Any defineable sytem of mathematics or logic is either inconsitent or incomplete; that is for any finite or infintely enumerable set of axioms, sufficient to encompass arithemtic there is either a statement “X” and a statement “not X” that can both be proved (inconsitent) or there is a meaningful statement X that can neither be proved not disproved (incomplete) within that system.

or

Truth is deeper than proof

or (more importantly)

Mathermatical Logicians will always find employment.