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.
> That misses the point that there may be breakthroughs that are much harder or near impossible to make if you're familiar with the state-of-the-art.
If that's the point, you should maybe try and find even a single example that supports it. As the article points out, Krapivin may not have been familiar with Yao's conjecture in particular, but he was familiar with contemporary research in his field and actively following it to develop his own ideas (to say nothing of his collaborators). Balatro's developer may not have been aware of a particular niche genre of indie game[1], but they were clearly familiar with both modern trends/tastes in visual and sound design, and in the cutting edge of how contemporary video games are designed to be extremely addictive and stimulating. To me, these examples both seem more like the fairly typical sorts of blind spots that experts and skilled practitioners tend to have in areas outside of their immediate focus or specialization.
Clearly, both examples rely to some extent on a fresh perspective allowing for a novel approach to the given problem, but such stories are pretty common in the history of both math research and game development, neither (IMO) really warrants a claim as patently ridiculous as "the best way to approach a problem is by either not being aware of or disregarding most of the similar efforts that came before."
[1] And as good of a video game as Balatro is, there are plenty of "roguelite deckbuilder" games with roughly the same mechanical basis; what makes it so compelling is the quality of its presentation.
