You raise a very interesting question. In the process of obtaining doctorates in both mathematics and the social sciences, I’ve lived in these two worlds and I think I can speak impartially about both. The lure of pure mathematics and theoretical physics is that they contain deep problems that are self-contained and require prolonged abstract thought–much like chess or GO–but of higher order. For example, in pure mathematics, the only tool a researcher needs is a pencil, or at most, a computer, and the capacity for deep deductive thought and/or abstract visualization. The problems are well-known within the community of scholars and the challenge to solve one of these outstanding problems is like live bait to almost anyone who sees himself or herself as intellectually gifted. Hence most of the high IQ people are drawn into the “hard sciences.”
The social sciences, as you say, are more complicated to the extent that the concepts are not as easy to define precisely, and therefore it’s rarely possible to express any variable as a function of other variables. Economists have made some inroads into mathematizing their subject, but the models of macroeconomics usually fail to have much predictive power, because the variables are not easily quantified. In the field of psychology, concepts such as intelligence are rather fuzzy and finding the variables that measure or define intelligence is open to controversy and sometimes ideology. Those who do not see themselves as mathematically gifted, will be drawn to the social sciences where lower levels of rigor leave room for some inductive rather than deductive thinking. A researcher can explore whether treatment A is better than treatment B in producing a desired result by merely collecting data and reporting their findings. This kind of research can be important, but it is usually not as cognitively demanding (with some exceptions) and therefore can be conducted by those from a lower strata of IQ. (Those having the very lowest IQ can only survive in some areas of social science that are nothing more than ideology and opinion.) In spite of these factors, there are some high IQ people in the social sciences who are making important contributions to human knowledge and they are to be valued and encouraged, because we do need very intelligent people in these highly relevant academic disciplines.
