Pure mathematics. There's virtually no one who does (genuinely important) research who doesn't have a PhD. And those who do manage to tend to contribute to relatively more accessible fields like combinatorics or things that can be filed under 'recreational mathematics'.
Lot of weasel words in there. "Virtually no one" and "genuinely important" stick out. You also say that these people have a PhD, not that they did the genuinely important research when they were getting their PhD.
The people doing research having PhDs does not mean you need one to do the research, and you are helping to demonstrate that. Even for the specific field you chose, you needed to add a bunch of caveats in order for your stance to be at all accurate. This shouldn't even need to be said, but many (most?) of the greatest mathematicians in history did not have PhDs.
I actually don’t need those caveats; I added them because I knew if I didn’t someone would come and argue, even though their counterexample probably won’t stand.
> not that they did the genuinely important research when they were getting their PhD.
Correct. I didn’t say that, and nor did I mean it.
So-called ‘weasel words’ are not as much of a thing as some make them out to be. There’s a reason scientifically-minded people overuse them — because we try to avoid premature generalisation.
Your last point about history’s greatest mathematicians isn’t correct as far as I can see. Who are you thinking of? Euler, Gauss, whoever else you name… they all had PhDs. The system has been in place (and has been necessary) for a long time now.
Anyway… if you want to prove me wrong, just give an example. It’s as simple as that. But you won’t be able to. Personally, I can think of one non-maths PhD guy who solved an open problem in graph theory, but that fits into the collection of more accessible subjects I mentioned above and he’s not a active researcher.
It’s quite surprising to me the misconceptions that otherwise well-educated people have about mathematics and the mathematical community. It’s quite different to other parts of academia in many respects — the teaching is different, the style of research is different, the style of communication is different, the level of specialisation and sheer volume of prerequisites required to carry out or even understand current research is different. There isn’t really a good analogue. The things you’re saying work for every subject I can think of — apart from mathematics. You may think that sounds like bullshit (and I wouldn’t blame you), but it’s true! And for that reason it’s odd that you’re so confident in your assertions. Go to a university and ask the mathematicians there if you need a PhD (in the everyday sense of ‘need’ — of course you don’t literally, logically need one) to understand/be involved in the research they do. Try reading one of their papers. See how far you get. Now try the same with another subject: computer science, for example. Some of it will be unfollowable, but much of it won’t be.
All of this to say that, yes, there are indeed subjects where without the time taken to do a PhD you’re not going to be able to meaningfully contribute. And by ‘meaningfully’ I mean in the form of actual research papers or new ideas. I get that this is not the case outside of mathematics, but that doesn’t mean it’s true everywhere.
...in some subjects (particularly those that are popular here on HN). Not in general. Be careful with such sweeping statements.