But even your reason for this is not accurate.
For example, I can write, with COMPLETE ACCURACY, the differential equation of motion of a 3-body system. There's nothing "approximate" about this. Mathematically, this description is complete. I've accounted for all the interaction or forces involved in the system.
Yet, if I try to solve the differential equation to try to solve for the equation of motion to describe its more complete trajectory, this is where I have to impose the approximation. But this has nothing to do with mathematics not being complete, nor is it a shortcoming of physics. It is simply a most generalized system that cannot be described by a closed analytical form.
The same can be said with a description of atoms. I can write, with complete accuracy if I know all the interactions, the Schrodinger equation or the Hamiltonian. In principle, this is ALL I need to write to completely describe the system. Solving it is a different matter, and again, it has nothing to do with "mathematics being incomplete".
I really don't understand what this is all about. Are people arguing that we do NOT need mathematics to describe our world? Or that there are instances where we don't have to use it? I want examples, please! Talk is cheap. If people think physics can get away with simply saying "what does up must come down" with having to predict when and where it will come down, then one has mistaken philosophy for physics.
Zz.