I expect this can get one past some limitations of raw ability that wouldn't otherwise be lifted using just problem-solving practice, but I'm not sure how far.
A lot farther than most people realize. Few people actually try going meta, because social structures don't encourage it. (At least not in a near sense.)
Not going meta for developing reliability of problem-solving took a lot of points from me. I just relied on the magical intuition, which was good enough to solve some hard problems (to figure out solution method, without knowing how it was being figured out), but not good enough to reliably solve those problems without errors.
As a result, when I was applying to college, I was afraid of the regular admission exams which I couldn't reliably ace (because of technical errors I wouldn't notice, even though solution methods were obvious), and instead used the p...
Lately I've resolved to try harder at teaching myself math so I have a better shot at the international olympiad (IMO). These basically involve getting, say, three really hard math problems and trying your best to solve them within 5 hours.
My current state:
What does the intrumental-rationality skill of LWers have to say about this? What recommendations do you guys have for improving problem-solving ability, in general and specifically for olympiad-type environments? Specifically,