[jstanley]

My view is that pure mathematics is true because it says so. It doesn't rely on any kind of structure from the universe to hold it up (that's why the universe can be made out of mathematics). If you define mathematics the way we do, then you get the answers that we do, no other ingredients required.

There are other ways to define mathematics, sure, and if those ways allow universes that our ways don't, then those universes "exist" too.

[defyonce]

> It doesn't rely on any kind of structure from the universe to hold it up

I am not sure that this is the case, for math to be it needs a set of axioms.

Axioms have to mirror some sort of universe. I am really curious what can be done if we remove all the axioms.

I am sorry if I sound dumb, I don't know much, but it is really interesting.

[jstanley]

You can have whatever axioms you want though. There's nothing to privilege any set of axioms over any other. And all of the implied universes will equally "exist".