Evolution is probably the worst way to design anything and yet all of biology is driven by it. It is basically a random walk that just flips bits and every so often it is inevitable that some of those flipped bits will have something to do with the brain's default networks and modes of operation. But I think genius is an unstable optimum and things inevitably slide downhill. There is no such thing as heritable genius, crazy or otherwise.
There are numerous examples of families in which talents seem to persist across two or more generations. The Bachs and Mozarts come immediately to mind. Myrna Gopnik and her children Adam, Sarah, and Blake. The Huxleys. The Darwins. Multiple acting and performing dynasties: the Barrymores, Ravi Shankar and daughter Norah Jones, Woody and Arlo Guthrie. The Assads: brothers Sergio and Odair, sister Badi.
That's just off the top of my head, though searching for intergenerational or family genius turns up surprisingly few useful results.
Of course, disambiguating nurture vs. nature effects is a challenge, and I'd be interested in examples where neither prior fame nor economic advantage were particularly beneficial. Cases of twins or siblings raised independently would also be of interest.
It's easier to understand if it's thought in a negative way. For "genius" you need the confluence of maybe a dozen genes. The moment one of them is not present, you don't get the whole potential. A genius' child could be very talented, but not quite the same as parent. There is also the "nurture" component, but people tend to underestimate or even discard genetics because it isn't just a single gene.
I disagree with this statement but is difficult to debunk unless 'genius' is nailed down. Nominally if a large part of socially communicable (and thereby recorded) analytical or creative capacity ("genius") is experiential rather than genetic, then it is heritable in the sense that it can be taught. If it is taught to many, however, then by some definitions it becomes non-genius.
Are the large number of documented ascetic/hermit traditions teaching genius? Preserving an alternative worldview? Simply crazy?
I mean as a complex biological system phenomenon genius is unstable a bit like unstable weather phenomenon. We don't have windstorms all the time but every so often global currents and temperatures line up and we get one. I imagine genius is a bit like that at the genetic level.
I think genius can be nurtured and as a society we can make better use of all our geniuses but I don't think it can be taught. It really has to do with brain wiring and although much of it is plastic some of the defaults can't be changed and those default settings are usually the ones that make or break a genius.
There is nothing mystical about it. It is possible for something to be genetically predetermined without being heritable in any meaningful way because the underlying genetic patterns are unstable. Going back to my windstorm example, windstorms don't last long because the energy inherent in the storm basically rips it apart.