Abstract

In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in the history of mathematics. In this framework, proof is understood not as a purely syntactic object, but as a social process that involves at least two agents; this highlights the communicational aspect of proving. We argue that historians of mathematics primarily study proof-events in their research, as the mathematical proofs they encounter in extant sources often involve informal components that are not entirely formalizable and convey semantic content that requires understanding and verification. We illustrate the application of this methodological approach in some outstanding historical cases, paying particular attention to the process of proof interpretation that brings a proof-event to life. Finally, we suggest a classification of proof-events, according to the conditions imposed upon problem-solving. This enables us to speak about broad classes of proof-events in the history of mathematics that share a common characteristic.