There are places on the Internet, if one is so inclined, to socialize and talk shop with other intelligent kids.

I'd recommend the ones I came from, like Gifted Haven and Cogito, but the former is a tiny community (really nice, but there are maybe a dozen regulars, total) and the latter requires talent search scores (although I might be able to bend an ear if you can't find one).

From what I've seen the AoPS community looks pretty good, but I have no personal experience.