Here's your chance though Mr Hoffman--is math invented or discovered, and why?
One of your unstated premises is revealed in your use of the singular math, contrasted with maths. There are many mathematics related only by their common root in logic. For example, the math (probably better calculus) of RAMANUJAN. As I recall he, an untutored Hindu, invented a complete calculus of partitioning. Its utility was not recognized until computer technology was quite mature.
Another 'for instance' is statistics. Here lies the frustration that makes me say...
The conspiracy of ignorance masquerades as common sense.
My +4 sd whatever you want to call it excludes me from the vast conspiracy of ignorance. I am solely responsible for my errors.
Numbers are a language: "The set of all sets that are simular to themselves" (I think thats correct)
So 'math' is an invention (language) that allows us to explore/discover 'logic' which is (we hope) an underlying 'law' of reality.
Then along comes quantum physics =)