What is the single most influential book every mathematician should read? [closed]
A Mathematician's Apology by G H Hardy. I did in fact read this in high school, and it raised my view of mathematics from a thing of utility to a thing of beauty and wonder. It inspired me to go on to study mathematics at Cambridge myself.
It's a pity that the "introduction" by C P Snow is longer than the original and contains a rather depressing view of Hardy's later life. I would recommend readers to skip the introduction altogether and concentrate on Hardy's own words.
Polya's "How To Solve It"
When I was in my fourth year of high school I got a copy of What is Mathematics? by Courant and Robbins. That book showed to me that Mathematics is far more than a "boring tool" to do Physics and opened up new worlds. I would recommend it to any bright high school kid with an interest in math and sciences.