TITLE: On the Math Mindset
QUESTION [18 upvotes]: I am a soon-to-be high school graduate with inclination towards mathematics. I enjoy doing math, and am relatively good at it, but I dislike the way I am being taught. I feel like I am being taught methods for solving a lot of problems, but I don't see how any of this fits together.
I was considering pursuing a career in mathematics, but I realized I don't really know much about it as a whole as opposed to how to solve specific problems that will appear on some test.
Are there any good books out there about the "math mindset", or whatever it is that it's called?

REPLY [4 votes]: Here are some further classics that you may find inspiring and enlightening: Polya: How to solve it; Rademacher and Toeplitz: The enjoyment of mathematics; Kac and Ulam: Mathematics and Logic.