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"This guy is popular with the CS crowd because of his views on infinity & constructivism"

I didn't know. I'll try to find his videos on infinity. I agree with his views on axiomatic set theory. To me the axioms of ZF read like hidden definitions. First they say "in ZF set is not defined" but then they define it with the Axiom of Extension.

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Most working mathematicians don't care about pure set theory. They're not thinking about ZFC axioms while they're doing math. This only becomes a topic of conversation because we start getting counterintuitive results down the line, or because of an increasing awareness of mistakes (see video below).

I think this a good video about foundations:

https://www.youtube.com/watch?v=btzE11jNbj4

He makes a point about how different foundational systems can interpret each other, eg Type Theory can be understood in Set Theory and vice versa, etc. I generally encourage people not to worry about these things.

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