This paper examines the mechanisms by which students' cultural background plays an active role in the study of mathematics. It does so with the aid of two main constructs: hybrid discourse and intellective identities. At the center of the article is an analysis of a classroom episode from a preparatory program in which adult ultra-orthodox Jews study high school mathematics for the first time. We show how different cultural resources, among them students' cultural preference for disagreement, are being used to create a new hybrid discourse of mathematics and the Talmud while discussing the veracity of a mathematical proof. The hybridity can be seen in four characteristics of discourse: routines for endorsement of narratives, interactional routines, authority structure, and purpose of learning. We elaborate on the process by which this hybridity is constructed through students' positioning actions and the ways in which these positions are supported by students' intellective identities.