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It's more of an arrogance vs. humility thing, which you'll find people of varying IQs with qualities of one or the other, and maybe there's feelings of inadequacy mixed in that prompts them to brag, be it explicit bragging or the more common, and 1000x more annoying "humble" bragging of finding a way to weave it into a conversation in a more subtle way. But I am of the camp that accomplishments in life are what ultimately matter, because no one gives a crap if a homeless guy has an IQ of 150.