@SculptorDad - I 100% agree with your second post! That was the point I was tying to make as well! There are many different right ways to raise a math genius (or a genius in every field), and single-mindedly concentrating on what will enhance their math potential is only one of them.
And this is to your earlier post:
No, but social development comes in stages, not all at once. Much like how in math you learn basic arithmetic before you learn algebra (even if you do it much earlier than everyone else), you learn certain social interaction skills and with your same-age peers as you grow up together. You can learn them from hanging out mostly with adults, too, but there are things learned through play and interaction with age peers that are valuable for development.
I highly doubt that the vast majority of prodigies in any area are “teenagers trapped in six-year-olds’ bodies.” That’s not really how social development works, and being really advanced in one academic area doesn’t necessarily go along with being really advanced in social development as well. I’m sure there are some, but I am also willing to be that they are few in number.
And I agree that the best way may not be (and probably isn’t) to keep them back academically just to ensure they are around people their own age - I wasn’t arguing for that - I was only countering the idea that a child’s social development wasn’t important or something that could be completely cast by the wayside in favor of the academic development.
Hmmm, I doubt that. Lack of social skills aren’t entirely genetic (or genetic at all, depending on who you ask). There are some parts of social behavior that are genetically heritable that may increase or decrease one’s sociability, but social interaction is also learned over time. Again, I don’t think that means being forced to stay behind if one is a prodigy in the classroom - there are different ways to learn how to interact socially.