Interesting thread which I'd avoided till now because I hate the p-word.
An eminent colleague whom I'd approached for advice about DS used it of him (without having met him). I'm still twitching, tbh.
Honestly, I think it's an unhelpful word. We see it in the list of prodigies on Wikipedia (getting a mediocre maths degree at 16 makes you a prodigy apparently!) and in people on this thread yet denying that Tao was one - honestly, if not him, then who?! It's a silly concept - even if we agree about it needing performance comparable to a talented adult in the field, how talented? Someone upthread (sorry, can't face trawling back to see who) in the same breath suggested that for music the comparison was a reasonable piano teacher, and that for maths it was a reasonable maths professor. Well, OK, but why not a reasonable piano soloist, or why not a reasonable maths teacher? You're going to catch quite different groups of children depending on exactly how you define it, and it's not clear that the resulting definition would be useful for anything, anyway.
About child-led vs parent-led: I think that's even harder than this thread has yet suggested. Parents push to overcome perfectionism, to provide challenge, etc, just as much for "prodigies" as for "HG+ children". When and how much that's the right thing to do is a genuinely difficult question. The presence of parental drive doesn't tell you much about the child, in itself, I think.
