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In the next year I will (hopefully successfully) graduate from a PhD programme in pure mathematics. The location is (continental) Western Europe, the topic of the thesis is arithmetic geometry, if it matters. During my PhD experience I have found out the following things

  • being a pure math PhD student is a relatively stress-free existence for me. I can just waste all my time learning some math and occasionally writing some papers;
  • the stipend does suck but I am frugal person from a very poor country so I do not care that much (nor do I have a family to feed);
  • if I could, I would not mind spending what is left of my life in a PhD programme. In particular, I do not feel any intrinsic motivation to try to get a tenure-track position.

The question is: is it feasible for me to keep applying and getting accepted to pure math PhD programmes before I die or decide to retire? To clarify, I don't really think that I will be a problematic student; during my PhD programme, I got 3 publications accepted in reasonable journals (rank A in AustMS ranking) and I think I could maintain a similar rate of work.

Are there any "magic words" I could tell the committee that considers the applicants to improve my chances?

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    The idea of PhD programmes is that you give back more to the society than a few papers and a low CO2 footprint. Also: What if you don't get into a new program when you're fifty? You think you'll still be thought hireable in industry? Also how to you want to buy a flat and save money for your retirement days?
    – Karl
    Jun 9, 2019 at 20:06
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    PhD scholarships and postdocs aren't awarded only on the basis of the likelihood that you will produce a certain amount of work during the PhD, but also on your potential to have a successful career afterwards. Being a permanent student isn't a career, plus you're taking a spot from someone who does want a career.
    – Elizabeth Henning
    Jun 9, 2019 at 22:17
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    @ElizabethHenning +1 if only for "plus you're taking a spot from someone who does want a career." To the OP, even if you somehow managed to convince university after university to admit (and fund) you as a grad student, given the very limited number of slots it's extremely unethical behavior.
    – Noah Schweber
    Jun 10, 2019 at 5:32
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    I can just waste all my time learning some math As you seem to place no value on mathematics, your time or (more importantly) other people's time and resources, I doubt we can dissuade you from this selfishness. I can only hope that screening committees can spot this too.
    – StephenG - Help Ukraine
    Jun 10, 2019 at 12:02
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    What is it exactly about being a PhD student that you like so much? It's probably better to figure out the answer to that question and then search for jobs with similar benefits.
    – David K
    Jun 10, 2019 at 16:40

10 Answers 10

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Holding a PhD in math would usually disqualify you from being admitted into a PhD program in mathematics. Even if it does not do so officially, I'd consider it next to impossible to get scholarships.

That said, being a postdoc in math is not really much different from being a PhD student. However, even being a postdoc forever is not easy. Many funding sources have restrictions on how long ago your PhD may have been - after 5 years you already have fewer options, and continuing long after 10 years will see you face exclusion from many funding sources, as well as a strong social pressure to get a "proper" job (i.e., a faculty position).

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    "Doesn't it only matter whether the research gets done or not?" -- no, if this is a professor's only concern, they would have structured the project differently (e.g., assigning it to a permanent scientist, or hiring a sub-contractor). Post-doc positions are specifically intended to bridge between recent graduates and permanent positions, and involve a mentorship component.
    – cag51 ♦
    Jun 9, 2019 at 20:36
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    "being a postdoc in math is not really much different from being a PhD student" -- It is. The teaching load is higher (and it's actual teaching, not just grading/TAing), at least in the places I know of. And usually no one is explicitly expected to mentor you, though sometimes you can still get an informal mentor.
    – darij grinberg
    Jun 9, 2019 at 22:16
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    @darijgrinberg: That probably really depends on the places. In the places I'm familiar with, for whatever reason, some phd students do what you call "actual teaching" while postdocs have no teaching obligations at all.
    – user109595
    Jun 9, 2019 at 22:36
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    Okay, I should indeed have specified that i was talking about the US.
    – darij grinberg
    Jun 10, 2019 at 6:56
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    @phd do you know any reasons why there is time limitation on the postdoc positions? - I think you don't understand the purpose/use of postdoc in math. It's not a like a research scientist/postdoc in some field that's just meant to assist the professor's research. They're meant to be transitional positions, and are a way of bringing in fresh blood and ideas. But there are permanent positions that are essentially research only, e.g. CNRS.
    – Kimball
    Jun 10, 2019 at 7:41
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In the U.S. at least, maybe also Canada and Western Europe, in science (math, physics, chemistry, etc.), contrary to legend, graduate school can be a very wonderful, low-stress, idealistic time of life, if one has no partner, no children, no mortgage, no car payments... to worry about, and simple tastes.

