I’ll give my take on this (as a mathematician).
As best I can tell, mathematics does not play any role at all in the cosmos. However, scientists find it useful to construct models of aspects of reality. And mathematics is very good as a modeling tool.
Mathematics works well in some sciences, because those mathematical models work very well. In fact, they work so well, that there is a tendency to conflate the model with the aspect of reality that it models. And that’s what make it look as if the cosmos is mathematical.
If you owe your bank $22, try telling them that your debt does not exist.
We model monetary transfers with mathematics, and the model works very well with negative values corresponding to debt.
Electronics models what happens with complex numbers, and imaginary numbers turn out to be very useful in those models.