Varieties Of Mathematical Prose

Varieties of Mathematical Prose ∗ Atish Bagchi and Charles Wells June 12, 1998 Abstract This article begins the development of a taxonomy of mathematical prose, describing the precise function and meaning of specific types of mathematical exposition. It further discusses the merits and demerits of a style of mathematical writing that labels each passage according to its function as described in the taxonomy. Key words Mathematical exposition, writing style, mathematical argument, formal reasoning, symbolic logic, definitions, proofs, terminology, hypertext. 1 1.1 Introduction Rationale Many students of mathematics are not experienced in reading mathematics texts. They may not understand the nature and use of definitions. Even if they do, they may not easily distinguish between a definition and an informal discussion of a topic. They may not pick up on the use of a word such as “group” that has a meaning in ordinary discourse but that has been given a special technical meaning in their text. They may not distinguish a plausibility argument from a careful proof, and in reading a careful proof they may not grasp the significance of the words and phrases the author uses to communicate the logical structure of the proof. ∗ Any reference to this paper should say “PRIMUS vol. 8, pages 116–136 (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 A