IIRC, you said that math in economics is often used to hide the lack of theoretical advancement. How does math in sociology differ?
Hard science is quantitative.
Physics, Bio, Chem, etc
It observes to confirm reality via bell curves. Real random samples, large Ns, solid statistical analysis.
Soft science is qualitative.
Anthropology, sociology, psychology, economics, etc
It observes to describe. Any quantitative analysis in soft science has gathered numbers from dubious 'random' samples and seeks to elicit causation via subjectively assembled factors.
Example
Polls (worded in various manner for perhaps unknown reasons) and personal observations are not as objective as truely random samples of soil from a given field.
The math is no different (significance = 5%+, p-values, etc) and some social studies have huge stats. What's different is where the numbers come from. Soft science is not objective quantitative observation of hard facts, it's subjective qualificative observation of causation. Personally, I do not see the point in gathering huge amounts of data for a subjective examination. To me it seems like fake armor: "Look, this is almost the same as hard science! See how many numbers and charts and graphs I have! Surely my quantity of numbers surpasses even some major studies by hard scientists. And it all proves: I'm the coolest." What's the point of having thousands of N generated via biased poll and selective observation?
Many soft scientists write books after completing a study. This is because soft science is qualitative. So after they have crammed all the quantitative data that could possibly be objective into their journal article/thesis, they write a purely qualitative book. You don't see chems or biologists writing books about the LD50 study done on a species of insect, or the biophysical study of x species. Why? Because those things are just numbers and thus are not interesting to laymen. Without questionable causation (LD50 isn't like 'well, maybe something else did it), the story is not so interesting (just boring facts... no sources to attack, no bias to discern