*Bob's brain starts cook as he debates on whether this belongs in Anything But or Misc, except it's not restricted only to piano but Anything But seems more like 'not quite music' so...*

Innovation came to mind. I was wondering what Mozart would be if he were born today -- Say they cloned Mozart and gave him the best music education so that's not an issue. But the original Mozart already wrote and defined that style. The cloned Mozart couldn't copy that. And if the Mozart brain were wired up to really connect with that style (say his brain really worked well with melody and harmony and the "in" chords for that period), this new Mozart would be stuck.
But if you make a new style and break new ground, that puts someone in the history books.
Possibly becoming well-known to the point that people know of a person's work. But popularity isn't everything.
Being intelligent of course. Having skills.
Being prolific seems to be important. What if someone only wrote one piece? A first work probably isn't that great or probably isn't going to be as great as later works they would create. But is it required for a composer to share their work with the world in order to be considered a genius.
Or maybe there are different types of geniuses -- the genius machine and the "knighted" genius by society.