Free and open to the public.
In the analytic tradition, the philosophy of mathematics has generally focused on justification, aiming to determine the grounds for mathematical knowledge and proper methods of inference. From that perspective, a body of mathematical knowledge amounts to something like an accumulation of definitions, theorems, and proofs. I will make the case that there are important mathematical resources that cannot be understood in these terms, but merit philosophical attention nonetheless. A theory of mathematical *understanding*, in contrast to a theory of mathematical knowledge, should provide a general account of these epistemic resources. In this talk, I will clarify some of the motivating intuitions and goals, and offer some suggestions as to how we ought to proceed.