but I think there wouldn't be an AI who is as smart as a 12 year old

Oh I completely agree. That was a totally bogus example because I think that if there were and it couldn't advance, it would be insane to not call that AI.

maybe only very briefly

Here's where I disagree with you and everyone else about the "singularity". We have such little understanding of what "knowledge" and "learning" is in humans. To me, the idea of an AI that can learn any arbitrary "thing" is totally bunk, because we define the "things" it should be able to learn as exactly what we can learn, but there's no reason an AI would work at all like our brain, or any organic brain at all.

By the time we have something approaching that level of sophistication, I don't think it will look anything like what we expect. For example, it may wind up being 10 years before some AI can learn about and "understand" poetry (e.g. could pass a "poetry turing test", rating other poetry, writing about great poets, producing its own work), but maybe it will never understand some human concepts like calculus (not that it couldn't solve some problem we would solve with calculus, but maybe it has some totally other way to "think" about these problems, that wouldn't make any sense to us). If we ever do create something with a "consciousness" (whatever the hell that is) I think it will be decades before we even realize we've done it, because it won't look human at all, and I don't see any reason to believe that any system will eve be able to process the exact set of available information in, say, wikipedia, and make good sense of it the way a human would (or better). I think it will be vastly superior in some ways, and infantile in others.

Interesting to think about, and I'm not saying something like the singularity is totally impossible, but I don't expect to see anything like it in my lifetime, and I definitely don't believe that it's inevitable. I'd love to make one of those "long bets" about it, but I can't get a anyone to define what sounds to me like a reasonable test.