Abstract

This chapter argues that a revival of the philosophy of geometry is long overdue. Reconsidering writings from the first decades of the twentieth century, we find that a rich form of intellectual enquiry faded away for no good reason. The flourishing of modern geometry, especially that used in mathematical physics, calls us back to the task of understanding geometry in all its forms. With the resources of cohesive homotopy type theory available, we now have the chance to consider our deepest mathematical conceptions of space.