In this study of the cultural history of mathematics, I consider the architecture of mathematical institutes as historical artifacts. The buildings in which mathematical research and teaching take place offer incredible insight into the work practices, as well as social and cultural identities, of the mathematicians who inhabit these spaces. As a case study, I consider the career of the mathematician Richard Courant (1888-1972), who served as director during the construction of two world-class mathematical institutes – the first, in the late 1920s at the University of Göttingen (where he was exiled in 1933), and then in the 1960s at New York University. In both cases, I consider the buildings’ planning, development, construction, and habitation processes, examining blueprints, committee meeting minutes, and correspondence between the mathematicians, university administrators, government officials and philanthropy representatives. Ultimately, I hope to explore how the built environment mattered to those whose work required a certain type of private workspace, desk, and chalkboard –- situated in the right relationship to shared workspaces, a mathematics library, classrooms, and other scientific departments. What can the physical environment of mathematical institutes tell the historian about the work practices and social identities of mathematicians?