I think that greatness of mind needs to be coupled with ambition, a certain level of arrogance and self-absorbtion, and a personality that doesn't make you a pariah.
I suspect that combinations like that, are, indeed, as rare as hen's teeth.
Many great talents probably couldn't be arsed to play the rat race game, and keep their domain humble, or they piss off other people so much, that they never get a break.
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