More Fundamental Mathematics

Topology is like geometry, but with a little less structure. (Don't confuse topology with topography. They are not the same thing.) In topology you don't care about actual distances, just a more abstract notion of "nearness". Planar topology is sometimes called rubber-sheet geometry, because two-dimensional figures can be deformed without their topology changing (though their geometry certainly changes) as if they were drawn on a rubber sheet. Topology developed as a mathematical subject much later than geometry, probably because it is more abstract and it's ideas are more slippery, but topology can be thought of as a stripped down version of geometry. Today topology itself is a full-blown branch of mathematics.

I know that you probably won't come up with a whole new branch of mathematics in the next few seconds, but try anyway. Think of a branch of mathematics that you know (maybe number-theory or sequence patterns) and try to strip it down to something more fundamental and abstract. Don't stress. Success is not expected. It's the journey that is important.