The birth and decline of disciplines are critical to science and society. However, no quantitative model to date allows us to validate competing theories of whether the emergence of scientific disciplines drives or follows the formation of social communities of scholars. Here we propose an agent-based model based on a \emph{social dynamics of science,} in which the evolution of disciplines is guided mainly by the social interactions among scientists. We find that such a social theory can account for a number of stylized facts about the relationships between disciplines, authors, and publications. These results provide strong quantitative support for the key role of social interactions in shaping the dynamics of science. A "science of science" must gauge the role of exogenous events, such as scientific discoveries and technological advances, against this purely social baseline.