Why does mathematics manage to represent a function of reality?

Why does mathematics manage to represent a function of reality? My question concerns how your logic and its structure (like topology, or the very fields of advanced logic in mathematics) manage to represent reality?

In Penrose words:

Plato made it clear that the mathematical propositions—the things that could be regarded as unassailably true—referred not to actual physical objects (like the approximate squares, triangles, circles, spheres, and cubes that might be constructed from marks in the sand, or from wood or stone) but to certain idealized entities. He envisaged that these ideal entities inhabited a different world, distinct from the physical world. Today, we might refer to this world as the Platonic world of mathematical forms. Physical structures, such as squares, circles, or triangles cut from papyrus, or marked on a flat surface, or perhaps cubes, tetrahedra, or spheres carved from marble, might conform to these ideals very closely, but only approximately. The actual mathematical squares, cubes, circles, spheres, triangles, etc.,

Particularly, I think this is possible because all statements in mathematics are ultimately conditional statements on chosen axioms. It does not tell us which assumptions are true, but it tells us what follows if certain assumptions are true (and also, if certain assumptions cannot be supported). For mathematical realists (radical Platonism), theorems have physically real consequences and our world is only one among the infinite ocean of mathematically possible universes.

But I don't understand why this abstract logic manages to "tangential" reality... why does this happen? I accept any suggestion for reading, or an explanation that might shed some light on this tunnel.

• Not clear.. calculus “represents” speed of real bodies as a mathematical function. Commented Jul 3, 2021 at 13:28
• This is sometimes known as the "unreasonable effectiveness of mathematics", if you want to look it up. A couple of comments: 1) Many (most?) mathematical constructions actually bear little resemblance to reality as we know it, 2) we do have a deeply ingrained (through evolution) sense of reality in terms of space, etc. If you believe that mathematics is a human construction, then it's not terribly surprising we've put into it rules and axioms that fit in well to model the natural world, since after all, we've had millions of years for our brains to get some intuition for it. Commented Jul 3, 2021 at 15:12
• Does this answer your question? What are the historic stances on the epistemological status of mathematics? Commented Jul 4, 2021 at 9:27

Here is my way of looking at "the unreasonable effectiveness of mathematics".

In the real world, counting macroscopic objects like pebbles or people is useful because in the real world, neither of these two things can spontaneously pop into or out of existence. Counting them has meaning. Then we discover that we can represent those counts conveniently using numbers instead of pebbles, people, or anything else. So, object permanence allows a 1-to-1 correspondence between counting objects in the real world and a mathematical representation of those counts; as such, arithmetic provides a reasonably effective tool.

Then we discover that arithmetic lets us usefully quantify not just pebbles or people but durations of time. Why is this possible? Because in the universe we inhabit, the rate of flow of time we experience happens to be the same in all ordinary circumstances, so that what we measure as one minute on a tuesday remains one minute on a thursday, and there is nothing inherently "unreasonable" about that effectiveness either.

To me, then, the reasonableness of quantification is at the root of the reasonableness of mathematical descriptions of the real world.