What do people think of when they think of "math?" We propose that individuals may have very different working definitions of the category of math, and that those with broader math conceptions may have less math anxiety. In Study 1, we introduce a method for indexing the "breadth" of individuals' math conceptions, and show that there is an inverse relation between conception breadth and math anxiety. These results suggest that math anxiety is related both to how expansive individuals perceive math to be, and how skillful they feel at the activities they think it could involve. Study 2 attempts an intervention on middle school students' conceptions of math. We find the same inverse relationship between students' math conception breadth and anxiety as found in adults. We discuss ongoing work that further explores qualitative variation in math conceptions, and the lessons this may hold for intervening on math anxiety.