You don't actually know this. I acknowledge it might be true but it also might not. How do you know what you're calling brilliance isn't a different kind of study, for example? Feynman suggests he got a buzz out of puzzles his whole life from a very early age and sought them out. With his local reputation among family, friends, school others brought them to him as well. He did inter-school stand-up math competitions, if I remember that story correctly, and described how he learned to "relax into the solution" not try to force it but look at it in a different way until it just all falls out and so on.

Then he also studied math and then won the Putnum. How would he have gone without doing all that "non-study" about problem solving and looking at problems from different ways and just doing math quite well? Maybe he was so brilliant he still would have won? I suspect not. How many others sitting for the Putnum had done similar amounts of the same quality work by way of preparation?

Genius? Or learned and honed? Both? In what proportions? Whatever I think about it is "Just like my opinion, man." Right?