[joe_the_user]

I think that's one useful way to view it. Math is infinite "mountain" and the higher you get, the rougher the summaries.

One thing I should mention. I have been reading The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age by Jan von Plato. One thing I notice is that a lot of mathematicians activity is not proving more and more complex theories but rather, producing a framework that takes a series of complex results and shows them to be much simpler within the framework.

And that's just to say, the organization of math isn't just a matter of simplification for the layman, it's part of the progress of math itself.