An interesting case study of the misuse (bordering on the ridiculous) of mathematics in (supposed) support of "positive psychology," here in The Guardian. The implications run through many, if not all, of the social sciences, in which formalization has a been a major trend for many decades.
Math can obfuscate and mislead as well as shed light. If often lures researchers to raise research questions "where the light is better" - the questions most easily answered using the available modeling tools. In some cases, formal modeling seems to result in articles that are virtually (if not actually) circular in their argumentation.
On the other hand, one of the prime advantages of mathematical modeling, also illustrated by the case discussed in The Guardian, is that bad math is relatively easy to debunk, at least for those who are mathematically sophisticated (a category that sadly excludes me). Bad arguments using conventional (non-mathematical) language, where terms may be poorly defined, are often more difficult to expose.
Unfortunately, for that reason many strong articles that do not rely on formal models are simply not acceptable to journal editors. In other words, an unwarranted presumption exists that non-formalized arguments are bad and formalized arguments are good. My view always has been that such presumptions should be abandoned; both formal and informal arguments can and should be assessed on their own merits. The plain fact that Ronald Coase's famous 1960 article on "The Problem of Social Cost" could not be published today in any leading economics journal, simply because it lacks a formalized argument, is evidence enough that the presumption favoring formalization has gone too far.
Agnar Sandmo presents a fairly balanced view of the dangers and advantages of formalization (in economics) in his book Economics Evolving: A History of Economic Thought (Princeton 2011), pp. 447-50.