[jkaptur]

This essay would benefit from results from computational complexity.

P vs NP, of course, but also the halting problem and Rice's theorem: non-trivial semantic properties of programs are undecidable.

In other words, if you say "this is the solution to that sudoku puzzle", that's easy to verify. "This sudoku puzzle has a solution" is almost certainly much harder to verify. "Here's a program that can solve any sudoku puzzle - impossible (in general).