Any good books for mathematicians in order to better understand the "physics way of treating things"? Any good books for mathematicians in order to better understand the "physics way of treating things"?

In order to understand physics calculations better from a math, but non-physics background.

I have speculated that part of physics is not that much about calculation or proofs, but more about forming proper intuitions about the problems ("what happens physically", "what are important parameters", "how do they interact").
The "physics way of doing things" often involves creating a mathematical model of a physical situation that is (a) complex enough to capture the significant parts of the physical situation and at the same time (b) simple enough to be solvable.

For example, a simple model of ballistic motion will neglect air resistance, wind effects and Coriolis force.

Of course, making the correct choice of which factors to include and which to leave out depends on some degree of physical "intuition".

The Feynman Lectures on Physics are a good place to start to understand this style of thinking.
Some theoretical physicists now believe that if you create an enormously complex mathematical model, with many more spatial dimensions than currently observed by experimental physicists and engineers, and incorporating an uncountable number of differing candidate model universes with vastly differing and mostly unrealistic physical properties; that you can then take make an extra a priori leap of faith - that the right answer to any given physical question is to be found in realm of the highly complex mathematical model somewhere and now all you need to do is spend your entire research career searching this "mathematical model" for the right candidate "mathematical model" that describes what actually happens in our "real universe".

However I personally doubt that theoretical physics has now basically morphed into engineering: that is into a field of study dominated by building bigger computers and finding more efficient search algorithms.