Mathematics has the highest attrition rate among all liberal arts disciplines (and among all disciplines, except for health professions) and the second highest attrition rate of all doctoral programs in the United State. In order to prevent the loss of so many students, mathematics departments must consider the root causes for attrition and determine what individual skills and knowledge and departmental systems and support will help more mathematics doctoral students to succeed. The purpose of this qualitative interview study was to explore the interactions mathematics doctoral candidates at one institution have had during graduate school and the value that the students place on the interactions in their continued pursuit of and success in doctoral study of mathematics. Nine doctoral candidates from the mathematics department at a large, public research university in the Southeastern United States who had attended United States schools throughout their K-graduate education agreed to participate in the study. I conducted a series of two, semi-structured, approximately sixty minute, one-on-one interviews with each participant. In addition to providing insight into the nature of several relationships already established in the extant research, the results of the present study indicated the possible existence of three new relationships. A series of themes were also found across the students’ experiences that depict key interactions participants had with peers and faculty and the meaning and value given to these interactions. For faculty, the themes were (1) Inadequacy and Importance, (2) Being Uninformed, (3) Self-Sufficiency, and (4) Collaboration; and for peers, (1) Insight Versus Deficit and (2) Gauging Their Experience. In addition, Living in a World of Paradoxes was an overarching theme in the findings. This study informs several lines of thought: (a) collaboration is more than just a crutch; (b) graduate students struggle to find a balance between independent scholar and active collaborator; (c) graduate school is not a uniform experience; (d) knowing and learning in mathematics is conceived from the cognitive perspective; and (e) there are multiple paths for socializing students. Recommendations for future research and practice are also presented.