A child prodigy shows a remarkable ability beyond their age in a certain area, usually at a very young age. Most recently these kids have been academics - you've read about them in the newspaper, those little ones who go to university when eight years old. What you don't read about in the newspaper is that, quite apart from the associated psychological problems, they are physically incapable of what's demanded of them.
Young kids have small brains. It's a scientific fact. The physical space within their skulls has a smaller volume than that of adults. Unusually intelligent children may have larger brains than their peers, but whatever the size of the brain, it's still growing when a child is eight or 10 years old. The brain continues to grow until the age of about 20 years, when the frontal lobes finally reach full development.
What this means is that a kid who does an abnormal amount of mental excersise will grow up with a lopsided brain. Most academic child prodigies don't puruse arts and social sciences because they don't have the emotional maturity required. Instead they do analystical subjects - mathematics, physics, languages. This kind of mental work draws almost entirely on the left side of the brain, the analytical side. If a child does extra work in this area while still developing, then the left side of their brain will develop more than the right.
In addition to this, there's the issues of self-control and emotional intensity. These things are controlled by the frontal lobes of the brain. The reason adolescents have severe mood swings and tantrums is that their frontal lobes are still developing. Pre-adolescents have practically no frontal lobes, so the tantrums are even worse for them. Children who are pushed far ahead of their age group in academic study don't have the ability to protest. They don't have the self-control to balance their activities - if they experience a lot of positive feedback from key adults in their lives related to academic success, they're likely to work obsessively at it, further distorting their brains and social development.
Many gifted children will want to pursue the activities they find easy. They must be permitted to do so, but also encouraged to participate in other activities such as social gatherings and sports. If this is not done, they risk severe social and mental problems in adolescence and early adulthood.