I am a junior in high school currently in multivariable calculus (online) and find it kind of boring since it's similar to Calc BC from last year, emphasizing applications of math to, for example, engineering rather than theory. I am highly interested in the theory of pure mathematics and love the rigor and proofs of higher math, and am constantly watching lectures and trying to learn as much as I can of these subjects. There are not really any teachers at my school that can help me with math beyond single variable calculus. However, I took the AIME math competition last year and got a 2, showing I might not have as strong of a base of mathematics as I need to prepare me for higher math later in college/grad school.
I've currently been working through a number theory book and Linear Algebra Done Right by Sheldon Axler, but I also have a less abstract (but still challenging) Art of Problem Solving: Geometry book. Should I devote more time at this point in my mathematical career to these fundamentals provided by Art of Problem Solving, or would I be fine to skip those and continue working on the more theoretical textbooks? (I also would really like to work through Calculus by Spivak or Apostol, though I'm not sure which is better.)
Any advice would be greatly appreciated.
I totally agree with the comments of Greg Martin regarding the absolute need to really master the fundamentals and understand them deeply. I got through four semesters of undergraduate calculus with solid A's for each semester by knowing how to solve the problems presented. Unfortunately, I didn't truly understand anything. When I got to my engineering dynamics course, where we had to actually apply calculus to solve real world problems, everything fell apart and I was totally lost. Get to the point where you understand the fundamentals deeply enough that you can explain them to your mother. Also, don't ignore the applied mathematics side. This is where a lot of the true understanding comes in.