Maybe because socializing entails mimicry, compromise and an appeal for approval that contradicts all-consuming, solitary mental exertion. But yeah, I've never believed that smart guys were socially awkard or weak; I think this imagery, just like the notion of villianous, antagonic popular/rich kids, came about during the social populism of the '60s and '70s.
Hawking has had interesting (to put it mildly) relationships with women. Yes, he's been married, twice, and has three children. He has a disease that should have killed him long ago, yet he remains and he thrives. A remarkable human being and one of the great minds of this, or any other time.
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