05
Few interesting bits from "The Emperor's New Mind":
- There are things we know but we can't prove (Gödel's theorem)
- Simplicity of lambda calculus introduced by Alonzo Church
- Halting problem which has a nice (and understandable!) sketch of proof on Wikipedia
- There exist a whole class of problems which cannot be solved with an algorithm: Diophantine equations, word problem and tessellation (with a special case of aperiodic tiling which Penrose tiling is an example)
"Gödel, Escher, Bach: an Eternal Golden Braid" is a book I want to read right after "The Emperor's New Mind".
