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

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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.

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Notes

  1. As ranked by the USNews.com “Best Graduate Schools” list of “top mathematics programs.”

  2. The items in Table 1 are organized and named by general theme (not any particular construct): questions regarding the purpose of reading proofs are named as P_, items related to the use of examples are named E_, questions regarding proofs as application of methods are named M_, items related to contextual/cultural aspects of proof are named C_, and foils are named F_. Participants completing this survey were not aware to which theme the questions belonged to. We did not necessarily anticipate a high correlation between survey items for each theme as in some cases they were discussing ideas that seemed to be very different.

  3. One of the 55 participants who stated he/she had refereed a mathematics research paper submitted for publication did not answer any questions in the refereeing section of the survey.

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  1. Rutgers University, New Brunswick, NJ, USA

    Juan Pablo Mejia-Ramos & Keith Weber

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  1. Juan Pablo Mejia-Ramos
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Correspondence to Juan Pablo Mejia-Ramos.

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Mejia-Ramos, J.P., Weber, K. Why and how mathematicians read proofs: further evidence from a survey study. Educ Stud Math 85, 161–173 (2014). https://doi.org/10.1007/s10649-013-9514-2

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