Here is the quote from Gödel supposedly supporting this:

"So the following disjunctive conclusion is inevitable: Either mathematics is incompletable in this sense, that its evident axioms can never be comprised in a finite rule, that is to say, the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable diophantine problems of the type specified" . . . (Gödel 1995: 310).

Wikipedia describes Godel as a nonreligious theist who believed in the existence of an afterlife. In that context, it is not surprising that he would draw far-reaching conclusions that a human being's behaviour cannot be described by a formal system.

It won't be contentious among people who know much about Gödel. He spent his later years working on things like proofs of the existence of God. Like many geniuses he went far beyond what his profession was comfortable with.