… My ultimate goal is to tackle difficult questions in mathematics … there is no particular branch of mathematics that I'm currently aiming at. Number Theory is the one that grabs me right now …

Sound great! As your motivation is recreational and not vocational, my thought is that you can start anywhere and go in any direction. Whenever you come across an unfamiliar topic or scenario, you can ask about the situation here (if you sense that you might be missing something obvious) or you can put the matter on hold and move onto a side track for discovery (then return to the main line, once you've filled in the missing pieces).

It takes experience to tackle difficult question in mathematics, so, when pursuing maths for fun, I'm in the camp that says, "Do what you enjoy in the moment, and learn as you go." (If you have a decent calculus text, then it contains a number of difficult questions.) Basically, for you, I'm saying that

*doing math* is a very good way to find not only what you need but also where you'd currently like to spend your time.

We look forward to helping you navigate the journey. Cheers