In this talk, I'll describe some approaches to agentic ai for exploratory research, for facilitating understanding of mathematics, for aiding in writing and editing of manuscripts, and some of the ways in which these ideas come together. To illustrate, I will take examples from some of my own work, both prior as well as work in progress. In particular, I will say a bit about problems related to Chow groups of homegeneous varieties and questions of indecomposability of finite dimensional division algebras.