“Let G = (V, E) be a graph”: Turning the abstract into the tangible in introductions in mathematics research articles

• Introductions in math RAs use some CARS model moves but not in chronological order.
• Math RAs may have a complementary introduction to highlight topic information.
• ‘Establishing presumptions’ is often the initiating move in math RAs.

While academic writing, especially the research article (RA), has been widely studied for its generic structure, organizational patterns, and linguistic features in a broad cross-section of disciplines, relatively little attention has been devoted to this genre in mathematics. This paper explores the rhetorical structure of introductory sections of RAs in mathematics. Using Swales' (1990) and 2004 CARS (Create a Research Space) models as points of departure, the study investigates the move structure used in the introductory material in 30 RAs in mathematics. The results suggest that the move structure of RAs in mathematics departs somewhat from patterns identified in other disciplines; notably, that ‘establishing presumptions’ about abstract mathematical objects is an essential building block for setting arguments about knowledge claims in mathematics. Authors in mathematics establish their presumptions as well as employ variations on the Swalesian moves to successfully Create a Research Space. We propose that these variations arise out of the hypothetical nature of the mathematical concepts, and the social grounds of mathematics as a logic-driven, argumentation-mediated discipline. These results have implications for using a genre-based approach in EAP classes of mathematics.