Is it Mathematics a mental construction or it's a reality in itself?

I've always thought that Mathematics is the language of the physical universe, and as such, it is only grasped, albeit imperfectly by human minds. I was struck when I read that some people think that Mathematics is a purely human creation. No wonder that many instances of mathematics have been produced by observing the human mind, or using human analogies. But this hardly constitutes a sufficient argument for proving that mathematics, is a purely human invention, or creation. Perhaps a distinction might help to understand the "human-origin" approach. There is a Mathematics in the universe which is absolutely accurate in describing the physical laws, and those for which there is no known application. This is the language devised by God. On the other hand it is the human mathematics which constitutes the human endeavor in understanding that real Mathematics. The latter, even imperfect, still tries to resemble the real, and as such it is the product of human observation, meditation, deduction, induction, etc. Therefore, it is far from being a human creation.

I came across a thought by famous Cambridge's mathematician G.H. Hardy (1877-1947) in which he believes the same thing. In his later years he wrote a reflection called A Mathematician's Apology in which he states that:

For me, and I suppose for most mathematicians, there is another reality [in addition to physical reality], which I will call ‘mathematical reality’; and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is ‘mental’ and that in some sense we construct it, others that it is outside and independent of us. A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all. I should not wish to argue any of these questions here even if I were competent to do so, but I will state my own position dogmatically in order to avoid minor misapprehensions. I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards...
I only disagree with the last part of Plato as the first to hold this view. Babylonians, Egyptians, and their disciple Pythagoras, long before Plato held that view.

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