Mathematical proofs and narratives may seem to be opposites. Indeed, deductive arguments have been highlighted as clear examples of non-narrative sequences by narrative theorists. I claim that there are important similarities between mathematical proofs and narrative texts. Narrative texts are read in a quite distinct way, and I argue that mathematical proofs are often read like narrative texts by research mathematicians. In this way, narratives play an important role in mathematical knowledge-making. My argument draws on recent empirical data on how mathematicians read proofs. Furthermore, my examination of mathematical proofs and narratives provides an account of what it means for research mathematicians to understand mathematical proofs.

This chapter investigates deductive practices in what is arguably their main current instantiation, namely practices of mathematical proofs. The dialogical hypothesis delivers a compelling account of a number of features of these practices; indeed, the fictive characters Prover and Skeptic can be viewed as embodied by real-life mathematicians. The chapter includes a discussion of the ontological status of proofs, the functions of proofs, practices of mathematicians such as peer review and collaboration, and a brief discussion of probabilistic and computational proofs. It also discusses three case studies: the reception of Gödel’s incompleteness results, a failed proof of the inconsistency of Peano Arithmetic, and a purported proof of the ABC conjecture.