I was specifically referring to the part of that sentence regarding "centuries of failed experiments and feuds." Yes, you don't need to go through all the models, but many of what people with a lay knowledge of physics call failed models aren't really failed, they just apply in regimes that they could probe at the time in terms of theory and experiment. You might not have been referring to that.

And yes, there is no single mathematical model of the physical world that I am aware of. None.

One last thing that I should say that I probably didn't say clearly enough: from physics comes the mathematical models, not the other way around. Relativity didn't come out of newtonian mechanics, it came out of a change of the underlying physical model which then yield relativistic models that reduce to newtonian mechanics.