But a genius is not like this. The genius does not have a specific, positive personality type - but geniuses are characterised by not being primarily social animals.
A genius is one whose main focus and motivation is not social, nor sexual; but instead abstract, not-social - whether artistic, scientific, technical or whatever it may be.
Could it then be that the genius uses for abstract thinking, those brain-systems which in most people are used for social intelligence? That in the genius, the social intelligence system is wired-up to internal stimuli instead of to social situations?
That the genius deploys the social intelligence parts of the brain for other purposes - and that therefore the usual spontaneous motivation and attention that goes to social material is instead - automatically - being harnessed and deployed to deal with other and inner-generated material.
So, it is not that geniuses lack social intelligence (the genius is not 'autistic' in the sense of having a deficit or defect in social intelligence); rather that geniuses have all the 'equipment' necessary for social intelligence, but are 'wired-up' to use their social intelligence for other and not-social purposes.
Specifically, the genius social intelligence may be wired-up to internally-generated material (instead of attending to to actual people in the environment and from memory). The spontaneous interest and concern with 'other people' that is characteristic of most people; is, in the genius, directed to whatever 'abstract' subject the genius has a vocation-for.
Another way of thinking about this is that the genius may be able to deploy extra 'brain power' in problem solving, by 'co-opting' the brain regions normally used for social intelligence.
And not only brain power - but the distinctive 'theory of mind' mode of thinking which characterises social intelligence. So the genius thinks about 'his subject' in a social-like way - as a world populated by entities with motivations and dispositions and each having a purpose (teleology).
Social intelligence could be much of what is creative about creativity; because to think about abstract things 'anthropomorphically' with social intelligence, or animistically as if they were sentient social agents, perhaps opens-up a new and probably more creative, intuitive and flexible way of thinking.