Why do theoretical physicists have limited knowledge of basic math while mathematicians have limited knowledge of physical concepts like the nature of an electron?

What do you call basic math? Studying Physics means studying math at the same time for many years. You seem to have absolutely no idea what physics means. And *theoretical* physics needs even more math. You cannot really comprehend any physics theory without knowing the underlying math. For the public one tries to describe the results without the math, but that is not physics, that is more like philosophy.

Mathematicians do not really need physics to be able do math, unless they are specialized in the same stuff as what physicists do. But there are disciplines in math, which cannot be used in physics, so those mathematicians may neglect their physics knowledge.