“Since Hadwiger's conjection … is still open”: Establishing a niche for research in discrete mathematics research article introductions

'Establishing a niche' has been shown to be an important rhetorical strategy in research genres to argue for the need for new research. Limited research has focused on this aspect of the rhetorical structure in research article introductions (RAIs) in mathematics. This genre-based study investigates how writers in discrete mathematics establish a niche for their research. We identify five steps that discrete mathematicians choose from among or combine to establish both a niche for and the significance of their work. In examining the implications of our findings for novice writers in the field, we propose slight modifications to the CARS model to accommodate the practices of writers in discrete mathematics and to assist newcomers in understanding the crucial features of structuring RAIs in this field.