Are Numbers Real?

It might be that all of mathematics is just a big castle built on sand and in the end, none of it is real. Is that the idea? Yeah, so the idea is if it is some sort of construction, mental construction, that doesn't mean that it's nothing. So, according to this line of thought, then some proofs aren't, in fact, not proofs at all. Why does it matter whether these things are real or rather than not these things are just constructed? And I think it goes to the heart of what we're trying to learn about the universe.