Educators often argue that mathematics should be taught so that the students in the course are actually "doing mathematics." Is there a consensus among mathematicians and mathematics educators as to the meaning of "doing mathematics?" In an effort to answer this question, we administered a survey to hundreds of university-level mathematics and mathematics education faculty members. Participants ranked the importance of various mathematical activities and also responded to several open-ended questions. Responses to the open-ended questions were analyzed qualitatively to identify patterns. In this paper, we discuss the patterns we observed in analyzing the survey data, with a particular focus on the similarities and differences between mathematicians and mathematics educators.