That, my dear, is where we have to part company.
There are two main schools of mathematical "ontology," respectively stating: (1) Mathematics is something that the mathematician discovers (e.g., the platonist school); (2) Mathematics is something the mathematician creates (the formalist school).
I identify with the former; evidently you with the latter.
There is no middle ground.
BTW, after two millennia and counting, this is still an "open question."
But it seems to me the mathematical platonists actually "get things right" more often than the mathematical formalists do. [I have a hunch Einstein, for instance, was a mathematical platonist.]
Actually, your above statement begs some questions: How does man get to be such a sufficiently creative agent, that he can "invent" mathematics and the physical laws? RE: the physical laws — how can he create them, when he's already subject to them? Would he be creating "ex nihilo" here? Or is his putative creative act somehow constrained by reference to the world outside of his mind?
Thank you for writing!
I argue, as others have done before me, that mathematical concepts and ideas exist objectively, outside of the physical world and outside of the world of consciousness. We mathematicians discover them and are able to connect to this hidden reality through our consciousness. If Leo Tolstoy had not lived we would never have known Anna Karenina. There is no reason to believe that another author would have written that same novel. However, if Pythagoras had not lived, someone else would have discovered exactly the same Pythagoras theorem. Moreover, that theorem means the same to us today as it meant to Pythagoras 2,500 years ago.
- Edward Frenkel
How about physical laws? Are those "created", or "discovered" (bearing in mind some of what we call "physical laws" have had to undergo revision).