I tend to think of math as having two parts: a way of thinking along with all the things people thought up by thinking that way. To learn the first, you have t

I tend to think of math as having two parts: a way of thinking along with all the things people thought up by thinking that way. To learn the first, you have to study the second. Examples of the second are calculus, group theory, algebra, etc. Examples of the first are being able to define useful words with useful logical consequences, knowing when you can infer things beyond what can be directly tested, detecting patterns that might profitably be abstracted, etc. It's a bunch of force multipliers for your logical mind. Specific subjects were developed with the goal of solving particular kinds of problems, so if you are faced with such a problem, it can be very useful to know what people have already figured out! However, if you're not, then it might not be so useful remembering these details.