Audience role in mathematical proof development

Abstract

The role of audiences in mathematical proof has largely been neglected, in part due to misconceptions like those in Perelman & Olbrechts-Tyteca (1969) which bar mathematical proofs from bearing reflections of audience consideration. In this paper, I argue that mathematical proof is typically argumentation and that a mathematician develops a proof with his universal audience in mind. In so doing, he creates a proof which reflects the standards of reasonableness embodied in his universal audience. Given this framework, we can better understand the introduction of proof methods based on the mathematician's likely universal audience. I examine a case study from Alexander and Briggs's work on knot invariants to show that we can fruitfully reconstruct mathematical methods in terms of audiences.

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

“…Argumentation, they claimed, was distinct from mathematics since argumentation was both social and the conclusions were probable (Perelman and Olbrechts-Tyteca, 1969). But barring mathematical practice from the domain of argumentation is inapproporiately limiting (Dufour, 2013;Ashton, 2018Ashton, , 2021. Misfeldt and Johansen's interviews indicate that mathematicians consider the interest of other mathematicians while choosing problems.…”

“…In addition to the internalized sceptic, one of us has argued that the audience under consideration in a proof is actually a universal audience (Ashton, 2021). This is a concept drawn from Perelman and Olbrechts-Tyteca: an argument to the universal audience is one that is meant to convince all people.…”