My apologies for such a general question, but as a 'math enthusiast', I've often wondered what the optimal strategy is to increase my mathematical maturity. Broadly, should I aim to hunker down & study one topic in detail (measure theory/analysis, which is what i'm doing right now), or should I study a broad swathe of different topics?
Also, are there specific fields of math that are better for developing mathematical maturity? I've often wondered whether number theory/graph theory/combinatorics are better for developing mathematical maturity as even basic proofs need one to think imaginatively.
My apologies again for such a broad question that will likely have many different contradicting responses. However, I don't have anyone to discuss this with, so thought I'd throw out my question here.
Hint: Try to teach what you learned (also what you want to learn) to people with different background!