How do we explain child prodigies? Is their talent inherited genetically? Are they reincarnations who brought their talent with them? Have they been possessed by the spirit of a dead genius? Or is there really a very simple explanation?

I think it is just the way their minds are set up (hard wiring) which makes some things obvious to them. In music, they seem to anticipate the notes that would sound good in combinations. In math, they are, I believe, more logical than the rest of us.  It could be that there are many people like this, but only some are given the opportunity to excel.

I saw a how some years ago that explained it is because some of their parents started teaching them at an extremely young age. I have read that even though an infant's dexterity is still developing their minds are absorbing all the information. As they develop physically the you can see the information surfacing. They showed someone who used flash cards for math as they changed their diaper. Another that would play language tapes. Another that started playing musical scales.