>This also suggests that mathematics is 100% constructed by the human brain, even if it is highly-influenced by relationships found in the physical world.

As I see it, mathematics is both discovered and invented.

We can model every existing thing in every possible world using math. Even if both the set of all things that might exist and all possible mathematical constructions are infinite, the later is larger. That's because we can also construct mathematical models of things that doesn't exist.

So it looks that from the set of all possible mathematical constructions, we extracted a subset that maps to objects in reality. That looks like a discovery process.

But we also constructed mathematical models of things that don't have corespondents in reality, so that much be more of an invention process.

Let's pretend for a bit that we forget all what we know and tomorrow we will start inventing things again. Or that a species of aliens start fresh on a planet.

The mathematic theories and notions we and the aliens might discover, build or invent might be different than the theories and notions we know today but would probably be equivalent. That suggests that mathematics just exists somewhere in its own world waiting to be discovered.

I too, subscribe to this view. In my mind, reality is nothing more than a vast integer variable field with interactions between some variables. All our mental models, from vision to math are attempts at approximating that complexity down to a level that our brain's limited processing capacity can handle...

Why integers one might ask. For me, even rational numbers are such an approximation.