Wait, you are saying mathematics exists independent of humans but logic does not. But mathematics is build on top of logic, how can it gain independence from humans if its foundation does not have such independence? Or am I just misreading your statement?
To me this seems backwards. Don't we define some basic objects with axioms and then use logic to find out the consequences of the axioms? We make up some axioms for natural numbers, then we define operations like addition and multiplication on them, and finally we investigate the consequence of those definitions, we discover for example that some numbers have very special properties and can be used to uniquely decompose all numbers, we call them prime numbers.
I would therefore say that mathematics is a human invention and build on top of logic, it seems in no way universal. All the things we discover in mathematics are nothing but consequences of the axioms, the definitions, and the logic used to prove things. If there is something universal, at least so it seems to me, than it would have to be logic.
