Issues of authority abound in education and schooling but have not been interrogated sufficiently. We describe a tool that we have developed to initiate dialogue with teachers about authority in their classrooms--using a diagram to represent authority in their classrooms. Our analysis of the diagrams mathematics teachers created and discussed in our work with them illustrates the importance of understanding teachers' perspectives about authority. To understand better how mathematics teachers think about the authority in their classrooms, we investigated what sources of authority they represented in their diagrams, and how the teachers related these sources to each other. The diversity in the teachers' representations exceeded our anticipations, indicating that research on authority in classrooms has merely scratched the surface of understanding the ways mathematics teachers think about authority in their classrooms.