Sipser's book was the point I tried to give up pencile-pushing/parroting, before every proof there is a "Proof Idea" that really fills the gap between the theorems and proof, and the more important ideas you should take away, I suddenly realized every thing I learned had this discontinuity between things you do in problems and proofs, and the general understandings and usefulness and philosophy behind it.

Thanks for this. "Proof idea" is a phrase that concretizes a vague intuition I had about something that exists between a theorem and it's proof

+1 to Theory of Computation. It was the book that got me excited about computer science as being a field bigger than just “how to write programs”.