# Why and how mathematicians read proofs: an exploratory study

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## Abstract

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, *Journal for Research in Mathematics Education* 39:431–459, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line-by-line reading, and modular reading. We argue that non-deductive reasoning plays an important role in each of these three strategies.

## Keywords

Advanced mathematical thinking Argumentation Mathematical practice Proof Proof comprehension Proof reading Validation## Notes

### Acknowledgments

The research in this paper was supported by a grant from the National Science Foundation (NSF #DRL0643734). The views expressed here are not necessarily those of the National Science Foundation. We would like to thank Sean Larsen for helpful insights on developing our theoretical model, as well as the anonymous reviewers for their comments on earlier drafts of this manuscript.

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