What's the proportion to breakthroughs that are easier with familiarity? How many accidental discoverers do we need to match the output of a Terrance Tao or an Erdős?
That seems like the wrong question to ask. After all, there's no shortage of people who are unfamiliar with Yao's conjecture.
Or alternatively, even the most well-read person is not au fait with the state of the art in almost all subjects, so they have a chance to make an accidental discovery there.
But this kid wasn't an outsider: he was already studying computer science at perhaps the most rigorous and prestigious institution in the world, and it's not a coincidence that he made this discovery rather than an equally talented twenty-year-old who works in a diamond mine in Botswana. There's no risk that we'll reduce the number of accidental discoveries by educating people too much.
Or alternatively, even the most well-read person is not au fait with the state of the art in almost all subjects, so they have a chance to make an accidental discovery there.
But this kid wasn't an outsider: he was already studying computer science at perhaps the most rigorous and prestigious institution in the world, and it's not a coincidence that he made this discovery rather than an equally talented twenty-year-old who works in a diamond mine in Botswana. There's no risk that we'll reduce the number of accidental discoveries by educating people too much.