I don't like the use of the terms.

we invented symbols to explain things we observed, then used those symbols to model unobserved possible things.

2+2 = 4 was neither invented, nor discovered, it was observed, those symbols are simply the language we use to describe the observation.

the gravitational constant was "discovered" in a very broad use of the term, but it's use in mathematics was a matter of observation.

if I had only these two terms to use, I would say that mathematics is a language we invented to describe the relationship to things we discovered, although calling simple observations "discoveries" has always stuck in my craw a bit.

One only need ask the question, ‘would an alien species have ‘discovered’ the same mathematics, or would they have ‘invented’ a language completely foreign to our brightest mathematical minds?’ I am of the opinion that physics is what we discover, and mathematics is a language we invent, not only to describe our universe, but to theorize about it, and what may be beyond.

One example only: the Fibonacci numbers which are to be found throughout nature. They also create the golden ratio which dominates nature and our art. They have always been there.
Alright, a second one that plagued me in high school: geometry. Note how easy Egyptian geometry came to us as we started to build and note how to do so in the best manner. It took the Greeks to discover or create Euclidean geometry which is just a means to list reasons and properties for why Egyptian geometry worked even before explanation.

"Mathematics is the language of nature." - Dr. Lawrence Krauss

Newton invented Calculus, Calculus is the mathematical study of continuous change

I think humans discover what is already there. We may need to invent ways to prove or discover what we don't know.

Certain concepts and properties are constant but the math to express them was invented. I have always wondered if we would have had only a total of 8 digits on both hands, three fingers and a thumb, would we be counting in base eight instead of ten.

1+1 has always equaled 2, we just put language to it....

First we invented the rules and then we began discovering what follows from those rules.

I think it's a meaningless distinction now.

Just like we didn't invent gravity, inertia, or the light spectrum.