David Hilbert

• Wondered if there was a universal algorithmic process to decide whether any mathematical proposition was true
• Then suggested that there were no unsolvable problems

Incompleteness Theorem

Kurt Godel

You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to come up with new rules and axioms, but by doing so you’ll only create a larger system with its own unprovable statements

Turing Machine

• Model of computation
  • Resolves whether or not mathematics contained problems were incomputable
  • No algorithmic solution

Church-Turing Thesis

Any algorithm capable of being devised can be run on a Turing machine