Does Newton's Theory of Gravity actually understand gravity or is it just a really good tool for 'predicting outcomes'. The understanding is baked in to the formula and is a reflection of what Newton experienced in reality.
Newton's theory is ultimately and slightly wrong but still super useful and many LLMs are basically like this. I can see why all this becomes confusing but I think part of that is when we anthropomorphic words to describe these things that are just math models.
Most of the "predictions" you'd make using it, when discovered, were wrong. it is a deeply unpredictive formula, being useless for predicting vast classes of problems (since we are largely ignorant about the masses involved, and cannot compute the dynamics beyond a few anyway).
Science is explanatory, not "predictive" -- this is an antique mistake.
As for 'math models' insofar as these are science, they arent math. They use mathematical notation as a paraphrase for english, and the english words refer to the world.
F=GMM/r^2 is just a summary of "a force occurs in proportion to the product to two masses and inversely in proportion to their square distance"
note: force, mass, distance, etc. <- terms which describe reality and its properties; not mathematics.
Regarding your last statement, what do you see as the distinction?
Take for example eg continuity. Students are first taught it means you can graph a function in a single stroke of the pen. Later comes epsilon and delta, this is more abstract but at that stage the understanding is that "nearby values map to nearby values" (or some equivalent).
If the student dives in from there, they're taught the "existence" of real numbers (or any mathematical term) is rather a consequence of a system of symbols and relations that increasingly look nothing like "numbers", instead describing more of a process.
Later that "consequence" and "relation" themselves are formalities. "Pure" math occasionally delivers strange consequences in this sense. But it always boils down to a process that something or another must interpret and carry out.
So I wonder whether the edifice is meaningfully a thing in and of itself. Methods developed in ancient China and India etc would have been useful to the Greeks and vice versa, however all of them though worked by means of the human brain. "Line" has a distinct meaning to us, the axioms of geometry don't create the line, they allow us to calculate some properties more efficiently. We always need to interpret the result in terms we understand, don't we?
Newton's theory is ultimately and slightly wrong but still super useful and many LLMs are basically like this. I can see why all this becomes confusing but I think part of that is when we anthropomorphic words to describe these things that are just math models.