Phrenology has long been debunked as pseudoscience.
From the OP:
Nerds
Poor social skills
Isn’t that by definition?
Subsequent to the OP I conceded that the way I phrased the question was based on faulty stereotypes, and this is one of them. However, you did not include the entire relevant portion:
the point of which was to examine why these two attributes correlate. In hindsight, this may be a false premise. I may have chosen some flawed examples to explain my question, but there are definitely other sets of seemingly unrelated personality traits that do correlate.
I’m sure you can find plenty of people with good math skills and poor social skills, but that is certainly a small subset of all people with either good math skills or poor social skills. If you get down to a small enough subset of traits you won’t just see correlation, you’ll probably see cause as well, but your set size has become too small to have significance for people in general. Your premise might be a combination of confirmation bias and the conjunction fallacy at work.
And more’s the pity, since that makes the practice of retrophrenology* ethically questionable.
*“Retrophrenology:
It works like this. Phrenology, as everyone knows, is a way of reading someone’s character, aptitude and abilities by examining the bumps and hollows on their head. Therefore - according to the kind of logical thinking that characterizes the Ankh-Morpork mind - it should be possible to mould someone’s character by giving them carefully graded bumps in all the right places. You can go into a shop and order an artistic temperament with a tendency to introspection and a side order of hysteria. What you actually get is hit on the head with a selection of different size mallets, but it creates employment and keeps the money in circulation, and that’s the main thing.”
― Terry Pratchett, Men at Arms
I have a theory.
People who are not likely to be introspective and questioning why they think the way they do. Will tend to be more narrow stereotypes.
And/or they happen to find success and fulfillment in a narrow range. Good for them. As long as they don’t bother my freedom to go other ways.