THE RHETORIC OF MATHEMATICAL PROOFS: COMMON STYLISTIC FEATURES 1 Annie Selden John Selden Mathematics Department Math Ed Resources Co. Tennessee Technological University P.O. Box 2781 Cookeville, TN 38505 U.S.A. Cookeville, TN 38502 U.S.A. We point out seven features that appear to partly constitute a distinctive rhetorical style in which mathematical proofs are written. As evidence for this, we report on a mathematics journal survey and on interviews with eight mathematicians. We also report on a survey of U.S. undergraduate "transition course" textbooks that suggest this style is part of the implicit, but not the explicit, curriculum. We conjecture that this style is useful in minimizing certain kinds of validation errors, i.e., errors in checking the correctness of proofs, and is thus important in learning to construct proofs. Finally, we suggest that it might be useful to treat this style explicitly when introducing undergraduate students to writing proofs. Ernest (1998) has pointed out that from a social constructivist view of mathematics, with its heavy emphasis on social acceptance, rhetoric should play a large role in understanding the nature of mathematics and how it is taught. In addition, mathematicians who often take a contrasting, less relativistic, more Platonic view of mathematics tend to regard the truth of theorems as determined by their proofs. Both of these views suggest that the way or style in which proofs are written is an important aspect of mathematical practice that undergraduate and graduate students in advanced courses should understand. In this paper we report on an exploratory study of the style in which proofs are written. While more work is needed, e.g., in examining a wide selection of mathematics journals, observing proofs presented in undergraduate classes, in interviewing a wider selection of mathematicians, and in examining proofs in languages other than English, these preliminary results suggest that mathematical proofs really are written in a distinctive, characterizable, and remarkably robust style which is part of the implicit curriculum. Since it seems to be common knowledge that mathematical proofs are difficult for novices to comprehend, this leads us to the question of whether their style yields some other benefit. We conjecture that it does and will offer an analysis suggesting that this style may tend to minimize certain kinds of validation errors, i.e., errors in the process of checking the correctness of 1 Partially supported by National Science Foundation Grant # 9355841.