As a practicing researcher in one of the areas you mentioned in point a, I actually don’t think a child should focus too much in them. I think social science is still relatively subjective and requires experience even a PG child would not necessarily have an easier time acquiring beyond their age. Time is better spent in mastering a more foundational subject. Math and etymology are both fine use of time.I think that learning math is very important for gifted children, as I argued in Gifted children could learn math much earlier. See also Cognito Mentoring’s page on mathematics learning benefits.I’d like to address the question of whether gifted children don’t have enough life experience to be ready for the other subjects that I mention, relative to their readiness for math. I’ve worked primarily with gifted young people of ages 10 and higher, so my remarks are primarily of relevance to that age group, though they may be relevant to exceptionally gifted children who are younger than that as well.

• Study of Exceptional Talent has found that many more children qualify based on the math section of the SAT than on the verbal section of the SAT. This suggests that gifted children can, on average, excel more in math than in subjects that require verbal reasoning. (On a recent thread it was suggested that the modern SAT’s verbal section isn’t a good measure of verbal reasoning, but many more people qualified for Study of Exceptional Talent before 1995 as well.) It’s been hypothesized that this is because high performance in math can come either from strong verbal reasoning or from strong abstract pattern recognition (of the type that the Raven’s matrices test measures).
• The case for learning the other subjects that I mention is stronger for verbally gifted children than for gifted children whose strengths are nonverbal.
• Because math is a subject that’s taught in K-8 school whereas the other subjects that I mentioned aren’t, one would expect gifted children to learn more math independently of whether they’re more developmentally ready for it. It can be argued that the reason that math is taught in schools when the other subjects aren’t is because children are more developmentally ready for math. But there are other possible explanations for this, such as the practical importance of arithmetic. In any case, one would have causality in both directions even if it were true.
• Similarly, the fact that there are more math enrichment activities (largely in the form of contests) available for gifted children makes them more likely to excel in math than in the other subjects. My understanding is that math contest culture originated at least in part from the Cold War, when the Soviet Union worked to train children in preparation for quantitative occupations in research and development to feed into the Soviet Union’s military power.
• It may be that life experience enables one to understand economics more deeply. But it’s equally true that learning economics early could prepare one to learn more from one’s early life experiences, on account of seeing relevant economic concepts in them.
• I think that for children, improving reading and writing skills is more important than learning the subjects that I mentioned. But one can pick up reading and writing skills through them.

Nontechnical, nonfiction books aimed at adults that have few prerequisites such as:

• Microbe Hunters (history of biology),
• Naked Economics
• The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
• Our Developmental Economics Recommendations.

may be well-suited to gifted children with broad curiosity who are reading at the adult level.