How to view "applications of maths" to non-natural sciences or drawing theories from mathematics to other fields?
For example, sociology sees a lot of "applications" of physics (e.g. thermodynamics) and maths/stats and while one can reason that they may be used as methodologies, then occasionally I think that this practice has at least the following pitfalls:
1) The fields have different epistemological basis and therefore the truth on the other is not necessarily truth in the other.
2) Since mathematics is a harder science than, say, sociology, then this can create a false perception of "more legitimacy" and e.g. distinctions between "computational sociologists" and "the rest". Particularly I've found that laymen can have an over-realistic belief into the accuracy of mathematics, because they may interpret mathematics only through some naive heuristical philosophies, like "it's the language of science".
It seems that in sociology etc. those doing these draws don't really get much bashing, on the contrary, they might be praised for being "clever". Even if the theory (from a mathematicians point of view) would be pseudo-intellectuality and irrational belief into numbers.
I am not sure what you mean by sociology exactly but if it includes the study of mammal populations then certainly the Lotka-Volterra equation is a perfectly respectable application of mathematics to sociology.