Totally agree. And I would like to add that I don't even think a degree is the best way to learn even for many who excel at them.
as someone who keeps thinking if i should go back to finish my ph.d., i can’t help but think of how dogmatic most graduate programs are in addition to being logistical nightmares. there’s basically no time or space for one to explore one’s own thoughts and program unless it specifically matches up with what someone else (namely an advisor) wants to do. there’s so much hand holding through required coursework (and homework) that one can’t hardly think deeply about anything actually original.
the book disciplined minds touches upon this. that those born in institutions will carry that institutional conservatism with them. i have felt this. i went to talk about some of my ideas to a well known and respected researcher. before i could even finish my sentence that began with “i’m interested in...” he cut me off shaking his head and, literally, said “i don’t believe in it...”. goddamnit.
Take an actual graduate course in pure mathematics, very little hand holding.
>there’s basically no time or space for one to explore one’s own thoughts and program unless it specifically matches up with what someone else (namely an advisor) wants to do.
Not necessarily true. Find an adviser that will support YOUR interest (they exist). Sounds like you have some biases against PhD programs without actual experience of being in a good one.
> Take an actual graduate course in pure mathematics, very little hand holding.
i have taken many. and you missed my point. i didn’t mean having one’s hand held through the actual material. that isn’t true at all of course, in part due to poor teaching and in part due to the difficulty of the material. i meant that one is forced to take x amount of courses. i believe, past a certain level, that this becomes extremely limiting. you spend all this time and time effort doing coursework and going to class rather than researching. learning within a context is much better than learning without context, aka most courses. and many schools hardly take any coursework transfers. there aren’t many good reason for this.
and of course i have a bias because that’s what personal experience yields. but there’s no reason for you to insult me. i would wager my bias is shared by many who have been through ph.d. programs. and of course it’s not necessarily true. there are excellent advisors. but they are rare.
I wouldn’t expect a pure mathematician to be good at this nor to care about it either.
Did you ever read “How to Solve it?” Polya says he became a mathematician because he was too clever to be a philosopher and not clever enough to be a physicist :)
I don't find this too troubling - it's important to have a shared fundamental knowledge so you can communicate effectively and not reinvent the wheel, and I don't think most programs are giving you busy work (that's really against the whole ethos).
Is it possible the problem is particular to the US postgraduate system? In UK PhD programmers you are not required to follow any courses. That said, at least at my university as a PhD student you have the right to follow any courses you want for the duration of your PhD (obviously at no extra fee), which I'm absolutely taking advantage of.
I should also point out that a PhD is not just a time to do research- it's an opportunity to become an expert in your chosen field. And you don't do that just by inventing new knowledge. You need to also become familiar with the work others have contributed before you- and by "familiar" I mean "learn it very, very well". Perhaps the US universities are just trying to make sure you don't spend all your time with your nose in your own research, while ignoring everything others are doing around you?
After that you enter into the Ph.D. for 3 years(max 4) and you are right, you can almost do whatever you want. Just bear in mind that either you publish in top journals or your academic career ends here.
Then there's the program itself. DTCs (doctoral training centres) now mostly run 3 + 1 programmes, where your first year is a master's, involving taught classes and a research project. This is to get everyone up to speed on how to actually do independent research, and to build core skills. While it's true that teaching doesn't always form a mandatory part of a doctoral degree, working as a teaching assistant for at least one semester is often mandatory.
In short, you've mischaracterised doctoral education in England and Wales (Scotland may be different) to quite an extraordinary degree. I see no reason to comment upon the "more than our top share" claim, for reasons which are, I hope, obvious.
Well I'm not sure that many people without a first would seriously consider doing a PhD, so this isn't relevant in most cases.
> DTCs (doctoral training centres) now mostly run 3 + 1 programmes
Right, which is a big disadvantage of them. DTCs are just one way to do a PhD and they're not the traditional approach in the UK.
> In short, you've mischaracterised doctoral education in England and Wales
I don't agree! This matches from I see of students going into and coming out of the system today.
Too many have come to believe a degree is the magic. In some cases it is. In plenty of others it's a curse. The time and money could have been better spent elsewhere.