Summary: 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, Keith: How mathematicians determine if an argument is a valid proof. J. Res. Math. Educ. 39, No. 4, 431-459 (2008); ME 2009d.00297] 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.