That means that for now, a philosophically resigned stance combined if you're contributing to research with curiosity to motivate you rather than an expectation of any results, is the most appropriate stance as far as anyone knows.
With physical abilities this is more accepted but I don’t see a reason why mental capabilities would be any different. Some people just have more powerful brains by birth. You can achieve a lot by exercise and discipline but some people can achieve higher levels than others.
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?
Yes, you tend to get good at what gives you a buzz, in a compounding way. But I expect 'buzz' isn't random, either: it'd make sense for personality formation to notice when you show talent at something valued by some of the people around you, and flip some motivational switches in your developing mind. This seems like a better bet for your genes than trying to engineer your motivation and talent towards a common target separately.
You can't just train to win the Putnam if you don't have the talents. Have you ever sat and worked problems with someone exceptional in that area? Try it if you get the chance. The variation in ability will blow you away.
I have been around many many many smart people. So many of them seem naturally gifted. It's effortless how easily they solve things. But if you hang around long enough, it's also impressive when they reveal their magic: they just used so-and-so's technique from some discipline I've never heard of. Oh. Of course! How easy, when you put it that way.
How long did it take them to read, digest, and master all those techniques? Hard to say. Nobody followed them around with a stopwatch 24x7x365 for years.
So, lacking data, I fall back to antecdotes. I personally know very intimately a handful of valedictorian smartest person in the room type people. The kind that everyone knows is just naturally smart. I know their family life intimately. I know that none of it came without enormous time and effort.
We have the testimony of the man himself about the price he paid. I'd be interested in anyone at his level in any endevour who claimed they were just born with it.
I do believe that different people are born with different abilities. But I have seen those "smartest person in the room" people fail elementary math, then spend 100s of hours drilling flash cards to master simple arithmetic tables. I have seen them with reading (I hate the word disabilities) challenges spend 10 years reading 100s of books, then get perfect scores on college entrance exams. I have seen in person some poor child spend 3 hours every single night for a year to master 5 spelling words a week. Just to be average. Then have people think they were born knowing the dictionary.
I believe that if you randomly choose any 20 students from any elementary school in the United States and let me select 10 people from that group, then subject them to what I have seen... those students will graduate high school with perfect grades and nearly perfect standardized test scores. I am certain of it. But I do not condone doing such a thing.
Of course, that doesn't make them Feynman. But I believe Feynman when he says that he was once ordinary and that time and effort transformed him.
I was valedictorian. That might be achievable through work. Fair enough. But that's nothing compared to what top-tier minds can do.
I also had a childhood friend who tested 4 standard deviations out on a psychologist administered IQ test in high school. We had similar backgrounds. We sometimes "tied" in grades, but there is a huge gaping ability gap between me and him. You cannot study your way to that level. The raw throughput, creativity, and abstract conceptual ability cannot be achieved through practice. Maybe you have to see it yourself to believe it.
And really this shouldn't surprise us. There is huge variation in athletic talent, and anyone can see it. Why should our brains be different?
I also believe the smartest people also come with a different family/life background that is unknowingly supportive in ways they cannot explain, quantify or teach others to be.