PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
How and Why Mathematicians Read Proofs: An Exploratory Qualitative Study and a Confirmatory Quantitative Study
Page: 1-496
In this paper, we investigate how and why mathematicians read the published proofs of their colleagues. Based on qualitative interviews with nine mathematicians, we posit that mathematicians understand proofs in three ways: as cultural artifacts with a social history, as a sequence of inferences, and as the application of methods. Each type of understanding is based, at least in part, on non-deductive evidence. A survey with 118 mathematicians confirms the generality of these findings. We conclude by arguing that more comprehensive frameworks for how mathematicians gain conviction are needed.