arXiv:2610.31804v1 Announce Type: new 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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