[zakk]

I suggest "What Is Mathematics?" by Richard Courant and Herbert Robbins.

https://en.wikipedia.org/wiki/What_Is_Mathematics%3F

[blendo]

My high school math professor recommended this to me 40 years ago.

I got it, then put it on a shelf for 20 years. When I picked it back up, it somehow had become delightful! Perfect subway reading.

Review: http://www.ams.org/notices/200111/rev-blank.pdf