Incompleteness Theorem

#Math
Veritasium Video
Essentially proves that math is incomplete, meaning that there are true statements in math that can't be proven. The example Godel gives is: there does not exist a proof for the statement with a Godel Number $\displaystyle g$. It turns out that the statement is described by that aforementioned $\displaystyle g$, meaning the statement essentially says, "this statement is unprovable." The only way to reconcile this without breaking Axiomatic Consistency of the Hilbert axioms is by allowing this statement to be true (if the statement were false, then the statement would be saying that it is provable, which contradicts with the statement saying that it is unprovable)