Education only partially accounts for overall intelligence. The majority is genetic. Currently, mass media outlets like to limit it at 55%, but actual studies range in stating that from 55 to 80 percent of your intelligence is inherited. Identical twins separated at birth also match up very closely in their IQs. Highly intelligent parents produce a high average intelligence in their children. My aunts and uncles being a good example of this. Multiple doctors. One self taught engineer. Lawyers. I also have a very high IQ despite going through public school, and living in general poverty during my early years.
I’m not debating there is a hereditary component to intelligence - though I think you’re wildly off the mark in stating it’s up to 80%.
This: https://ghr.nlm.nih.gov/primer/traits/intelligence says it’s 50%
This source: https://www.scientificamerican.com/article/is-intelligence-hereditary/ says “Genes make a substantial difference, but they are not the whole story. They account for about half of all differences in intelligence among people”
This study https://www.nature.com/articles/ng.3869 on the other hand concluded that up to 4.8% (not 48%, just 4.8%) of the differences between study cohorts could be attributed to genetic factors.
And this study https://www.nature.com/articles/ng.3285 points out that twins, in fact, do NOT have closely linked intelligence traits.
What I’m saying is that IQ is not a particularly good measure of intelligence, and no study which only relies on it as evidence of intelligence is a quality study. Anyone who claims to be ‘smart’ based on their IQ alone hasn’t investigated the question of what IQ is measuring.