A thing to realize here is that there is no "fundamentally, cosmically true" in math. While math can be used to model reality, it is not bound by reality.

The only thing that matters is what you choose to take as granted for a particular question.

It's like how you can draw a map of a place that doesn't exist.

Or like coming up with rules for a game and then trying it to see how it plays.

Or it's like a material used for construction. You can build a house out of it, but there's no inherent "houseness" to it, despite how common such a use is.