The biggest risk factor I've found for a PhD student is lack of research experience during the undergrad degree.
I've seen it over and over.
A newly-minted bachelor's student without research experience has no preparation for the frustration, isolation, and sense of futility that real researchers face.
When it hits them, many discover they lack the temperament to actually move a research project forward. By then, they will have sunk 2-3 years of their life (or more) and a major amount of prestige into a failed attempt.
If you're an undergraduate and harbor the slightest ambition to get a PhD, drop what you're doing right now and start looking for a research group to join. You're going to need 2-3 years of experience actually doing research to know if it's something you'll enjoy long term.
You may well discover that you don't like what you find. If so, better to know that now than when you're in your late 20s.
If things do work out, you'll have a better idea of what to look for in advisors and schools.
I have known plenty of people who didn't feel like they had the skills (both technical and/or social) to go in to industry so they applied to grad school.
I also struggled with mental health during my PhD, but there were a lot of compounding factors. The PhD was fuel on the fire, but not the spark.
Now I've transitioned successfully into the "data science" field, so I'm much happier!
Previous research experience might help, but there still are a number of factors that need to align in order to have a relatively smooth PhD. In my mind, it depends on the quality of your previous research experience, your advisor, and your goals upon graduation.
For my experience in particular, I did two summers of research at an R1 when I was in undergrad. Continuing on that path, I went to graduate school for my PhD. I am five years in; looking back, I was still extremely unprepared for the realities of research. When I did the undergraduate research, my hand was being held by the PhD students I was working under. Sure, I did some interesting stuff, but I received a substantial amount of guidance. Now in graduate school, my PhD advisor is very hands off, and our group tends to work in isolation. I have to push my research forward on my own. It took me years to get used to this, and not feel completely incompetent. My previous research experience was not a good predictor of my life as a PhD student.
In my mind, the best preparation would be to do a thesis-based masters degree and try to publish during that.
Find someone who got a PhD and works in industry, or who got a PhD and works in an unrelated field, or someone who didn't finish their PhD. More viewpoints will give you a better picture.
All my friends with PhDs are unhappy, and do not enjoy doing research. They are all intelligent, some a little bit creative, and only curious when forced. They are experts of citations (a tease that never gets old to me, sorry) and I’m afraid are most concerned with not being left behind or achieving prestige.
Having had countless long late-night chats with them in empty bars about this, I gather their habits of conformity got them that far and let them down once they were on their own. They consistently think what I’m doing in my life is more interesting than theirs. I think the opposite and would die to be in their shoes.
These friends are all in mathematics or humanities, and for those in humanities, I would especially die to be in their shoes. I recommend them books on a regular basis, collaborate with them on papers for fun, sending loads of notes that get chiselled down to whatever the editor is expected to prefer.
The whole process is nasty from my perspective. A pile of people desperate to wiesel off the next because that’s the skill they were selected for from early on. In my best effort to put bitterness aside, I can only rationally conclude it’s rotten to the core.
To be clear, these are very intelligent people. But, the system of schooling most go through selects fiercely against curiosity at it’s earlier stages. This is only a theory. Feel free to point to research on the topic.
People here are also seemingly very conformist. For the most part, they work extremely long hours, are in hetero-normative relationships, with similar life goals (get a high paying job, buy a house, have kids), they don't do drugs or rarely even drink. If they have any hobbies, it's going to be your typical going hiking and camping sort of deal.
I'm surprised that STEM research doesn't attract more "freaks" and free-thinking people. People who want to challenge assumptions and do things differently, explore new possibilities. Unfortunately, I guess where I am, the main draw is prestige and the possibility of getting a high paying job when you finish.
Running across an interesting book might feel like gold, makes you imagine research must be gold. You forget about the countless days, months, or years (sometimes even more depressing, decades) spent digging in between the gold veins.
I suffered from much the same disappointment when I started my PhD, after a masters that left me imagining research is a world of fun. Shortly after, I dropped it when I found a job/career that really brought me satisfaction. A move I have done more than once over the years after that.
