I am out of my depth with this really. What I am saying is that categorisation is a position that is convenient but we could take the view that it is flawed; that there are no true categories of things. So it is convenient to assume every hydrogen atom belongs to the same category: 'hydrogen atom'... but we could equally say there is no such category 'in reality' ie there is no true number of atoms belonging to that category; that they are in truth, as with snowflakes, unique. Just like we can say individual humans belong to the category 'human' but in truth that assumption has a deep metaphysical flaw. Mathematically there are numbers of humans but in truth that number is a category assumption. The physical reality is that there are unique individuals. So mathematics is basically convenient in its categorical assumptions but is an inaccurate tool for modelling existence....Oh, and God is not a mathematician. Isn't maths prdicated on the notion of quantities of things classed as instances of many such kinds? i.e. of equitable relationships between different things where one kind is a number of many such equal kinds.
You have to put things in categories to count them. I can count two apples and three oranges or five fruits - I haven't made any metaphysical assumptions in doing this - I don't have to assert truths about fruits to claim that things can be put into categories to be counted ...I could also count orange and red things or fresh and rotten things ...
The assumption of maths is that this constitutes an accurate reprsentation of reality... so of course, reality must conform to this notion as an accurate description.
Can you give some support for this ... ? I've not seen that anywhere ... mathematicians worry all the time about their equations applying to the real world - but then again mathematicians (and you) drive over bridges built on assumptions all the time - on the other, other hand, bridges collapse, even when the mathematics is right - see the Tacoma Narrows Bridge collapse.
But if we assume the contrary that there is no example of any kind that is a number of many such kinds, i.e., that every kind is unique, then mathematics does not exist as an accurate description of reality, just an accurate description of the reality we assume reality to be.
One unique kind plus one unique kind equals - two unique kinds. That can be very useful whether or not it's an accurate depiction of reality.