children who are 10+ years ahead in math
Yes, math tends to follow a standard, predictable progression, making it relatively easy to measure how advanced a student may be, beyond other children their age.

I don't know children who are anywhere near 10+ years ahead in a social science (nor adults who were as children) ... don't have a good intuitive sense for what's going on from the inside. What experience do people gain as they get older that prepares them for social sciences?
A common trait in gifted children, often listed amongst identifying characteristics, is alternately described as "advanced moral reasoning", "well developed sense of justice", "moral sensitivity", "advanced ability to think about such abstract ideas as justice and fairness", "empathy", "compassion". This humanitarian concern may inspire young gifties to be attracted to studying psychology and philosophy, two of the areas of social sciences listed in earlier posts in this thread. Links to lists of gifted characteristics include several articles on the Davidson Database here and here, SENG (Silverman), SENG (Lovecky).

While gifted kids may choose to pursue interests as varied as juggling, astronomy, and people watching, lists of Davidson Fellows, Theil Fellows, Jack Cooke Kent Scholarship recipients, etc may be especially inspiring by showing what can be accomplished at a relatively young age.

The confidence of gifted children may be boosted by reading about others like themselves (bibliotherapy). There are reading lists of books whose characters are gifted.