Most of the child prodigies I've read about have been subject to a lot of hot housing.
I've no doubt these kids are exceptionally bright/talented but what seems to elevate them to prodigy status is the single mindedness with which at least one parent "nurtures" them.
I suspect there are a number of gifted children who aren't perceived as prodigies simply because their families - to their credit - have taken a more rounded view of their overall development rather than laser focus on their gift.
As such I find myself quite sad seeing these prodigy stories because inevitably (though there may be the odd exception) you find they are the boiled frogs within the cohort of gifted children who've been brought up to believe the schedules, expectations, study, practice are driven by their parents is reasonable and normal for someone "like them".
It's very rare I would say for these children to look back on their childhood as adults and say they even had one, never mind enjoyed it.
Finally, just because a child is gifted it doesn't always mean they will be ultra successful. A pre-teen sporting or prodigy may lose that "status" when puberty levels the playing field
and their adult bodies are no longer "optimal" for their pursuit (hand span for example in a pianist or stride for a runner) and they are vulnerable to injury.
A maths/science prodigy might do well in academia but never produce a ground breaking proof or perhaps they lack the self discipline as an adult to dedicate themselves to years of "tedious" research that results in a breakthrough of note.
All of them can also be burdened by a weight of expectation and resulting depression that they never achieved their potential because the bar is set so high - what is enough? A Nobel prize?
My own DS is brilliant at maths and whilst DH and I (and his school) are keen to support him we feel it's important to keep him on a "regular" timetable. Yes he could have taken certain GCSE's early and is was capable of doing his maths/further maths A Level at the same time as GCSE's but what's the point? He needs the experience and social aspects of school as much as the education.