Comments by "kazedcat" (@kazedcat) on "The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy" video.

  1. Yes you can add the statement as an axiom but Godel built a constructor that creates new statement that needs to be added as a new axiom. Ultimately you cannot have a complete and finite set of axioms that can prove all true statements.
    2
  2. Translation is shorthand for very advance meta mathematics. It is like the geometric circle and the algebraic equation x^2+y^2=r^2 is the same thing.
    2
  3. Godel did prove it. This is the whole idea of the incompleteness theorem. He found a way to prove that there are true statements that cannot be proven.
    1