CMV: nothing is actually invented

So I was arguing with someone about whether or not math was invented or discovered. My original position was that math is invented, as everything in math is purely conceptual and abstract. Numbers and quantities are invented, and are more or less adjectives. You can have "tall" but you can have things that fit the description of tall. But then his argument was "well in the realm of abstract and conceptual concepts were discovered these abstract ideas".

Now this seemed interesting to me, my first instinct was just saying that logic is axiomatic in nature thus math is invented, but even if you put a set of stipulations you can still discover logical ideas within those terms, like discovering chess sequences in the rules of chess.

Anyways, if we go by the way of thinking the other guy mentioned, nothing is truly invented. Design for a car? Not invented because we discovered the conceptual design of a car. Nuclear reactor? Same thing with the car, the design for a nuclear reactor exists abstractly regardless of the human mind, and we simply discovered it.