Although the title is "How to Study Mathematics", I think a more accurate title would be "How to Study Mathematics as a Mathematician".
I am studying some maths right now with the goal of understanding some statistical methods. Having a rock solid understanding of all the underlying maths is counter-productive to my end goal though (Applying the statistical methods), because it would be extremely time consuming.
If you want to learn maths for the sake of understanding maths, then this could be the right approach. But it's definitely not a pragmatic approach.
I am sort of facing the same problem. On one hand I like math, abstract algebra, calculus etc but on the other hand I know I am not great with it. I am slow, I am not creative. So, when trying to learn something for programming like differential geometry, when I go deeper than I need to, I feel like I am wasting my time. And sometimes it is particularly hard to read a book written for mathematicians because my knowledge of it is not as "continuous" as theirs.
Well, a mathematics degree is one of the highest income earners for a reason so its usefulness is beyond dispute. I personally have life and artistic goals which take priority of my time over math but I’m willing to allow mathematics (together with high-level scientific understanding) a place in my life as a tertiary goal or drive. We are all a little too hard on ourselves to get everything done before we turn 30 or 40 as though it were some kind of deadline and then why bother, right?
If you find pure math interesting then give yourself the slack to learn it long term. Think of it like a rock garden which you tend to over the years.
I want to go back to school, and if I do, it will probably end up doing CS because it’s about the only “useful” degree accessible to working professionals, but if I had a choice, I’d probably pick a mathematics degree given how widely applicable the learned concepts can be.
I highly suggest you push through it. Mathematical knowledge ties in together very well. It's like snowboarding. Once you get over the initial hump, it'll come fairly easily to you (what's often called "mathematical maturity"). Then you'll be able to easily learn about statistics and ML if you want to experiment, or scene rendering, or differential geometry, or audio processing, and on, and on. Computers were originally created to be calculating machines, and they remain great ways to blend math with instructions.
I am studying some maths right now with the goal of understanding some statistical methods. Having a rock solid understanding of all the underlying maths is counter-productive to my end goal though (Applying the statistical methods), because it would be extremely time consuming.
If you want to learn maths for the sake of understanding maths, then this could be the right approach. But it's definitely not a pragmatic approach.