By Anonymous
When we beginning thinking about what necessarily makes a genius, there are a few concepts that jump to the front of our consciousness. Some of those are logical/analytical intelligence, scarcity, exceptionality, and exceeding outcomes.
Someone mentioned a distinction which makes me think all those others are secondary to one factor alone, the attainment, use or introduction of difficult to have attained ideas.
To make this point clear, consider the difference between a virtuoso and genius.
A virtuoso may apply exceeding logical/analytical intelligence to refine their techniques to a point at which they become exceptionally, and achieve unparalleled outcomes, and it could be the case that the percentage of people who can or do become virtuosos are indeed very rare, i.e., they are scare. And yet, we can conceive of something else. Something that would be different, and in someways, more than that. Nikola Tesla comes to mind.
What is different is the ability to attain ideas which are incredibly difficult to have gathered from all the available collective understanding and physical things around you.
Also, consider a person who is not so exceedingly analytically brilliant as say an outstanding virtuoso, but who is able to conceive of a new idea or interpret some aspect of their world around them in a novel way. They may fail in comparison of all those other factors when compared to a top flight virtuoso and yet what they may have more claim to being called genius.
When all the other factors are held equal, the ideas put a person in a qualitatively different class than a virtuoso, which we can call genius, and even when the other factors lean in favor of the virtuoso, the ideas can make a person still more competitive for the title of genius.
It seems like the ideas are what make the genius.