stem/CS/Turing Machines.md
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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