So I have one advice for people who feel the disappointment of being "stuck" and not knowing what to chase: Consider just the work that passes the threshold for a decent standard of living and then pick the one that fulfills you more, rather that the one that makes others say "wow". Living on "kudos" means you're at the mercy of others to get your satisfaction.
Jeff Schmidt's book "Disciplined Minds" makes a similar argument. I have not read it all, though, so perhaps I should pick it up again.
The book has a good description of the problem, but in my view the author views the process as more political than it necessarily is. I also think the book's solutions are unlikely to help. But I still recommend the book as one of the few on the subject.
> Having had countless long late-night chats with them in empty bars about this, I gather their habits of conformity got them that far and let them down once they were on their own. They consistently think what I’m doing in my life is more interesting than theirs. I think the opposite and would die to be in their shoes.
Huh. You'd think they'd just leave academia and go into industry after getting their Bachelors or maybe their Masters.
I mean, I'm fairly uncreative and conformist, but I noped out of college after getting my Bachelors and went right into industry. I'm currently more than happy working at an enterprise telecom in a conservative suburb, and I'm glad I didn't stick around in academia.
The grass is always greener
Why? Some things are hard and those things will by definition have higher dropout rates. The fact that PhD programs have high dropout rates is not necessarily an issue unto itself.
> You're going to need 2-3 years of experience actually doing research to know if it's something you'll enjoy long term.
Is it realistic to expect a college sophomore to know whether or not they want to pursue a PhD program? I wish more undergraduate programs focused on original research but if yours doesn't you may not get any exposure to it until your senior year (if even then).
Don't you need a master's degree to be eligible for a doctorate program?
> If you're an undergraduate and harbor the slightest ambition to get a PhD, drop what you're doing right now and start looking for a research group to join.
How does undergraduates find a research groups to join?
Can't speak for all schools, but NC State accepts bachelors into their Masters and PhD program. While getting your PhD, you have the option to earn an MS "en route".
> How does undergraduates find a research groups to join?
For larger, research-oriented schools, this is as easy as visiting each professor's website. Most will have a link to their current or archived projects and their recent publications. Similar to the joke that you can get any academic paper for free by emailing the professor, the same can happen with research. Ask them about it and if you can join in on any of the on-going projects.
For teaching-oriented schools, this can be a little more difficult. My bachelors program only had 1 (maybe 2) labs, so if that wasn't your interest good luck. You can still do the same process, find a professor in a research area you're interested in and speak to them. There may not be funding, but you could be the spark under that prof's butt to start applying for some grants.
There are 8 or 9 former classmates of mine with PhDs and only one went out of his way to get a Master's prior, and only because it was a much more prestigious institution (Georgetown) than our undergrad (unknown liberal arts college). Everyone else either entered their respective programs directly from undergrad or had industry/life experience first.
At least at most US schools, you do not. Having one helps your chances of being accepted in most cases though
> How does undergraduates find a research groups to join?
Research fairs like career fairs, or just asking profs from classes you enjoyed - every undergrad I knew in grad school just asked my prof if they could try out research.
Sure, if you are unprepared to do research then you shouldn't do a PhD, but my parents' students are hand picked, and it is very rare that they end up with a student that doesn't want to, or is unprepared to do research.
Being a PhD student should be one of the most fun parts of an academic career. You get to focus on your research, and are mostly removed from the politics and stress of securing funding. You aren't constantly being barraged by requests to review papers or having your time used up by a myriad of other responsibilities.
I guess it is totally possible that the corner of academia that I grew up around (ocean sciences at a lab removed from the main campus) is an outlier, but my impressions of getting a PhD were always positive, and the reason I never did it was because the part after your PhD seemed like it sucked.
* dropped out (some changed field completely)
* failed to pass their defense
* were miserable until they obtained their PhD
* managed to obtain their PhD after a looooong time and a lot of financial trouble. After that followed a long quest to look for a job (humanities).
