Your premise is basically false. There is no theory regarding quantum gravity that has been fully worked out. There are a variety of approaches to coming up with a theory of quantum gravity that works, and some good hunches about how it should work in particular situations, but so far the set of theories of quantum gravity that work is a null set.
The difficult math comes with the territory. Really understanding quantum mechanics requires introductory graduate school/senior year undergraduate level math for math/physics majors degree of mathematical knowledge to really grasp. General relativity also requires seriously difficult math.
There are two main approaches to quantum gravity. One is to treat gravity as one more force carried by a hypothetical particle called a graviton. The other is to treat space-time as if it is not perfectly smooth, continuous and flat, and is instead discrete in some sense. Neither, however, can claim the prize of successfully coming up with a mathematically rigorous way to unite General Relativity and the Standard Model of particle physics.
