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In the Simpsons episode 'Lisa the Simpson', it is established that Homer and Bart carry the Simpson gene, which contributes to baldness and laziness. The Simpson gene is only carried by males so Lisa and Maggie don't need to worry; as a matter of fact, from what we're shown in this episode, it seems that Simpson women in general are very successful.

However, during the second part of 'Who Shot Mr. Burns?', Marge claimed that she shared everything with Homer when they were married, including Homer's DNA.

Homer has an unusual condition — "Homer Simpson Syndrome" — where his brain is cushioned by an especially thick layer of fluid, acting as a helmet of sorts. It is unknown whether the Simpson Gene causes Homer Simpson Syndrome, though the males in the Simpson family seem to have a thing for putting pots and pans on their heads and head-butting, suggesting a connection.

Another reason for Homer's stupidity is that a crayon was lodged into his brain when he was six. His IQ without the crayon was 105, placing him in the "average" bracket (90 to about 110, generally). However, in that episode, he was regarded as a "genius."