I read these in HS, they doomed me to grad school (Score 1)

Godel, Escher, Bach even though it has been mentioned before. Also Hofstadter's "Metamagical Themas" is easier and is a collection of columns, so can be taken in small bites. Davis & Hersh, "The Mathematical Experience" Anything by Martin Gardner Lakatos, but one has to have some background in proofs Isaac Asimov's book on algebra, long out of print Feynman's Character of Physical Law