Godel, Escher, Bach; An Eternal Golden Braid - It's a bit of a tome, but when I read it in high school I started thinking about everything differently.
I've only read Metamagical Themas by Hofstadter, is it worth reading GEB;EGB as well or does it just cover very similar thoughts.
It covers everything. I'm not sure how much hyperbole is in my last statement there, either. The book is about the size of a standard sciences textbook, and "Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself." - Wikipedia I haven't read Metamagial Themas, but wikipedia's summary of the articles makes it look like a relatively small subset of what is in GEB. In short, I wholeheartedly recommend it. Maybe with some asprin. It's quite a lot to take in.