Apologies for the soft question, but I was wondering whether it is a good idea, in mathematics, to learn/study things simply for the sake of studying it. A very good example comes from category theory. I've seen many people here on MSE who wish to study category theory for the sake of studying the abstractness and the richness of category theory. While pure category theory is fun, it was built to be applied, like in algebraic topology and homotopy theory.
Is it alright to have this attitude when studying "abstract concepts" (like (higher) category theory)? How about when publishing research? Does research always have to have some applications to something known previously?
I think that a good work (for instance, it which are obtained new and beautiful results) is worth to be published. As a mathematician and a referee, I am pro such works. I think that the essence of development concerns with creation of new things. I think that a theory has own growth and development, and, therefore it is not restricted to serve to applications. And a study is a form of own development of a mathematician. Now I step back, and Alfred Tarski give the final remarks.