Are Some Fields just Harder?
On one hand, there are so many things that just need doing. They haven't been done, not because they are so hard that humanity hasn't figured out how, but because no one has gotten around to doing them yet.
On the other hand, there are other fields. Like math.
You'll note that I don't try to modestly say anything like, 'Well, I may not be as brilliant as Jaynes or Conway, but that doesn't mean I can't do important things in my chosen field.'
Because I do know... that's not how it works.
Also, Scott Alexander:
The standard psychiatric evaluation includes an assessment of cognitive ability; the one I use is a quick test with three questions. The questions are – “What is 100 minus 7?”, “What do an apple and an orange have in common?”, and “Remember these three words for one minute, then repeat them back to me: house, blue, and tulip”.
There are a lot of people – and I don’t mean floridly psychotic people who don’t know their own name, I mean ordinary reasonable people just like you and me – who can’t answer these questions. And we know why they can’t answer these questions, and it is pretty darned biological.
And if our answer to “I feel dumb and worthless because my IQ isn’t high enough” is “don’t worry, you’re not worthless, I’m sure you can be a great scientist if you just try hard enough”, then we are implicitly throwing under the bus all of these people who are definitely not going to be great scientists no matter how hard they try.
There is definitely a gap here. Are there some fields where we could always use some extra work? Are there some where you most definitely need to be a thousand year old vampire to make any sort of contribution?
Math, for example, definitely has a reputation of people unlikely to contribute anything of value once they are older than 30. Or 40. The exact numbers and their reliability is somewhat questionable, but the myth (if it is one) is coming from somewhere. You must push the edge of human knowledge, and to do that, you need to be better, for a brief moment, if only in a narrow area, than anyone who has come before you. You should have sufficient fluid intelligence (because handling interesting new math concepts just needs the mental firepower), while also having accumulated enough knowledge to have a reasonable starting point.
Compare that to the work of laying floor tiles by hand. You clearly would not need to push the edge of humanity's knowledge to do it. Once you know how to do it though, laying twice as many of them is not equivalent to doing it just once. You most definitely do not get all credit to the work if you lay two tiles and disappear, leaving a note saying "the rest of the tiles exist by induction".
It is a spectrum. It is often surprising to programmers, who are used to the idea of writing the code once and seeing it run for all eternity after, that their job rather resembles laying tiles in many important ways. You don't need to write down the code each time you want to run it, but you might have to modify it more often than expected, due to how the real world is more messy than often anticipated.
So... is math harder than laying tiles?
Distributions
Running speed in humans is fairly variable. In order to become an Olympic champion in running, not only do you need talent, but also you need to train really hard while you're young. (You also are likely to get worse at it as you get older.)
Sounds a lot like math so far.
If you were, on the other hand, to establish a local post service involving people running on foot to deliver packages, only recruiting the best Olympic runners would be kinda silly. There is not enough of them, and you do not see much downside of packages being delivered, say, 20% slower (at which speed you have plenty of candidates to choose from).
The difference is that you do not get much success in sports as a median runner; you do get to earn a good salary by being a mediocre delivery person though.
Despite the activity being very similar, there is a great perceived gap between the difficulty of the above two endeavors. It's because doing them "well" requires being at a very different percentile of skill / capability distribution.
In a way, being a math researcher requires having unique, novel insights and proof ideas in a field which everyone else is interested in. Also, you need to come up with them first; if you are second, it doesn't count (and you might not even get the chance to discover something again since it now has a well-known solution). There is no need for mathematicians to repeatedly re-derive proofs that we already know are correct (proofs are pretty powerful in that way).
In other fields, rewards are less like a step function. You do get paid to write code that is remarkably unimaginative. (In fact, more often than not, writing unimaginative code is a better idea than being original & coming up with something that is brilliant but no one will understand it two weeks later.)
In that sense, math is not harder than programming; it's just there's a higher threshold in math to count as being good.