> If you have to intuitively understand them, it isn't very objective is it?

They were talking about things that you don't have to (and indeed can't) intuitively understand.

> What in math are objective facts about the nature of reality? Where in nature is the number 1?

In all sorts of places, not least counting things. Mathematics is about equivalences; the point of saying 2 + 2 = 4 isn't to make some funny marks on paper or pray to the platonic void, it's to say that if you have something that's 2-like and combine it with something that's 2-like in a way that's +-like, then the result will be =-like to something 4-like, in the same sense of "like".