Which Came First: Theory Or Application?

This is a question I've had for about a year now: Which came first, theory or application.
I know this is equivalent to asking "Which came first, the chicken or the egg?" However, it's still intriguing.

Last semester I took three of theory courses. This semester I'm taking two which are more application than theory, another which is more balanced (numerical methods), and a theory. My current problem is jumping back and forth between application and theory within the same context. It could just be mathematical immaturity, but I have to wonder if some people are just meant to silo themselves either into pure theory or pure application without spending too much time trying to bounce back and forth. Perhaps that's why many research projects take years.

So which came first, the chicken or the egg?