Lessons of Gödel, Escher, Bach
This is one of the greatest books I’ve ever read; it’s a true masterpiece. I first encountered it in high school. Ostensibly it’s a gorgeous web interconnecting art, mathematics and music, but that’s actually instrumental to the book’s true purpose. Quoth Wikipedia:
Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.
And now MIT offers a free class geared around this book, using it as a kind of textbook, bracketed with a syllabus and class notes in PDF. All this for free. Wow. Props to the instructors, Justin Curry and Curran Kelleher, and to MIT for providing this to the world gratis.