Abstract

A characteristic feature of the philosophy of mathematical practice is to attend to what people do when they do mathematics. But what does it mean to do mathematics? This question raises several issues regarding the nature of action, activity, and agency in mathematical practice. The present chapter reviews contributions in the field that have attempted to theorize about these notions. It begins with some motivations for taking agents seriously in the philosophical study of mathematical practice. The core of the chapter discusses, in turn, what it means to carry out mathematical activities, do things with mathematical artifacts, engage with mathematical proofs, and perform mathematical actions prescribed by mathematical texts. Taken together, the various lines of work reported here provide an initial, but already sophisticated, picture of what it means to do mathematics. The chapter ends with some suggestions for future research on agency in mathematical practice.