It strikes me that genius is largely random, and the quantity of genius within a population is based mostly on functional density. Intelligence is certainly somewhat genetic, and education is certainly based on culture, but genius is somehow different than either of those and more than a mere combination of personality traits. There appears to be a lot of luck involved, and a suitable person must be in the right place at the right time in order to perform feats of genius -- and then everyone benefits. The best way for society to take advantage of this situation is not to institute a eugenics program or to inflict mandatory grad school -- not to try to increase the number of suitable people -- but rather to increase the number of "right places" and "right times" by fostering liberty.
Eh, maybe that's obvious. Consider the contrast between America and Europe. Both are wealthy areas, but America produces and attracts far more geniuses than does Europe, despite Europe's larger population. Why? Because America has more liberty -- and thus more functional density -- than Europe. To argue differently, can anyone name any geniuses who were related? (And who didn't work together, which would make it harder to prove they were both geniuses and neither was just along for the ride.)