* was uber successful and loved it
Note that these are people I know from all over the world, not just one country or one school.
The one guy that was uber successful absolutely loved what he was doing. The others either did not have the passion, or found out later that they did not enjoy doing research that much, or worse loved it but could not afford being poor.
This is the absolute most most important thing. I could have taken an increased scholarship however I would be bound to researching what the top-up provider wanted. Instead I opted to be on a base level scholarship but I got to choose exactly what path I wanted to take.
This is definitely not normal in the humanities. Want to continue working next year? Win this annual contest for your subfield that 800 other people are also applying for. It will cover your costs for 5 months if you win, after you spend an entire month preparing your submission for it. Didn't win this time? I guess you'll have to spend 20 hours per week every week on course prep readings and grading essays for the next six months. Good luck getting your research done at the same time.
Humanities PhDs also on average take significantly longer than STEM PhDs. 7 years post BA is normal in the humanities. 5 years post BS is normal in STEM. Guess where all that extra time goes.
It's because DARPA and Dow Chemical don't drop $30 million on your advisor for Enlightenment history.
If only there was some way to investigate your statement. Like some sort of study that went for a few years and produced a report...
"Many academics enter science to change the world for the better. Yet it can often feel like contemporary academia is more about chasing citations. Most academic work is shared only with a particular scientific community, rather than policymakers or businesses, which makes it entirely disconnected from practice.
...
This new PhD would see students go out into the field and talk to practitioners from day one of their research, rather than spending the first year (or more) reading obscure academic literature."
So... do industry research? Let's be clear: a PhD is a training program for research. As such most research done during a PhD is generally not that impactful, certainly not to go beyond fellow academics and to non experts. In my experience most people who go into it don't have much of an idea of what they want to do afterward -- they mainly know they enjoy research and are interested in the topic. AFTER a PhD is finished they can go on and try to influence society using their skills, or not.
Exactly this. The primary skill developed during a PhD (for me, and those around me), is knowing the difference between:
1. solutions that can be pulled from literature (bake),
2. solutions that should be easy to assemble from existing solutions (buy),
3. what technology requires a small-to-medium delta above and beyond the bleeding edge (build)
All those are research, but far too often (3) is what everyone targets.
> Mental health issues are rife: approximately one-third of PhD students are at risk of having or developing a psychiatric disorder like depression.
The baseline percentage of the population which experience depression (and other mental illness) each year is known to be pretty high -- and highest in for people in their 20's. One third sounds fairly normal; at any rate, there is a burden here to show that this is an exceptional proportion.
> For instance, a PhD in Germany is supposed to take three years, according to university regulations, but most students need five years to complete one.
If you are starting from an undergraduate degree, you probably need at least two years to take the PhD intro classes. One year to start a research program might work in a subject like the author's where your papers are chats about social implications, but there are plenty of subjects where even the data collection is going to take longer than that.
> In the US, meanwhile, the average completion time for a PhD in education sciences surpasses 13 years.
These programs are dominated by people who are working teachers, working on PhDs part-time.
> One study found that for every 200 people who complete a PhD, only seven will get a permanent academic post and only one will become a professor.
Being a professor is only one possible goal and for some fields, it isn't even the primary one.
http://www.mentalhealthamerica.net/conditions/depression
1/3 is not normal at all.
My peers who went onto get PhDs without going to industry were... different. Not necessarily super smart, but not the best socially or in leadership positions.
I can think of 3 people that were getting their PhDs in engineering, but I thought they were average students at best. One was an average to below average working with me on labs. Another was just a goofy weirdo, I couldnt be friends with him because he'd shoo me away. Another was somewhat a brainiac, but to a fault, He'd get As, but didnt really have friends from what I could tell.
I imagine lots of this is correlation not causation, and that things are different at big names schools.
That can very well mean 1/3 of Americans get depression over their entire lives, and a PhD program would seem like the time to get it.
