Why and how mathematicians read proofs: further evidence from a survey study

Abstract

In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N = 118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians.