There is a tension between applied and theoretical mathematics, and it's as old as the whole science itself. Mathematics arose to solve practical problems (land surveying and division, as well as trade) and recognizing the underlying principles make it possible to abstract that knowledge. That might lead to centuries of ivory tower activity and what could be regarded as a purely artistic pursuit until somebody figures out how to apply a theory to a new practical problem. Or relations to another theory are discovered, and suddenly there is a new approach to previously intractable questions. A good example is be number theory, which is the foundation of modern cryptography.