The generation growing up today is the first that can broadly learn mathematics from mathematicians rather than from teachers, and we should encourage them to do so.
When I was 12-16, I was interested in physics enough that I would study it in my free time just for fun, solving problems from the Physics Olympiad. I could solve lots of the problems with just intuition, until I stumbled upon the sliding chain problem. I spent about a week pondering over it with no results. I approached my math teacher. He admitted defeat and referred me to the physics teacher. If I remember correctly, the physics teacher avoided admitting he didn't know how to solve it and didn't give me any pointers. That was the last Physics Olympiad problem I tried to solve, after dreaming of attending the competition for years (I should mention that at that time my primary interest already were computers; physics was just a hobby). I wonder whether this could still be a problem today when anything can be found on YouTube. There's a lot of noise, too. How long does it take the average curious kid to find the signal that is 3b1b, MIT OCW, etc?
It is certainly much easier. But if that kind of self study culture doesn't already exist in one's own school, either encouraged by teachers or classmates, it may take a much bigger leap to discover that material.
When I was 12-16, I was interested in physics enough that I would study it in my free time just for fun, solving problems from the Physics Olympiad. I could solve lots of the problems with just intuition, until I stumbled upon the sliding chain problem. I spent about a week pondering over it with no results. I approached my math teacher. He admitted defeat and referred me to the physics teacher. If I remember correctly, the physics teacher avoided admitting he didn't know how to solve it and didn't give me any pointers. That was the last Physics Olympiad problem I tried to solve, after dreaming of attending the competition for years (I should mention that at that time my primary interest already were computers; physics was just a hobby). I wonder whether this could still be a problem today when anything can be found on YouTube. There's a lot of noise, too. How long does it take the average curious kid to find the signal that is 3b1b, MIT OCW, etc?