What could a superintelligent AI do, and what would be physically impossible even for it?

A superintelligent AI could do anything that we can imagine humanity doing (and more), with the only hard limit being the laws of physics.

Our understanding of the laws of physics has changed in important ways throughout history. Although current models are supported by extensive observations, so was Newtonian gravity — until some regimes were found where it failed to match experimental observations, leading to Einstein's development of the theory of relativity. If a superintelligent AI were to discover any discrepancy between how we think physics works and how physics actually works, it might be able to do things we currently believe to be impossible. (For example, if faster than light communication or travel were possible, the AI could theoretically affect things outside of its light cone.)

Even if our current understanding of the limits of physics is correct, the physically possible includes radically transformative technologies such as Dyson spheres or nanotechnology.