My instructor was telling us in class today about his days in graduate schools and somehow our topic got to "what area in math is most difficult" or something along those lines.
He talked about how it is harder to get "started" in some fields (in terms of learning) because you just need about everything.
He gave an example how almost everyone can get started with say, Graph Theory or some elementary Number Theory without knowing too much of math; however, areas like Algebraic Geometry or Differential Geometry is harder than other areas because you need to know pretty much need to know everything to get started.
Is he implying that some area in math just require a focus in one area? I am not the greatest mathematician on this planet, but are there fields in math where one doesn't need to learn too much about one subject? I know at some point they are all interwined with one another. So say I want to learn more about Graph Theory, do I need to learn Topology in order to "master" Graph Theory?
Unreleated: Then he started giving us personal advises (opinions?) that we should focus and build on Algebra and Analysis more over every other subject because it will be easier for us to pick up the other subjects after we master those two.
Is he actually right?