[fsloth]

But observations of real world systems can be identical to a specific mathematical system. I.e. the time it takes for a thing to fall at specific gravity at specific height, the frequency of a particular pendulum, and so on...(i.e. the rest of modern physics).

True, it is our observation and our model which are similar, so I suppose the philosophical question then is up to what point we can trust our observations. And if we trust our observations, I would conclude that the similarity of our observations and math means that the real world can at least exhibit 'maths', which means our minds are not the only place where math can exist.

The smartphone I'm typing this on leads me to conclude that lots of our observations are highly trustworthy :)

[calibraxis]

Yes, I think that humans have some ways to make sense of the external world, and math is one of them. May not be highly developed, could be buggy. Probably lots of things we could never figure out, like rats who can't solve mazes where they need to turn at prime numbers.

Our math sense could even conflict with our other useful facilities (as is the case with how easily fooled humans are when it comes to statistics).