Mathematicians have long claimed that the aesthetic plays a fundamental role in the development and appreciation of mathematical knowledge. To date, however, it has been unclear how the aesthetic might contribute to the teaching and learning of school mathematics. This is due in part to the fact that mathematicians' aesthetic claims have been inadequately analyzed, making it difficult for mathematics educators to discern any potential pedagogical benefits. This article provides a pragmatic analysis of the roles of the aesthetic in mathematical inquiry. It then probes some of the beliefs and values that underlie mathematical aesthetic responses and reveals the important interplay between the aesthetic, cognitive, and affective processes involved in mathematical inquiry.