I would argue that math is both invented and discovered at the same time. Our expression math is obviously invented but that's not very important (but not total

I would argue that math is both invented and discovered at the same time. Our expression math is obviously invented but that's not very important (but not totally unimportant either, because it drivers further discoveries). The set of axioms we chose is way more invented than discovered, although we won't like others, it is likewise we won't like e.g. a too random or too complicated a mechanical apparatus, or even it would be useless. Given a chosen set of axioms, the theorems we can infer are so constrained that the only reason we can find an invented component is that we chose the places to look for in an absurdly large research space. So like we can argue that we don't "discover" a novel in the large research space of random characters, we can in a way argue that we in part invent the theorems. In the end does it really matter though? Is it maybe not just that inventions and discoveries have more things in common than some intuitively think? Tons of people are not really found of patents, or at least of some class of patents, because the line is arguably blurry (so yeah there is a practical way in which case it do matter, but only because of a completely arbitrary social organisation)