I took courses in graduate level QM and Newton-style calculus sufficed. The only unusual artifact that stands out in my memory was the Dirac delta function. Pe

I took courses in graduate level QM and Newton-style calculus sufficed. The only unusual artifact that stands out in my memory was the Dirac delta function. Perhaps physicists (e.g., your example of Newton above) somehow intuitively step over the "holes" in the underlying analytical frameworks that mathematicians fall into with regularly. Mathematicians are wont to build "manholes" to cover those holes and physicists have no desire to stop them, seeing that it is honest labour and keeps the mathematicians busy.