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This article discusses some methods of describing and referring to mathematical objects and of consistently and unambiguously signaling the logical structure of mathematical arguments.
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On the Communication of Mathematical Reasoning∗ Atish Bagchi and Charles Wells June 12, 1998 ∗ Any reference to this paper should say “PRIMUS vol. 8, pages 15–27 (1998)”. PRIMUS stands for “Problems, Resources and Issues in Mathematics Undergraduate Studies” and its home page is at http://www.dean.usma.edu/math/resource/pubs/ primus/index.htm. 1 Contents 1 Introduction 2 2 Referring to mathematical objects 2.1 Suggestive names . . . . . . . . . . . . . 2.1.1 Cultural dependence . . . . . . . 2.1.2 Cognitive dissonance . . . . . . . 2.1.3 Overdependence on connotations 2.2 Type labeling . . . . . . . . . . . . . . . 2.3 Associating fonts to types . . . . . . . . 2.4 Suppression of parameters . . . . . . . . 2.5 Mnemonic Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 3 3 4 5 5 6 6 3 Definitions 7 4 Signaling logical structure 8 5 Consistent usage in proofs 11 5.1 The Telegraphic Style . . . . . . . . . . . . . . . . . . . . . . 11 Abstract This article discusses some methods of describing and referring to mathematical objects and of consistently and unambiguously signaling the logical structure of mathematical arguments. Key words Mathematical exposition, mathematical argument, formal reasoning, symbolic logic, proofs, terminology. 1 Introduction This art