I don't know if you've been through a PhD program, but as someone who has, it's really difficult to explain the pressures and stress that you encounter during it to someone who hasn't.
https://www.sciencemag.org/careers/2014/02/paying-graduate-s... https://psychcentral.com/blog/highlighting-mental-health-in-...
In Germany, you need a Master's with the coursework done before starting a PhD.
Outside of the US, I don't think most PhD students take 'classes'. In Europe a PhD is purely a research degree.
There has been a study in Belgium that showed that Grad students had a relative risk of psychological disorder scored according to a questionnaire used to decide whether psychological/psychiatric care is needed were about 5x times more at risk than the general population, even when matched for the age, education attainment and several other known common confounding factors for mental health disorders. https://www.sciencedirect.com/science/article/pii/S004873331...
> If you are starting from an undergraduate degree, you probably need at least two years to take the PhD intro classes. One year to start a research program might work in a subject like the author's where your papers are chats about social implications, but there are plenty of subjects where even the data collection is going to take longer than that.
In Germany, you need a master's to start a PhD, as such your classes load is minimal...
> Being a professor is only one possible goal and for some fields, it isn't even the primary one.
Not according to the professors mentoring you. That's changing, but the normal consideration is that if you are not on a tenure track, you are a failure. If you acknowledge it, quite often you will lose the support of your PI and your peers.
I don't think this applies well to all fields of study. I have my Ph.D. in physics and there are loads of people researching problems that don't really have counterparts "in the field." I'm assuming "in the field" means industry or possibly a government service. I would think the same is true for mathematics at least.
>I research how to mitigate the social impact of hydropower dams.
Of course in this case, contact with people in the industry makes lots of sense. In fact, I'm not sure how this research would be conducted without this contact.
I certainly have gripes with academia but I don't think there is a monolithic motivation for students. For me, I think of academia as having the goal of advancing human understanding of the universe. Whether or not that has a social impact is probably up to some debate. I believe that one of the cool things about academia is allowing some people the ability to pursue ideas and work on problems that don't have obvious, short-term impacts.
Well, there is chasing funding. In your area of the universe, does the money follow worthwhile problems?
I was trying to say that I believe there is value or at least there can be value in the advancement of human understanding without it being tied to a social or business outcome. It seemed that the main thesis of this article was implicitly denying that value by stating that Ph.D.'s should be required to show the real-world impact of their work.
As others said, the Ph.D. students themselves don't really "chase funding" but their options are a result of chased funding, I suppose.
>A PHD should be about improving society, not chasing the metric which we measure to check if you are improving society.
It seems to be Campbell's law in action. Of course you can determine a different metric to use, or just tune the current metric some, but you'll eventually see the same problems emerge, maybe worse, maybe better.
I also think this issue shouldn't be viewed in isolation of other related issues, such as how the current system discourages reproducing the research of others and of publishing trivial results (we tested to see if we found this unexpected thing and we didn't).
Figuring how who is a good scientist, given that some theoretical good scientist could spend a decade chasing down an issue that ended up being nothing, is not an easy problem to solve. Tenure is one attempt to fix it, but it largely just re-frames the problem into deciding which scientists deserve tenure.
https://en.wikipedia.org/wiki/Campbell%27s_law
>Take my example. I research how to mitigate the social impact of hydropower dams. My core paper on this topic has been cited three times so far. I read in the promotions guidelines at my university that if I want to be promoted from assistant to associate professor I need to accumulate significant citations. As a result, I have now published a paper in which I reviewed 114 definitions of a current academic buzzword, circular economy, to propose the 115th definition of this term.
>In academic terms, this paper is a hit: it’s been cited 39 times since its publication. It is in the top 3% of all research outputs ever tracked by Altmetric, a tool measuring a paper’s influence among academics on social media. People I’ve never met before come up to me at conferences to congratulate me. But I’m not celebrating: this paper symbolises everything that’s broken in the academy. Academics love definitions, not solutions.
This feels like the pure distilled essence of Campbell's law.
