Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with problem-based learning (PBL) which builds on such authentic real-life problems. How can the learning of pure mathematics benefit from these education approaches? We present a taxonomy to classify types of problems encountered discussing the notion of the problem context -- it can be internal or external to mathematics, or both.