I think we may be talking about the same thing. It is just that for me mathematics is not about _using_ some formalisms. It is about developing the skill which allows you to create and evaluate different formalisms.
https://fosstodon.org/@bookwar/107389047199043428
Where it may differ is that mathematics does not just create the language, it also validates it for correctness.
And it is important too.
When defining a new abstraction you need to recognize when it doesn't make sense.