The Importance of Set Theory

I don't want any part of math to be an island. So I would hate to think that set theory is somehow some, I mean, no one would say it is but even the part that contains the continuum hypothesis. If you take a Hilbert space and you look at the bounded operators and the compact operators, these are well studied algebras of objects that are studied in mathematics. Taking what's called the automorphism group of that is something that a mathematician might ask about. It's known that whether the continuum hypothesis is true or false is related to whether they are very complicated automorphisms of that algebra or not.