Division by Zero

Why is quantum gravity so hard? One reason is that standard mathematical techniques that we use so successfully to describe other interactions like electromagnetism and the weak interactions do not work for gravity. This is because gravity differs mathematically from the other three interactions.

Roughly, we can't figure out how to avoid dividing by zero in quantum theories of gravity. That division gives infinity, which we don't know how to use in a meaningful physical theory. The superstrings mentioned in the left panel can avoid the infinities, which is why they are the most promising approach to quantum gravity.