On one hand, yes, in some ways grad students are exploited by The System (low pay), but, on the other hand, there is a short-term (5-year!?!) job security, interesting work, and no increase in (student-loan?) debt. And grad students are not terribly experience teachers nor researchers, so there is some kind of quid-pro-quo apart from the low salary.

At my university, it is possible to maintain that lifestyle and employment style by being a "teaching specialist": low pay forever, substantive uncertainty about employment from term to term, but very low stress/responsibilities otherwise. Some people do apparently deliberately choose such a lifestyle. Why not?

But, as @Karl mentions, if nothing else, what about planning for old age? Low pay-ins to pensions (and/or Social Security in the U.S., apart from other complications) will result in low pension payouts later.

Part of the point here is that aiming at "postdoc in perpetuity" almost universally at best would collapse back to "getting paid like a grad student, with no security, no pension". In particular, not getting paid nearly as well as post-docs, in any case.

So it's not that it's impossible to have that lifestyle, but that there are details and complications that would almost surely make you very unhappy later, without any option to go back in time and change things.

(And, yes, I'm sympathetic to your impulse, not being very materialistic myself, etc., but the realities of aging (not to mention having a partner and kids or other dependents, possibly including one's own parents at some point) have long ago burst that bubble for me.)

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    Also, the stress of constantly applying for new postdoc positions
    – Kai
    Jun 10, 2019 at 5:14
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    +1 for "if one has no partner, no children, no mortgage, no car payments... to worry about, and simple tastes."
    – YYY
    Jun 10, 2019 at 8:26
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    no children, no mortgage, no car payments, simple tastes, wait aren't those the basic features of being a monk?
    – candied_orange
    Jun 10, 2019 at 15:04
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    @candied_orange, exactly. The monastic concept of academe. :)
    – paul garrett
    Jun 10, 2019 at 15:20
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    Academia: all the benefits of taking holy orders without that pesky vow of celibacy!
    – Michael Seifert
    Jun 10, 2019 at 16:47
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There's no point in trying to do repeated Ph.D. programs in the same field when you can easily replicate the lifestyle you want in the normal way. If you don't want to pursue the tenure track, go to a less good institution and get a part-time teaching job. It won't be much money but it will likely be more than you made as a Ph.D. student. Continue your studies and publishing. You can work with folks from other insitutions in order to keep up your intellectual progress.

There is no easier thing than finding a lifestyle that works for a smart, hard(ish) working, highly skilled person who is happy with an extremely low salary in a developed country.

There is nothing special about a Ph.D. program except that it prepares you for better things.

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  • +1 but then of course, without a PhD program, you don't have a mentor who does some occasional mollycoddling. ;-)
    – Karl
    Jun 11, 2019 at 16:52
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I'm not going to answer the explicit question as others have done it pretty well, but I'd like to address the underlying assumption.

being a pure math PhD student is a relatively stress-free existence for me.

But first, let me congratulate you for that! I don't have any data but I'm pretty sure that most PhD students wouldn't describe their PhD experience as stress-free... so good for you!

During my PhD experience I have found out the following things

You have discovered things about yourself during the PhD. You will also discover new things about yourself after the PhD... even if what you do after the PhD is another PhD. What I mean is that you shouldn't be afraid of what happens after the PhD: you feel comfortable in this environment now so it's natural to wish to keep it, but actually it's likely that you will like other environments as well. Actually it looks like what you like is simply academia, so why not give a try to postdoc positions?

A friend of mine used to say that a PhD is like an initiation ritual into "academic adulthood". For many PhD students the end of the PhD is a time for questioning: self-doubt is very common, fear about the future, sometimes even depression. While it's common to go through this stage, it's important to keep in mind that we might not always see things clearly about ourselves, especially at the end of a long-term project like a PhD. In my experience most people realize what they really have learned (including about themselves) during their PhD only after graduating, because it takes a bit of perspective to see the whole picture.

In conclusion my advice is: don't be afraid, be open to opportunities and keep enjoying the science :)

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As the others mention, staying in math would be hard, but if you keep jumping to closely related fields, then it should be possible. For instance, you might find a professor in Eletrical engineering or one of the other "mathy" fields who is working on a topic that requires only a little bit of domain-specific knowledge.

