Busy Beaver Function

“Axioms of set theory can only determine finitely many values of this function. Okay, so in some sense, beyond a certain point, you know, the standard rules of mathematics cannot even prove what are the values of this function.”

“The amazing thing about this function is that it increases more rapidly than any function that could be calculated by any computer program. This is provable, right? So you know, it is a ridiculously quickly growing function.”