Creative polymathy at the very highest levels is rare, but this is largely the result of a long period of training usually necessary to become proficient in any field. We explain why creative polymathy is not ruled out by arguments for the domain specificity of creativity and argue that consideration of multiple levels of creativity (Big-C, Pro-c, little-c, and mini-c) leads to the conclusion that creative polymathy may actually be fairly common. We introduce a hierarchical model of creativity (the APT Model) to help understand some constraints on and possibilities for creative polymathy, suggest different ways creative polymathy may be expressed, and offer guidelines for recognizing and nurturing creative polymathy in students. (Contains 1 table.)