Two of these are not like the others.
One of the things that is so deceptive is the way so many people think that ways to make money need to be both obvious and proven.
Of course you have to be very good at math or natural science to be able to figure out how to support your own research so you can get way more accomplished than you could at a unversity.
All others need not apply.
Most universities wouldn't act on your application anyway, if you got very far without being on the academic track, that could make lots of people look bad who would prefer to keep the status-quo more restrictive.
Edit: The threat to the status-quo must have gotten bigger than I thought, defensive reactions are popping up quicker than ever.
I have to be honest, I do not understand what you want to say with your comment.
My point is that outside of fields which can somehow make money through research, not much scientific progress is made outside of universities. I don't see how you address this.
Very legitimate question.
I address it with my whole life.
It would have taken my whole life if I had stayed and gotten my PhD anyway, so why not?
People can't expect dramatically different approaches to research to do anything but make it difficult for deep understanding between them.
You really have to have an open mind.
I see raw scientific progress that many outside of instiutions do not recognize, because so many brilliant experimentalists do not have institutional credentials.
So I had a head start and took advantage of it, kept giving chemistry lessons to colleagues as they went through graduate school.
Even invented something really cool in one of their labs when I wasn't even a student any more.
Naturally I have the greatest respect for PhDs in general because that in itself is a major achievement.
But I wouldn't have gotten this far in such a non-industrial environment, core industriousness might just be a differentiation factor.
It took a long time but eventually I came to the point where I just do science every day because I'm a scientist, and make money as a byproduct of what I do.
No different than a university lab where 90% - 99% of your experiments will never pay off, if you can't handle it under a variety of financial and/or institutional situations you might need to look at reasons why like I did.
Plus with a lifetime of more intense experimentation than if I had a PhD (really do not compare myself to others) I've got zillions of financial opportunities with chemicals in particular. The most important thing turned out to be curtailing the desire to make as much money as possible, most of this stuff is toxic.
Any kind of treadmill could have led to a much worse outcome.
That is kind of my point. Outside of a few fields (some branches of chemistry certainly being one of the exceptions) will someone pay you to do your research.
I just pulled up the newest published math paper from arxiv. No one except universities will pay you to research "Quenched path limits and periodization stability for tilted Brownian motion in Poissonian potentials on Hd"
Just because your specific thing you are interested in researching has value to the free market, doesn't mean that all are so lucky.
I'm with you to a very good extent, but there are so many more promising individuals that universities just haven't had enough room for the vast majority, for quite some time.
We are all lucky that universities will still pay for advanced math progress like you have cited.
Especially math, I stuck with that pretty good before I was allowed to touch chemicals.
One of the real advantages is that all you need is a blackboard and chalk, the progress you can make is quite a bit compared to so many other things.
As an outsider I observe the lucky ones to be the few that the universities are willing to pay. I think it would be better if there were more openings and better pay too.
I know what you mean, but nobody has paid me to do research since 1982 when I was working for a commercial research startup.
That's just what I do, and never wanted to stop.
I needed to be able to pursue whatever was within reach, knowing that almost none of it was going to be interesting to anybody else, financially viable or even worth money at all. Otherwise I would have actually stayed at the university.
My most valuable milestones may be in electronics anyway where I have no university training. Had a whole lot earlier start there though.
After a lifetime as an outlier, the consistent observation is that most of the institutional systems screen out more raw talent than they employ.
I may seem extreme but it's good for somebody to strongly represent viable alternatives for that talent so maybe there will be more alternatives someday.
I have always thought that universities should expand to encompass more of what they are doing right too, but I wasn't going to hold my breath :)