Choosing an area is hard. Only listing the pros and cons here.
Algebra: Very hard to advance. When you are only one step away from the truth, you still don't know where you are. And too abstract to let intuition guide you.
Topology: Kind of random. I have liked the subject. There are cool things. For example, if we only have local observation we won't know we live on a torus or any kind of 2-manifold. The stablest knot could really have some influence on material science. But it seems too random to put bread on my desk.
PDE: Need a lot of physics.
Analysis: Well, life is very different from a test and I think research is probably different from tests too like I said here. I've always done good on analysis tests but wonder what it'll be like to do real research.
Number theory: Potential the one. But I haven't taken enough courses to say that. Let's wait and see.
I don't know whether meeting a right advisor is more important or choosing a right subject. Sometimes I even think when you find your "gang", guys you can sit down and guys that are interested in what you are interested in too, you can study anything. The great mathematicians and the not-so-great mathematicians are the same at the level of intelligence. The not-so-great ones are just the ones who are not lucky enough to find their inspiration (or they didn't actually work hard, that's another story).
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