First, I link the following video: https://www.youtube.com/watch?v=Vfh21o-JW9Q
It demonstrates the 'Dirac belt trick', which was created by (I believe, Dirac) to demonstrate the calculus of spinors. Particularly, it demonstrates the double-covering of the 3-dimensional rotation group SO(3) (essentially a set containing all the possible 3D rotations) by the group SU(2) (a set containing 2D complex matrices). A 'covering map' essentially describes the way that one space can 'wind' around another.
The demonstration of this trick is absolutely independent of science - we live in a (locally!) flat 3D plane which we can assume to be normal 3D space and demonstrate the belt trick. This belt trick is mathematical truth - not science. Science does not actually have anything to do with this. It's just a mathematical fact about the topology of rotation group SO(3).
We can derive the mathematical fact and then see it in our real 3D world.
Does this prove that mathematics is real? Does this prove that 'abstract' mathematics is indeed real and right in front of us? Can I therefore justify that my mathematics is not 'made up', and rather is indeed real, if you look in the right places?