Vladimir_Nesov comments on Training for math olympiads - Less Wrong
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One core skill is ability to solve problems eventually, to not stop before you solved the problem. Bringing this to contest setting requires speeding up to a level that is probably unattainable because of limitations of raw ability, and might benefit from lots of training. But another failure mode is stopping right after you solve the problem, so that you won't notice a stupid error, even though you've got the solution. This is a piece of low-hanging fruit that doesn't necessarily require any significant effort (in comparison), but still needs to be collected.