This post is up for anybody wanting to constructively discuss MO question 16587 (please read it first if you come from somewhere else).
Remember, we all love maths and science🙂 the aim is only to discuss efficient ways to teach them…
To sum up:
I’ve made the assumption that the main reason that very few scientifically-enclined people of age 16-20 do research is not that they are “less intelligent” than at say age 25, it is that simply they didn’t have the time to learn all the background.
So the question: could it be that with a bit more focuss on a topic, i.e. basically an earlier start than today just for that topic, we could see more youngsters doing real research at age 20?
Of course the key point in this proposal is to organize at the beginning a one-week or two-week panorama of science and maths, with lots of interactive presentations of scientists in the classroom and labs. That would give the youngsters a basic but wide scientific world-view, and offer them a real choice.
And of course they would still follow other courses to learn other topics, just as today, but they would learn them a bit slower.
But all this is open to discussion…