Abstract

When thinking about the concept of proof in mathematics, the connection to conviction and certainty seems inevitable. The task of the proof in mathematics is supposedly to convince someone of the truth of a proposition. Proof then appears to be a monolithic concept, and our requests for proof appear to be motivated by a single, uniform need: to be persuaded. A natural reaction to this seeming uniformity is a will to explain why a proof can have this convincing effect. It is, however, worth considering whether this tight association between proof and certainty does justice to the concept of proof. This essay explores our need for proofs through the consideration of an example of a simple rule of arithmetic, which one wants to see proven. This shows that there may different motives behind a request for a proof and that some of these do not necessarily stem from a need to be persuaded. A proof could have provided an answer but something else might have been sufficient too. Thus, in mathematical practice proofs are found to perform different tasks and cannot be understood exclusively in terms of conviction. This has consequences for the philosophical understanding of mathematics in general.