I was not trained as a mathematician so perhaps I should keep this to myself but I am going to answer in one word: YES. By that I mean that I think some of math is invented and some of it is discovered*. I suppose that one might first think about what mathematics is. Again, as a non expert my view has been that mathematics is: 1. A science of patterns. 2. A language. 3. A game. When I use mathematics to talk about patterns I see in nature I have discovered things about those patterns. Perhaps I describe mechanics using Newton's laws of motion and then discover recurrence phenomena. If, on the other hand, I am creative and extrapolate I may be able to create mathematics that has no parallel in the natural world. In that case I have invented something, perhaps new concepts** that I will later use in my languages.
* Wikipedia says most philosophers of mathematics believe that mathematics is discovered rather than invented.
** One of the longterm goals of A.s.a. H. is to invent new and useful concepts with which to think (new or old thoughts).
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