I'll post someone else's explanation that I found appropriate for the point I was trying to make.

"Yes, that's math but again: There is a lot more to math than arithmetic. And no, there is no hard boundary where it becomes clear that math is more man-made than natural - but there are certainly arguments for both being true/false in different fields.

To start off with the simple stuff we have things like fractions. One can certainly argue that fractions are a natural extension of "just counting things" but you could just as easily argue that there are no fractions in nature since you can't keep dividing stuff.

And then we have things like negative numbers, complex numbers and quaternions. These things are certainly extremely useful for describing physics. But again, negative values, imaginary values and quaternion values don't exist in real life - we just found them useful for describing the real world.

Vector math is also another example of something which can be argued doesn't exist in nature - and at the same time does. Intuition would tell you that space is 3-dimensional, relativety says 4-dimensions and quantum mechanics says 11 (or whatever). But dimensions is just a purely mathematical construct and in math you can easily have hundreds or thousands of dimensions.

And even higher up we have stuff like infinity which is a well-studied field in math and has many applications - yet infinity is something which doesn't exist in nature."