Even in think-y land, so much depends on instinct, "taste" for problems/approaches, an aesthetic of ideas. Frank Oppenheimer points out that play is so important because it's one of the only ways adults hone their sense of taste. (from Something Incredibly Wonderful Happens)
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It's interesting to contrast this to the approach for developing style which Hamming recommends in The Art of Doing Science and Engineering—analytical, reflective, retrospective. But maybe this is a kind of "play," too.
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Hamming's approach is definitely play. The chapter on n-dimensional space stands out--he develops a sense of what higher order spaces look like by playing with distances and shapes
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You’re right! It’s funny, though, he’s often very right-brain-ish when he talks about style. e.g. in another chapter developing style by carefully analyzing the minute practices of scientists who have made discoveries you find important; etc…