Why Mathematicians Aren't Interested in Proofs?

For me, philosophy of mathematics was an excuse to kind of do a bit more mathematics. And mathematicians, some are interested in such questions, some are not. So it's just a particular bunch of questions that some mathematicians are interested in. They're like, look, proofs work. Why do we care why they work? It depends, again, on the mathematicians. As you rightly point out amongst physicists, you've got things like trying to sort out the interpretation of quantum mechanics. If that's a deeply philosophical question that a lot of physicists are engaged with, you don't want to just dismiss that as philosophy. That's crucial to quantum mechanics to have an appropriate interpretation of