I know a few people (less than 5) that have 2 PhDs. I think one of them was applying for a 3rd. They lived in a poorer Eastern European country, so the pay actually wasn't that bad. Furthermore, finding a job in industry would have been difficult due to their advanced skillset. So although getting more than one PhD sounds crazy, it wasn't actually that crazy if you think it through.

In principle, the others are right though... a Postdoc is intended for people who want more academic training in the same field.

EDIT:

There are 2 overarching scenarios that I have seen lead to someone getting more than 1 PhD. We might as well enumerate those:

  1. Vanity. In Germany, when you get a PhD of a certain type, you can call yourself Dr. (e.g. Dr. Foo). If you get 2 PhDs, then your title is Dr. Dr. Foo. And this could technically go on ad nauseam. Once I saw somebody who insisted on being addressed as Prof. Dr. Dr. XXX. In principle, you could be Dr. Dr. Dr. if you really wanted to (although this doesn't seem to be the desire here).

  2. Some countries have very little industrial technical sophistication. So if somebody wants to stay in their country after a PhD, then they are almost forced to either take a mind-numbing job in industry, or try to find something in academia. However, due to the high number of people in a similar situation, jobs for professorships or other paid academic jobs are hard to come by. So in principle, if one is curious enough to explore other disciplines, then getting a PhD in another field is not such a bad option. I would imagine that at some point a professorship would open up to a person with 2+ PhDs, but there is also the question of whether you would want to become a professor. The work of a professor is often quite far removed from pure research. So if you want to only do research, being a professor is not necessarily a good path.

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    Two PhDs is extremely unusual. I have never heard of anybody with three. The asker is proposing to get eight or nine. Why would anybody want to be an advisor for somebody doing their third, fourth, fith PhD?
    – David Richerby
    Jun 10, 2019 at 9:30
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    Why wouldn't somebody want to advise somebody like that? If they are bringing in a lot of background in other fields, I would have gladly accepted such a person in my group. In fact the hot trend in research lately is crossover work, and such a person would be immensely helpful
    – bremen_matt
    Jun 10, 2019 at 11:27
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    Because somebody whose only interest in is getting a never-ending PhDs has shown that all they're interested in is narrowly focusing on one aspect, and probably doesn't have the breadth of big-picture knowledge needed for effective interdisciplinary research. Because, after four years, they'll just say "OK, done with that. Time for something different." and go back to square one instead of moving forwards.
    – David Richerby
    Jun 10, 2019 at 14:29
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    I concur with @DavidRicherby. Doing multiple PhDs (certianly more than two) is a sign only that someone is unsure of where they want to go, only that they like being an academic. It shows a penchant for serial specialism rather than generalism (i.e., big-picture knowledge or highly interdisciplinary work).
    – Noldorin
    Jun 11, 2019 at 1:49
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    There used to be someone in my office who was doing a second PhD but I have never heard of anybody doing a third in my life.
    – Tom
    Jun 11, 2019 at 5:59
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It is immoral and anti-social of you to try this. So don't.

You're asking about feasibility, but are ignoring the detrimental effects such an attempt, or practice will have on the academic community and PhD candidates in particular.

  1. Universities and academic staff members invest resources - including time and money - in PhD programs. Young graduates aspiring to train as researchers need those resources. You'll be taking other PhD candidates' positions.

  2. You would be making PhD-level researcher skills available to universities for the price of a PhD salary/stipend. That undercuts us - everybody else - who have expenses and need to support a family, or buy a home (someday...) and so on. You would be hurting us.

  3. You have an obligation to pass on your knowledge to other, younger and less experienced, students and researchers. From your description, it seems you expect not to have to teach nor to advise younger students during your subsequent PhDs. Don't shirk that community responsibility.

I suspect it many not be psychologically beneficial for you to be "stuck" in that place in life, but that's very speculative and I don't have evidence, so I'll just put it out there as a possibility.

