Recently Numberphile uploaded a video on Godel's Incompleteness Theorem, and the Professor in the video made the conclusion that
if you can prove a statement cannot be proven true or false by the axioms and if that statement happened to be false by some counterexample, there would be a contradiction,
and so the statement would be true.
Then if someone could prove the Collatz Conjecture was unsolvable would they have proven that it is true? Or is that overreaching from the conclusion in the video.
Also, has anyone attempted a rigorous proof that the Collatz Conjecture is unsolvable?