Gödel’s 1931 Incompleteness Theorem (as simple as possible)

∃G (G ↔ ~Provable(G))
“there exists a proposition that is materially equivalent to a statement of its own unprovability.”

If G was Provable this contradicts its assertion: G is not Provable.
If ~G was Provable this contradicts its assertion: G is Provable
Therefore G is neither Provable nor Refutable and does not exist.

2019-07-16 update
If G was false then it would be ~Provable (F ↔ T) is false
If G was true then it would be ~~Provable (T ↔ F) is false
∴ ~∃G (G ↔ ~Provable(G))

Copyright 2018 Pete Olcott