This guy is popular with the CS crowd because of his views on infinity & constructivism I believe. I've studied math quite a bit and I don't really have any stake in the field (I'm not an academic). But modern set theory is a deductive theory. You have assumptions (axioms) and there is a formal reasoning involved to arrive at facts. If you specified set theory to a computer, I have confidence that it would validate the work of the academics.

I tried to skip through the video to find his reasoning.