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Document Details : Title: Proving with Graphs Subtitle: The Mathematical Toolkit Author(s): GIARDINO, Valeria , PATRAS, Frédéric Journal: Logique et Analyse Volume: 266 Date: 2024-2025 Pages: 285-319 DOI: 10.2143/LEA.266.0.3294841 Abstract : An increasing number of studies have recently been devoted to the analysis of segments of the contemporary practice of mathematics. An important element of mathematical practice is proof, and proofs are often supplemented by diagrams and a specific terminology. Carter discusses a case in analysis in which some of the formal definitions arise from original proofs where diagrams were massively employed, irrespectively of the fact that they were then discarded from the final publication. In this paper, a case study of an article in which Feynman diagrams are indeed published as elements of a proof will be introduced. The main objective will be to try to unveil the complexities of what is accepted as a 'graphical argumentation' in an informal proof by pointing the attention towards what Connes and Kreimer defines as a 'toolkit' that is available to mathematicians, involving the familiarity with not only some form of intuition but also the appropriate context, in an interplay between different diagrammatic practices. This analysis will contribute to a wider discussion of the role of several kinds of diagrams in contemporary mathematics, going beyond geometry and across disciplines. |
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