Through Pure Thought, Human Mind devises theorems, postulates, axioms, etc. with no entreaty from Everything Else, but only from the logic of its own structure. But, alas, eventually there arises Application, that one-to-one mapping to Everything Else.
How can this be?
Because Human Mind is that aspect of Everything Else Plus that was created To Know.
Math is not a creation of man. It is not artifice, any more than discovering the process of photosynthesis is artifice. It is discovery. Revelation. The mathematical structure of the universe is Real. And what is truly staggering, is that it is Knowable.