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 conve

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 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.