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tl;dr an interview with five mensa members about how they perceive genius and their hi IQ peers. They mostly associate genius with accomplishment or creativity that expands a frontier.
I would also like to add that they saw their intelligence as a very specific one well tuned to doing IQ tests/logic puzzles.
There's no such thing as an idle genius. An idle genius is an oxymoron.

I like to think of genius in terms of perspective and thus measure it by how rare and valuable a perspective is. Genius is the extreme form of insight. It's really not a measure of IQ, although a high IQ helps.

Getting to a rare perspective is usually a product of building up a mental framework and then seeing patterns in- and making associations or connections among seemingly unrelated phenomena. True genius is seeing associations among things previously unseen.

A high IQ gives you more ability to build the mental framework needed to see these associations, and a genius has actually applied it.

Genius is a dynamic thing rendered via the lens of social value.

If scientific progress is our goal, then I would argue that forming cliques around a clique-governed definition of "most likely to elicit genius" is not only wrong, but dangerous. Heuristics can be ugly things.

Also, MENSA reminds me of church. Church is boring.