It's not unreasonable to assume that some of humanity's problems are NP-hard and so while science won't be able to solve those problems, neither will anything else. However, that's if we're looking for exact solutions, for we can get far with statistical modeling - we might even be able to get to good enough. I have a sneaky suspicion you would find such good enough solutions highly unsatisfying because I suspect you're after Truth, which may not be knowable, even in principle.
