I know this sounds like a weird question, but I'm interested. So I've always loved math, especially pure mathematics. I spend a lot of time reading about theorems, mathematical proofs, and I try to come up with my own proofs. Recently I had the idea that maybe I can spend my time reading some high mathematical theories and try to come up with something new. So my question is, are there some specialised areas that you would recommend in mathematics, preferably pure mathematics, that I can put my focus on, and maybe make a contribution like discovering something new or proving a theory or whatever? I know that these stuff happen at random, but I'm wondering if someone could maybe have an idea or anything, or just an advise on what to focus on. Thanks.