In this paper I take a positive view of ambiguity in the learning of mathematics. Following Grosholz (2007), I argue that it is not only the arts which exploit ambiguity for creative ends but science and mathematics too. By enabling the juxtaposition of multiple conflicting frames of reference, ambiguity allows novel connections to be made. I describe a classroom episode in which students discuss their understandings of volume and surface area and in which definitional ambiguity plays a significant role. Had precise definitions been offered explicitly beforehand, the potential for rich mathematical thought would have been dramatically diminished.