In this article, nine mathematicians were interviewed about their why and how they presented proofs in their advanced mathematics courses. Key findings include that: (1) the participants in this study presented proofs not to convince students that theorems were true but for reasons such as conveying understanding and illustrating methods, (2) participants believed students did not appreciate the complex processes involved in reading a proof but often did not teach these processes to students, (3) the participants used superficial methods to assess students' understanding of a proof and (4) some participants questioned whether proof was the best way to convey mathematics to all of their students. (Contains 3 tables and 5 notes.)