Abstract

What does rhetoric, the study of argument and persuasion, have to do with mathematics, the study of patterns of relations (in number, geometry, topology, …) and their necessary entailments? The following chapter explores a growing body of research that seeks to address this question – scholarship that pursues the counterintuitive idea that rhetoric and mathematics might just have more to do with each other than we have been taught to believe. It argues that many of the seeds for contemporary study of rhetoric and mathematics emerge from Imre Lakatos’s tour de force, Proofs and Refutations. There we find a rejection of mathematical formalism and the telos of absolute truth, an emphasis on the arts of mathematical practice, and a model of informal mathematics that positions rhetorical argument as an engine of mathematical innovation. The book thus opens the way, however unintentionally, for understanding informal mathematics as intimately intertwined with rhetorical practice. The chapter concludes with discussion of how contemporary scholars have built upon Lakatos’s work and, in recent years, expanded beyond it.