Okay, first, “intelligence” in the colloquial sense is not even properly defined, much less measurable.
“Intelligence” in the sense of somebody doing IQ tests (ie “Intelligence is whatever the test measures”) is heritable, that means it correlates with your parents results. This means if your parents score high, you have a better chance of also scoring high, and vice versa.
This does not mean that all of that correlation is genetic. An example for a non-genetic causal relation would be that if your parents are “smart”, they earn more money, and with that can make sure their child gets a better eductation, which makes the child “smarter”.
“Highly gifted” children are a combination of factors. Genes, a good upbringing, the opportunity to actually get their talent recognized and to do something with it, luck. Genes are merely a small part in all of this.
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