Do you know what is model do not you? Model are representations of reality, but not the reality it self, you whole speech that by the way was way too long and boring honestly, goes to fail to say something very simple, if a mathematical model fails, is because the model is not correct, so then you have to modify the model, of course experimentation validates the model, however the language is math, not some obscure magical reality.
To put it simple, new equations are made when the original ones cannot explain reality and the model falls short, in example Maxwell equations that fixed some of the short comings of the Gauss, Ampere and Faraday`s laws.
What you are simply hiding is the fact, the whole language of engineering and science is Math, no modern theory is purely theoretical, since the scientific method demands experimentation.
Now no modern engineer will express his words with pure human language, you need Math, once the Math is clear, the theory can be expressed with words.
Here you have guys, how only say, due to their ignorance, that Math is not important, experimentation is everything, give me a break, engineering`s language and only real tool is math.