Why is this about the author's feelings? There are plenty of links in the piece to underlying data sources, and these show that the problems mentioned don't vary a lot by discipline. For instance: http://phdcompletion.org
As the author points out, it’s doing a decent job destroying itself.
Unfortunately, the social impact factor has been creeping in, in the form of more 'applied research' funding which is not fundamental and does not move scientific knowledge forward. The government has limited role in funding applied research, since industry is better positioned to understand what applied research is important and has a strong incentive to fund it.
Academia is imperfect, but the genius of the system is that letting scientists chase down interesting things does end up improving society dramatically in the long run.
The professors wanted to push their own ideas rather than my own. I knew the problems I wanted to solve were highly desired as I was getting hundreds of people visiting my website a day.
The two professors were pushing that the PhD process would teach me how to research, but I realized that I would be the professor's tool.
I talked to someone I looked up to, while he wasnt incredibly successful, he told me that- I was ready to do something, I no longer needed school.
I'm very thankful, I had a bachelors and masters degree in engineering fields with industry experience. I had products people were paying money for. The PhD didnt seem like it would be as valuable as 2-6 years of working on my website or other projects.
My take- If you arent going to work, school can force you to work hard. If you are already inspired, you are ready for life, go go go.
Many people share your view, though, and it's a shame. We have all of private industry to focus on short term benefits. Grad school is one place where the grinding expectation of immediate return-on-investment can be suspended. PhD students take low compensation hoping they can use curiosity and passion to direct their research. Increasingly, that's not the case.
>> appreciate the fact that the public is giving you grants and funding because the alternative is you get nothing.
This is cutting off the hand to spite the face. Taxpayers get an _unbelievable bargain_ for the work of PhD students and postdocs. Gutting research funding won't hurt them for long, they'll easily move on to much higher paying work, it's future society that will suffer.
I'd argue you get the best and most significant contributions to society in the long run with stable government funding of basic research. Don't believe me? Ask Steven Chu, Nobel Prize winner and energy secretary:
"letting scientists chase down interesting things" as per the OP's comment is how the "human knowledge base" grows in the first place.
Besides, who would decide what research is useful to pursue, other than the experts in a given field? If you don't really understand a research subject, how can you figure out whether it's useful or not?
A PhD is a degree in doing research. When students start, it is true that many think they want careers in academia. Many then realize that academia isn't what they want after a few years in and seeing how their advisors live, realizing salaries are lower, and realizing how competitive it is. There are plenty of amazing career doors that open with a PhD besides being an academic... any career that requires the ability to conduct, interpret, and/or communicate research.
The comments about meeting practitioners are pretty foreign to my experiences doing a PhD (in AI) and being a scientist. If anything, when I meet people in industry they often think non-practical research isn't worth doing even if it might have long-term value.
I think the author would agree, although he is making the distinction between impact in academic circles vs impact in society. His claim is that impact in academic circles has become out of touch with impact in society.
> If anything, when I meet people in industry they often think non-practical research isn't worth doing even if it might have long-term value.
Is there a way to measure how much non-practical research ends up having long-term value? Intuitively, the marginal utility of a 115th definition of a circular economy doesn't seem worth the academic man power yet that is what the author is being incentivized to work on because citation culture in academia.
These seem like different questions to me. There are plenty of ways to "pursue a career in science" that don't involve academia.
Writing a PhD is a very ambitious endeavor. You will inevitably have your downs and crises, because research is hard. This is independent of the research topic. Now asking that the PhD thesis should not only advance research, but also 'improve society' will only increase the pressure.
The author also has the purpose of a PhD wrong: this is your research journeyman time, and delivering the PhD thesis is like creating your masterpiece as craftsman (in the original meaning where you create a fine piece of work which earns you the right to call yourself master of a craft). The real, unsupervised research career starts after PhD. This also means that it would be a very bad idea to start with high-risk research. Do this as PostDoc, when you have acquired all the necessary skills.
