Audience role in mathematical proof development

The role of audiences in mathematical proof has largely been neglected, in part due to misconceptions like those in Perelman and Olbrechts-Tyteca (The new rhetoric: A treatise on argumentation, University of Notre Dame Press, Notre Dame, 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.

Automated summary

The paper argues that mathematical proof is essentially a form of argumentation with the mathematician's universal audience in mind, reflecting the standards of reasonableness embodied in that audience. By reconstructing mathematical methods in terms of audiences, the introduction of proof methods based on the universal audience can be better understood.