Epistemic Roles of Diagrams in Short Proofs

Recent case studies in the philosophy of mathematical practice have pointed out that certain types of diagrams play epistemic roles in mathematical proofs. To complement such case studies and provide a quantitative basis for further analysis and discussions, we undertake an empirical study based on a large and contemporary corpus of mathematical texts. Following an a priori assumption that diagrams in short proofs carry more epistemic warrant, we focus on 1- or 2-sentence proofs that refer to diagrams, and we build a corpus of such proofs from the arXiv. Based on this corpus we analyze and develop a typology of such proofs in order to conduct selected qualitative close-readings of diagrams in their argumentative contexts. This leads us to discuss tensions between visual and syntactical aspects of diagrams that suggest that hybrid diagrams play distinct roles in mathematical practice.