathematics with AI
AU - Helmut H. W. Hofer
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31804
UR - https://arxiv.org/abs/2610.31804
AB - Repeated mathematical work with AI leaves behind corrections, failed arguments, and sometimes useful ways of asking questions. I propose keeping these in a research profile that the mathematician develops and controls. The profile marks parts of the mathematical landscape according to the researcher's understanding and makes those markings available to later work with AI. This suggests experiments with individual profiles, shared readings of papers, and graduate education. It also raises mathematical questions about the landscape itself: its connections, distances, and changes under discovery. I describe two examples, searching for branches of mathematics with a common base and recovering useful questions from the history of Floer theory. The aim is to give mathematicians something to try and a part in deciding how mathematical AI develops.
ER -