It feels like mathematics is something invented because you can do things in math that have no correspondence in the real world. Where do negative numbers exist in nature? Imaginary numbers? (Serious question - I'm not a math person.) Like language, we can create words (and conceptions) of things that don't or can't exist.

Feels to me like mathematics is an interpretation of nature. Nature is discovered, but nature is not math. Math is the language we use to understand nature. In that sense it feelss like it's more communication than anything, a worldview or conception. I think there are several ways of understanding nature, math being just one of them.

What do you all think about the notion that maths, being perfect a perfect system (100% consistent, no issues, contradictions, etc) cannot be man-made?

I'd say first: Is math perfect? How can we know? Is it complete, growing, changing? Then I'd say: why can't humanity create or conceive of something perfect?