Not focusing on publications is the worst advice one can give aspiring academics. Research is about advancing shared knowledge, and the only way to do this is to share your results. If you don't manage to publish, either your results are not relevant, or your work is not considered sound by your peer researchers. Successful publishing in reputable venues validates your research, and is the most effective way to disseminate new insights. I agree that the publishing system is broken. You have to work around that by choosing the right venues. This is another academic skill you need to learn.
If you really want to improve society and feel insufficient if you 'only' improve your research field, then don't pursue a research career. Better go work for some non-profit organization, or found one.
I'm not being facetious here. Politics is one of the primary avenues of bringing about social change. Ditto civil service.
A PhD should be about novel contributions that increase the sum total of human knowledge.
I agree that we should prioritise STEM, but within STEM the research areas should be decided by the scientists themselves.
However, these “kudos” are the principle measure of academic ability/productivity used by those making hiring and funding decisions so...barring a top-down change, we are stuck with them.
And what does it mean to improve society? Basic biomedical science rarely promises improvements, but has given us revolutionary technologies (the structure of DNA, the genetic code, cloning, transgenic animals, etc, etc). The essence of basic science is that you do not know what you are going to learn, or whether it will be useful. You cannot plan unimagined discoveries.
Should graduate students start doing "research" sooner? That is certainly the standard in biomedical research, where very few courses are required. But the consequence is that students know a lot about what they have done, and very little about other disciplines. How does a graduate student in biology become a computational biologist without learning programming and algorithms?
The comments about having research experience are spot-on. And many of the frustrations people describe could be reduced by learning more about one's advisor before joining the group.
The university where I am currently doing my PhD has a very heavy focus on the outputs of a PhD contributing something worthwhile not only to academia but also to industry or the world. It isn't a massively high ranking university but it does force academics to think practically as well as theoretically. We are required to have an industry (non-academic) advisor on our supervisory panel who helps guide the research so it can be useful and not just gather dust once finished.
But I still think some people should be isolated from the daily torment of humanity to push us forward. Maybe we just need less PHD.
The (sometimes literally) million-dollar question is: how do you align incentives to bring about that desired end-state? Ph.D's are not unique in struggling with this age-old conundrum; if the government is willing to pay for robotics research for drone warfare but nobody is putting up the cash to pay for nursing-care robot research, then we can make some pretty firm predictions what kind of robots we'll see mature and reliable in twenty years.
The evaluation of whether "general good" is advanced when answering a scientific question is subjective. Might I remind you that our foundations of probability - a pillar of mathematics and more - was furthered with the intention of winning gambling games? Or that our understanding of the limits of human physiology - how much force a skull can withstand, time before death under hypothermia - was furthered by Nazi scientists at the expense of Jews and other minorities?
While born out of sin, these two examples of science unequivocally better the "general good" - now...
And even some reputable programs will let some people "buy their way" if they don't qualify as for a fellowship/funding.
- it was incredibly political, much, much more than companies I worked at.
- most students were just trying to tweak some equations and get the hell out of that place.
Overall it was a very unhealthy environment and wasnt worth It.
Academic kudos translates directly to money (tenure, research funding) and power (gatekeeper positions) and that makes it microeconomics problem. Highly competitive person with high scientific achievement may not be the best person to judge and distribute kudos of others.
We should find a way to quantify kudos distribution to create good incentives. Researchers should get impact factor for mentoring, accepting papers to journals or giving voting for tenure to others who produce high impact studies after they get the tenure.
"Improving society" as academia's objective will have its own set of misaligned incentives, potentially much worse than the pursuit of "academic kudos". How would this be measured?
I just finished my Bachelor's and am starting my Master's this month. I have no formal research experience, but I planned to dive in during my Master's. For anyone who has done/is doing there PhD, if there is any advice you all could give me in order to get the most out of this next year before I apply for PhD programs, that would be great.
Do you already know your area of interest? This would be tremendously helpful for trying to pick an advisor.
I think part of the problem is people jumping straight into PhD without any research experience. I watched quite a few students struggle when taking this road.
I do agree that it's a problem if grad school costs money, but a large stipend is only really available in STEM or medicine.
