Using the work of philosopher Henri Bergson (1859-1941) to examine the nature of movement and memory, this article contributes to recent research on the role of the body in learning mathematics. Our aim in this paper is to introduce the ideas of Bergson and to show how these ideas shed light on mathematics classroom activity. Bergson's monist philosophy provides a framework for understanding the "materiality" of both bodies and mathematical concepts. We discuss two case studies of classrooms to show how the mathematical concepts of number and function are themselves "mobile" and full of "potentiality", open to deformation and the remapping of the (im)possible. Bergson helps us look differently at mathematical activity in the classroom, not as a closed set of distinct interacting bodies groping after abstract concepts, but as a dynamic relational assemblage.