How Do Mathematicians Learn Mathematics?

In this paper, I present preliminary results of a study investigating how experts make sense of unfamiliar mathematical phenomena. Specifically, 10 mathematics graduate students and professors thought aloud and responded to questions as they read and tried to understand an unfamiliar, but accessible, mathematical proof in the domain of geometric topology. Interview data was coded for experts' descriptions of their own understanding of the mathematical phenomena presented, and for instances in which experts systematically linked different types of knowledge to make sense of new information. While experts' pre-existing and post-interview understandings of the topics presented varied, general strategies for connecting specific types of information to make sense of the proof were identified across participants.