Sabine Hossenfelder in Back Reaction:
Einstein’s theory of general relativity is more than a hundred years old, but still it gives physicists headaches. Not only are Einstein’s equations hideously difficult to solve, they also clash with physicists other most-cherish achievement, quantum theory.
Problem is, particles have quantum properties. They can, for example, be in two places at once. These particles also have masses, and masses cause gravity. But since gravity does not have quantum properties, no one really knows what’s the gravitational pull of a particle in a quantum superposition. To solve this problem, physicists need a theory of quantum gravity. Or, since Einstein taught us that gravity is really curvature of space-time, physicists need a theory for the quantum properties of space and time.
It’s a hard problem, even for big-brained people like theoretical physicists. They have known since the 1930s that quantum gravity is necessary to bring order into the laws of nature, but 80 years on a solution isn’t anywhere in sight. The major obstacle on the way to progress is the lack of experimental guidance. The effects of quantum gravity are extremely weak and have never been measured, so physicists have only math to rely on. And it’s easy to get lost in math.
More here.