Recent years have seen an interest in the generic structure of empirical research articles across a variety of disciplines. However, significantly less attention has been given to theoretical articles. This study aims to begin to address this imbalance by presenting the results of an investigation into the organizational and rhetorical structure of theoretical pure mathematics research articles. The data set combines a close analysis of 22 peer-reviewed articles and semi-structured interviews with their authors. While there is considerable variation in terms of the major section headings and content, the results reveal an overall structure that differs from a typical empirical research article. We argue that this alternative structure is produced by the dual argumentation—mathematical and meta-mathematical—which runs throughout the text. Moreover, triangulation with the interview data indicates that the structural patterns of the theoretical pure mathematics research article can be viewed as a reflection of the research practices and epistemology of the discipline.