Maths is just a model which attempts to explain the real world
This is the bit I disagree with. As a statement, it is simply incorrect. However, if you replace the word maths with physics, it would be a perfectly good statement.
As a very simple example, you can define all sorts of different geometries, all of which are mutually inconsistent with each other hence at most only one of them representing the real world. They would all be mathematically valid however.