This may be trivial, but many people wonder why mathematics is so useful in science. In the twentieth century a philosophical turn was made in linguistic philosophy, many philosophers thought that the structure of language corresponds to the structure of the world, as it turned out to be so, the language is redundant with respect to the world. But not the language of mathematics. In my opinion, the relations between numbers and functions correspond to relations and functions in the world are homomorphic, because the principles of solving mathematical equations are applied in physics, but the phenomena are described by them. For this reason, the world of mathematics is a form of the world, and Platonic ideas are simply shapes. So no colloquial or strict language, but the language of mathematics is homomorphic to the world. To describe the phenomenon we use the same relationships and functions that are used in the study of numbers.
Your preamble concerns the kind of question raised by Eugene Wigner in his article, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences”:
http://hep.physics.utoronto.ca/~orr/wwwroot/JPH441/Wigner_Math.pdf
These issues are taken up in a recent book by Jane McDonnell, The Pythagorean World: Why Mathematics Is Unreasonably Effective In Physics:
https://www.amazon.com/Pythagorean-World-Mathematics-Unreasonably-Effective/dp/3319409751
I myself remain skeptical of the idea that the world is at bottom Pythagorean or of sine qua non homomorphisms between mathematics and the world; in fact your opening phrase "This may be trivial" captures my worry, for it seems to me that the world can be arbitrarily carved up, conceptually, in indefinitely many ways and a matching homomorphism can always be contrived.
I actually think the homomorphism between mathematics and the world is best explained by the notion that mathematics are ideas in the mind of God, namely, the blueprint God used to create the universe. If mathematics is not grounded in the mind of God, then it seems that the homomorphism simply becomes a matter of luck. The odds against our just "getting lucky" here, especially when we don't "get lucky" in any linguistic field, seem too remote to be a credible alternative.
In one story, S. Themerson wrote that God Father make matery, Ghost make form or mathematic resp. logic, and God Son give us morality. I did not basis on that story. But I read Halliday's physics textbook and I noticed that structure of phenomenon is desribed by the same functions as mathematical functions. My opinion is tahat mathematic is form of universe, and We substitute material objects to mathematical form and described fhenomenon in universe. Philosophers of language thought that language is form of universe but language is reduntant to world, dragon could not be 5m lenght from right to left and 2m lenght from left to riight, but We could write it, language allows write infinity numer of sentences, mathematic operates withe the concept of infinity but in physics this notion is used as idealization. Arithmetic is non contradiction and continuum hypthesis we could confirm from standpoint of metamathematic as recursive function określona by relations bigger than and smaller than. I do not know whether is infinity numer of particles, but even is infinity, species of particles is not infinity, then posibilities are limited.
Mathematics is the pencil of the true physicist.
If this principle had still been maintained since the 20th century as it was before, several scientific domains wouldn't have become a farce, like the domains of gravity, astronomy and cosmology...
Nowadays, the pencil thinks it *is* the physicist.
In my opinion mathematic is form of universe.But not every We know how substitute.
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