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Vaniver comments on Reaching young math/compsci talent - Less Wrong Discussion
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Galenson's book on artists fascinated me: he identified two clusters, experimental artists who liked to sketch and rework things and whose quality increased with age, and conceptual artists, who liked doing preparatory work and outsourcing the actual production, who made massive contributions when young but whose productivity rapidly tapered off.
With art, there's room for both types, but I imagine that math and related fields are heavily biased towards the conceptual style, especially the theoretical components of those fields.
Actually, one of the first things that new researchers have to learn is that just thinking about a problem and coming up with ideas will get you nowhere -- you have to actually get your hands dirty and try things out to make progress.
Oh, definitely. I don't mean to imply that, say, Warhol never got his hands dirty- but that Rembrandt's skill was in the realm of dirty hands and that Warhol's skill was in the realm of insight.
(I know in my research the act of sitting down and writing out an idea or sitting down and coding an algorithm or sitting down and going through the math has been indispensable, and strongly recommend it to anyone else.)