 Our mathematical intuition provides intrinsic evidence for mathematical principles. Virtually all of our mathematical knowledge can be deduced from the axioms of Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). In Gödel’s view, we have compelling intrinsic evidence for the truth of these axioms. But he also worried that mathematical intuition might not be strong enough to provide compelling evidence for axioms that significantly exceed the strength of ZFC.