[0] Not just "in my day"-ism. According to "We the corporations", demonstrating this was originally part of the legal requirement for many governments' approval of articles of incorporation.
By that metric, most fundamental discoveries in the last 200 years would not have been enough to finish a PhD.
Even Hamming's error correcting codes took 10+ years for Bell Labs to implement it. And even then it was because they had no other alternatives and were in a bind.
Measuring the utility of academia is futile. If anything should be said about utility it is that empirically, the average ROI on academia from the point of view of The State is always net positive: economically, culturally, socially, etc.
I think it is worth taking a hard look at the value all of this mathematical research actually produces.
I understand how number theory has been useful to cryptography. I understand how branches of pure math can have a surprising influence.
But when these examples are given by pure mathematicians, it often strikes me as anecdotal and motivated reasoning. Where are the hard numbers? Where is the cool-headed evaluation?
They very much want the NSF to continue giving them grants so they can keep funding their mathematical interests. Because it personally and immediately benefits them.
It may be true that 80% of the mathematical research that is valuable to society is done by 20% of mathematicians. In this case, not much can be lost by reducing research funding.
This is how I look at it: Funding mathematical research means your society is wealthy. When the vast majority aren't worried about putting food on the table, it is a privilege when you can get paid by them to pursue your mathematical hobby. A hobby that has some relatively low chance of impacting society.
Obviously, it would be nice to fund only things that are eventually useful, but this is virtually impossible to predict in advance so....we fund a bunch of things and see what works. (Also, math is shockingly cheap compared to lab sciences so it makes even more sense to spread the bets widely.)
The number theory that makes up the basis of cryptography was established in the 1700s. For example, Euler's theorem is the basis of RSA and was proven in 1763. The theorem is a small generalization of Fermat's little theorem which was known (but not proven) in 1640. These theorems are really just simple facts about groups and other cryptosystems, such as elliptic curve cryptosystems, are essentially the same facts except the multiplicative group of integers is replaced with an elliptic curve group.
These concepts could be taught to advanced high school students with no formal pure mathematical training. The "hot" areas in modern mathematics require not only an additional 4 years of undergraduate mathematics but usually ~2 years of a PhD program to begin to understand the current papers.
This is extremely different from other fields such as theoretical computer science which seems to have applications almost immediately. Even professional mathematicians likely do not research in hopes of applications hundreds of years later.
I will not claim that modern mathematics cannot possibly have applications. I will, however, claim that pure mathematics is an extremely poor way to allocate funds if you are simply looking for a return on investment in terms of "useful theorems proved per dollar". Mathematics research should be justified by stating that people trained in pure mathematics can be useful in industry, other applied fields or to teach mathematics.
As opposed to more important pursuits, such as advertising.
The entire field of computing was invented by pure mathematicians like Turing and Church working in the 1930s. At the time, no one had any idea what the applications, if any, would be.
It's like any science. Some work has immediate applications. Other work is pure exploration of the unknown.
And it is pure exploration of the unknown that leads to the truly revolutionary discoveries. You can't set out to discover penicillin when you don't even know it exists.
I strongly, strongly disagree. A PhD should be about science. Not about utility for society. I am pretty sure that Max Planck did not think about the utility of computers when he proposed this completely absurd, little mathematical trick of discretising energy. Still, without quantum theory: no computer, no laser, no magnetic resonance imaging...and I could go on forever.
Progress in science is necessarily chaotic - if you disallow incoherence, absurdity, non-applicability, you will kill science. The author is conceptualizing "science" (maybe he talks about engineering and not science?) only as a tool of problem solving for the society - that is actual the role of science in Orwell's "1984" and that was the role of science to a certain extent in socialism. By making science teleological, one makes science ready for totalitarian abuse. Thank you very much!
By the way, comparing PhD systems from different countries is absolutely rubbish. In Germany, it is already rubbish to compare PhDs from different faculties from the same university....
It's such an absurd assertion when you consider that different people have different ideas on how to improve society.
