I'm not talking about elementary school, I'm talking about masters or bachelor's level advanced mathematics that has nonetheless been established for decades or

I'm not talking about elementary school, I'm talking about masters or bachelor's level advanced mathematics that has nonetheless been established for decades or centuries. All I'm saying is that teaching and researching are different skill sets. One does not prepare you for the other except indirectly, nor is one a prerequisite for the other. One could just as easily say some pedagogy is required to communicate original research. It's true to an extent, but you don't need to be a excellent teacher to be an excellent researcher, or vice versa.