Hardy, A Mathematician's Apology
In my teen's I treasured this book, I also inherited the anti-applied math slant, with the probably unhelpful idealism (but we are all young once). Would also add 'Discourse on the Method' by René Descartes, a must for all! The motto, 'the world is the encyclopedia of life' I have tried to adhere to since.
I never liked number theory.
The world's greatest mathematicians got their inspiration from the world around them, Hardy was a dead-end.
I think the schism applied/schism is silly. Unfortunately, maths has gone downhill since Henri Poincaré.
I liked Cartesian geometry at school. Many years later I wrote a C++ OOP library for CAD, graphics and optical technology.