I would really like to see an alternative to going to grad school for a Ph.D. spring up for people who want to do research, particularly in math which doesn't require expensive labs. The overhead, the poor job prospects, the cost, the obsession with prestige all need to go.
A PhD in math does, however, require a motivated and interested supervisor. A supervisor who can tach you how to write papers, how to get them published, to tell you where you are wasting your time and to help you over the humps that may otherwise stop you. It needs a supervisor who can introduce you to others in the field, even if they live in other countries or on other continents!
That may exist as a culture in Open Source, but does not exist in Mathematics without universities - and I don't know how you make it exist for research that is hard (impossible?) to commercialise.
To do solid research requires a lot of time. Even if you don't need any expensive facilities, you still need a home and to eat, etc. If the government decided to fund maths PhDs directly, they'd need a ready-made corpus of people who could decide who gets funding. They'd need people who have published and who have proved that they know what they're talking about. These people would likely gather in central organisations where they could supervise their charges and collaborate on further publications to prove their bona fides. They may even teach lower level courses to bring in some extra money and share their administrative costs with similar worthies in other subjects...
You can rail against the cost, the prestige, and the lack of faculty positions all you like. Until your proposed solution is more than "do it at home and put it on the internet!", nothing will change.
> If the government decided to fund maths PhDs directly, they'd need a ready-made corpus of people who could decide who gets funding. They'd need people who have published and who have proved that they know what they're talking about.
Government research grants already fund maths PhDs and this process (a corpus of people who decide who gets funding) is how NSF, DARPA, IARPA, etc hand out grant money.
One problem is that the university takes a 60% cut off the the top of government grant awards. What for? I dunno, many places, the football team, padding the endowment, building new B-school buildings, hiring an army of mid-level administrators. It certainly isn't to pay for researcher (professor and postdoc) salaries, they are paid from other grants, again, from the government. It isn't to help with the grant award process, professors (and their students) write all their own grants.
The Academic tradition is alive, but the University has become a bloated beast siphoning life from the researchers and the government. What was a support infrastructure has a life of its own. It needs to be stopped.
>What for? I dunno, many places, the football team, padding the endowment, building new B-school buildings, hiring an army of mid-level administrators.
Are there really schools where the B-school is a net cost center rather than profit center? I thought it was more standard for the business school to be subsidizing other parts of the university.
I'm not saying you're wrong but it seems incredibly difficult. The problem is, how do you choose who to fund to go and do maths, how on earth you'd track their progress if any, and how do you achieve a return on your investment - even if 'you' means a sovereign nation and you have very general and long-term goals. If you can come up with something distinct from a university mathematics department to achieve this, it would be an achievement. I think we should count ourselves lucky that these departments have come to exist, and they provide such unreasonably useful output.
It might well be possible to use modern communications to distribute the work, improve efficiency and reduce overheads, basically turn all the world's maths departments into one big one - but I bet you still need something like the PhD thesis and viva.
I think what surprises me is the discrepancy between reading about mathematicians who worked with younger students out of seemingly altruistic motives (Kolmogorov and Erdos come to mind) and then a contemporary math department that might only accept 1% of applicants out of a pool of qualified people because of perhaps funding concerns or some interest in maintaining exclusivity. On top of that, there is a long history of mathematicians who worked on problems without any monetary compensation and perhaps without being associated with any university. Decartes and Fermat were both lawyers and even recently Yitang Zhang didn't seem to be paid to do research, and I don't count adjunct lecturer as a paid research job.
Given these, I don't see why an organization can't get together and simply agree to communicate, work together, somehow find a way to minimally provide access to journals for its members and dutifully train new students and grant them degrees. A Phd may or may not be optimal, perhaps something less stringent. A lot of people I know personally didn't get in to the field because they wanted to get rich, some sacrifice may be required but at least there is no denying a sort of "volunteerism" in mathematics.
This is more or less how the Royal Society started.
Academia should now be considered a conglomerate of business corporations, dedicated primarily to increasing profits and income and cutting costs.
Like other corps there's a trend towards increasing perceptions of value by marketing mediocre products and experiences to death, rather than providing actual social value with products and relationships that are truly inspiringly awesome.
So I don't think the current model is sustainable. It won't collapse next week, but I'd be surprised if we're still here twenty years from now.
As for PhDs - in my own area of interest the tenured people are pretty mediocre (believe me - I've worked through their papers) and most of the innovation and invention happens in industry.
So, there's no obvious benefit to spending the money. As it happens I earn enough to do research part time - no special resources needed in this field - and I'm getting a lot of satisfaction from making my own way for my own reasons.
overhead -> time taken and requirements to write and defend a thesis, in addition to teaching and writing papers with advisor. rhetorical question, is having a phd the only way to prove without a doubt that you are an expert in a field and know how to do research?
poor job prospects-> Did you read the article? How many tenure track positions do you think there are for someone who researches pure math?
cost-> are you paid as much as you could if you worked in industry? Are all costs monetary?
obsession with prestige -> Credentials are certainly something that people value in any field. Rankings are kept of the various departments. Of course people think about prestige, but should they? I do not believe people should worry about their own or their school's rank but simply do math if they like it but of course those thoughts occur.
Overhead, I'm on a fast-track 3yr EU PhD admittedly the US system is a different animal in this regard. Is it the only way to become an expert, of course not and I don't think anyone is making that argument.
Yes I did read the article. So you're equating "job prospects" with "chance of being a tenured professor in a specific field", more usually it means the opportunity to enter a well-paying or otherwise respectable career of any type.
Costs, sure I imagine I would earn more as a technician in industry with an MSc but if you're driven by immediate-term financial gain I'd agree a PhD is not for you.
Prestige, at PhD level it matters less about the institution than your specific advisor. Also I'd argue science is ahead of most careers in being a meritocracy, the quality of your publications should count for more than your institute's ranking. Should people care about the level of research of their institute as judged by an independent group of peers, probably yes.
A fast track 3 yr phd would be really great and yes the US system would make that very difficult.
I am equating those things under this context, if the majority of PhD grads are not becoming professors, I would like it if they "released" more of them sooner with something like your 3yr degree.
I think I can somewhat quantify prestige if you look at where some CS professors got their PhD[1]. I do think science is meritocratic but that doesn't mean all scientists are or statistics like these mean that all scientists won't experience self doubt or even get in to pissing contests with others about credentials. That sort of attitude really detracts from the altruistic community effort I imagine.
Can I ask where you are studying? I have genuine curiosity about the Euro grad schools.
edit: I should add that in no way am I saying these results prove prestige has influence or that things aren't meritocratic. But can you envision how someone might look at this and interpret it so it reinforces stereotypes or misconceptions? Spots for grad students shouldn't be zero-sum.
full disclaimer: I went to a university with a top 5 program in my field and I don't think there is a very large difference in research from these universities over time.
edit2: Another clarification, it shouldn't be that someone says "oh I didn't get in to XYZ U, I am a failure" nor should it be "oh I got in to XYZ U, I am superior". It should be, simply, "I got in to grad school, now I will study and perform research." The former attitudes are things I have encountered and find it distasteful.
Maybe too late to see this now but to answer your Q I'm at Edinburgh; IMO an ok university but not prestigious. Most EU PhDs are 3.5-4 years, I have a friend with dual US-UK citizenship that chose to do his PhD over here for this reason.
I agree wrt differences between similarly ranked institutions. I'd say similarly that the variance within groups at a top 5 school is greater than the variance between groups when compared with slightly lower ranking institutes.
