Mathematicians often reprove the same theorem over and over (and over and over!) again. Why do they do this? One reason is that mathematicians want proofs that exhibit different, sometimes competing, virtues. This means that a given proof may have some, but lack other, desirable features, and thus the search is on for a new proof! Philosophers of mathematical practice are interested in identifying and analyzing these virtues and their relationship to one another. In this talk, I will focus on one particular virtue, being well motivated, which I will explore using case studies from the history of number theory.