I had a horrible physics teacher in school, a horrible chemistry teacher, and a horrible math teacher. Just my luck. They were like that "if you don't eat your meat you can't have any pudding" teacher from The Wall. Borderline psychotic, mean, vengeful, corrupt, you name it. So all I did in school for those subjects was the absolute minimum I could get away with, if that. But then for some 2 months we had a substitute math teacher from another school (a specialized math-slanted school where he was one of the teachers known as genius-makers). He started giving us strange math problems of totally unfamiliar design that weren't hinged on whether you had memorized the formulas, and instead required something else, maybe pattern recognition, don't remember what exactly they were about of course. And what a shocker! -- turned out I was a natural for those, and for two months I was treated by the teacher and my surprised classmates as a math star. (We did have a resident math star, with many citywide math competitions victories under his belt, and he was sort of average with those strange different problems. He managed, but not as spectacularly as he usually did with the usual.) It was surprising and exciting.
That was the first time in my life when I discovered I may have something mathematical going beneath the surface... sans the mathematical apparatus... but those two months weren't enough for it to emerge, it just peeked out through the hole in The Wall... And then our wall-building regular teacher returned and it was over.
What I'm driving at is, there's not enough progress maybe at least in part because educational systems as we know them aren't catching those who could potentially facilitate it, and instead discourage some (many) potential "progressors."