While there are some attempts with evidence-based policy, these sciences just aren't really at the point where math is useful (yet).
Math mostly requires reducibility: the ability to split it into small parts and look at these individually. That approach worked incredibly well in physics, and with the Manhattan project at the latest, it proved that it was mightier than any human endeavour before it.
But while, theoretically, everything could be reduced to physics, that isn't always the level of abstraction that works best. If you're depressed, a physicist isn't going to help you. Medicine may – but a psychologist, even though the discipline is scientifically flawed - is still an important tool in the set available to us.
Sociology is psychology on a population-scale. In that regard, it may be almost impossible to reduce because of nonlinear effects, chaos etc. That severely limits applying results from prior experiment X,Y,Z to situation B – because what you usually do is split situation B into components (B1=X,B2=Y,B3=Z,...), each of which is quite generic and has been studied in detail. So you'd have to run your own experiment on B, and the questions of sociology would require you to run an A/B experiment, with both A and B being, for example, New York.