These stories always bother me, mostly because they treat a PG kid like a newsworthy oddity and they all take same form: they flash complex equations or classic works of literature around, use the word genius liberally, and present the child as though s/he's the first person with an IQ that high in the last hundred years and/or compare the child to Albert Einstein.
To me, this stuff risks creating a kid who'll think he's failed if he doesn't figure out a set of equations for quantum gravity, invent a new kind of space drive, and win at least one Nobel prize. I've seen this effect before (perhaps others reading this message have, too). I knew a star athlete in school who had his pick of full, 100% free-ride athletic scholarships at colleges and universities around the United States. There were stories in the paper about him all the time in our last year of high school. I'm sorry to say that no one ever thought to tell him that maybe, just maybe, there were people out there who were more skilled than he was, and that things would change when he got to college. People were too busy adulating him, I guess. He wilted when he didn't start on the varsity team in the first game of his freshman year, and things went downhill (quickly)from there.
I've also seen this kind of problem develop when the guy who thought he was always going to be the smartest kid in the class gets a B or the Best Girl Scientist Ever gets critiqued during the weekly lab meeting or meets someone who has better research ideas than she does. They fall apart.
The other side of the coin is that these child-genius stories may set the bar for giftedness in some people, and even a kid with an IQ at the 99.9th percentile is probably not going to be finishing up multivariate calculus when he's 12. So what do all the rest of us with IQs <170 do when we try to tell the teachers that little Janey is gifted because she was reading when she was two or three and they compare her their gold-standard of giftedness: the kid who was doing algebra at that age?
And back to the kids who get featured in these stories, even if they can finish multivariate calculus before they're teenagers, there's no guarantee that they'll come up with those magic gravity equations anyway. Success at that level requires an extremely high level of creativity, an ability to challenge dogma, an ability to live with being an outsider, and the stubborness to keep at it even though you can't get a faculty position and you have to walk a thousand miles on a highway of broken glass to get there. Plus some other stuff too, I'd bet. Einstein wasn't working at the patent office because he had a love for the arcana of the language of claims. He couldn't get an academic job.
So I guess I'm saying that I prefer to nurture high ability and respect it quietly, but honestly, and celebrate achievement.