TITLE: What other math fields wouldn't require learning a huge amount of material in advance?
QUESTION [5 upvotes]: From An Introduction to the Theory of Surreal Numbers:

[...] Thus the reader has the opportunity which is all too rare
  nowadays of getting to the surface and tackling interesting original
  problems without having to learn a huge amount of material in
  advance.

What other math fields would be in the same class as this one? What other math fields wouldn't require learning a huge amount of material in advance and would allow one to tackle interesting original problems?

REPLY [2 votes]: Ramsey theory on the integers has research problems in every chapter (presumably still open) and I think it's pretty accessible to most levels.