Mathematician: My two cents are that astronomical evidence (what we can tell about galaxies from here on earth) indicates that the laws of newtonian mechanics and gravitation in space are just the same they are here. I imagine that some quantum mechanical laws in space are harder to verify, but no one has ever observed an experiment that varied as a function of the location where it was performed. In other words, I would say that there is no evidence that the laws of physics function differently elsewhere in the universe. Of course, that doesn’t mean that there is NO CHANCE that they differ, just that there is no reason to think they do.
Physicist: To date there is strong evidence that physical laws are identical everywhere. At the very least all the laws governing atomic spectra and fusion are the same (starlight) which covers just a hell of a lot. You could also argue (not a proof) that the fundamental postulates or relativity need all positions (and all constant velocities) to have the same physical laws.
Most importantly, there is absolutely no evidence to imply that the laws change anywhere/when.