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  • @DavidRicherby: I think OP implied s/he won't be teaching. See edit.
    – einpoklum
    Jun 12, 2019 at 9:32
  • I added "during your subsequent PhDs" to highlight the difference between the asker's plan and the plan of somebody who's leaving academia. Roll back if you don't like it, of course.
    – David Richerby
    Jun 12, 2019 at 9:54
  • I don't think OP should be made responsible for the lack of good positions in research and education. It's a policy matter, nothing an individual can do anything about. Should one also feel guilty for taking a six year full-time position, even if six two-year part-time positions could be financed with the same money? We're sitting in one boat, solidarity would be more useful than blame-games.
    – henning
    Jun 12, 2019 at 11:44
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    @henning There is a clear difference between offering to do, e.g., half a job for half the pay (job-share, which is only useful if somebody else only needs half the money) and offering to do the whole job at reduced pay (undercutting other workers and generally driving down wages).
    – David Richerby
    Jun 12, 2019 at 12:09
  • @einpoklum henning was trying to set up some sort of equivalence between job-sharing and your point 2.
    – David Richerby
    Jun 12, 2019 at 12:33
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You might consider making, for example, a PostDoc in some more or less computer science field. I guess you will be able to find a connection between arithmetic geometry and some kind of theoretical computer science. (I know Emmanuel Haucourt, a bright researcher and a very nice guy who made the connection between topological algebra and computer science)

Then, I do also recommend to not only care about theory, but also a bit about practice (at least, being able to develop some free software research prototype).

I know excellent mathematicians who became computer science professors with a stellar-level software engineering ability (one of them is Roberto Bagnara, the architect of the PPL....)

With such a resume, even if you don't stay in pure academia, you will continue doing a lot of math. Both in industry (think of large corporations like IBM or Google or MicroSoft or SAP) or in applied research institutions (like Fraunofer institutes).

The point is that, at high enough level, computer science is a sort of math. I'm guessing that arithmetic geometry is strongly related to cryptographic techniques. And these have a lot of highly qualified jobs, even in industry. The lifestyle is almost PhD like (but the pay and job stability is better, with of course more pressure).

As others told you, getting a second PhD might worth it only if you want a tenure-track, purely academic (university) career. If you want anything else, the second PhD is a loss of time. But a PostDoc in a different field is very different story. So my suggestion would be to start a PostDoc in Computer Science (in a theoretical field close to your current skills).

NB. Not even wanting some kind of job stability could be consider as dumb behavior (and is hurting you).

PS. I am almost 60 years old and still employed at CEA, in France, and in 1985, when I entered it, the lifestyle was PhD like (I actually started my PhD at university, but defended it while at CEA). But not more today.

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It would be a pretty pointless endeavour.

After circa 50% -> 100% of one (1) PhD you should probably have managed to crank up your general study speed and techniques so that you can perform quite a bit faster on your own without distractions like

  1. teaching courses to MSc and BSc student,
  2. dealing with rewriting papers,
  3. finishing your courses,

endlessly nagging on you. To voluntarily head back in for a second or even third one would be a huge waste of your productivity. ( If you're any good, that is. ). The reason people don't quit when they feel they have reached this level where self study would be more efficient is that they are simply a bit scaredy-cat:y of looking like "drop out"s. It's quite natural. Most humans are a bit scared of that.

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    Once people have finished a PhD, they no longer have to teach or rewrite papers? News to me!
    – David Richerby
    Jun 11, 2019 at 23:11
  • @DavidRicherby : Sure, if they stay in academia.
    – mathreadler
    Jun 12, 2019 at 11:57
  • And the asker does want to stay in academia, as shown by their desire to just spend the rest of their life doing PhDs.
    – David Richerby
    Jun 12, 2019 at 12:39
  • @DavidRicherby We do not know this. All he says is that he did not find it so stressful and painful he could not imagine keeping doing it. Maybe he would prefer other better alternatives if he could think of any. We don't know what his alternatives would be. Maybe he imagines doing PhD to avoid the increased other duties often associated with taking a step into academia, getting some more permanent position entailing more duties than "PhD student" usually does.
    – mathreadler
    Jun 12, 2019 at 15:09
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    If you're suggesting that the asker should leave academia and do something else, your answer should make that much clearer. Because if they do stay in academia, they'll have to teach and they'll have to rewrite papers.
    – David Richerby
    Jun 12, 2019 at 15:17
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There is someone who works in my office who actually seems to be doing just that. She is doing a second PhD even though she apparently already has one, but I'm not sure if there is some loophole because she obtained the first one in a different country or something like that.

In general, it's not a viable option though. It's like having multiple Bachelor's degrees. Some people do have two Bachelor's degrees, where they somehow re-trained and paid for the second degree in order to change career paths. In the same way, they are likely people who have two PhD's (or equivalent) for some reason related to change of career path or something like that but in general living from one PhD to the next is not going to be possible any more than a person could just perpetually live doing one Bachelor degree after another: at some point funding is just not going to exist as you can't just fund someone to be a perpetual student indefinitely.

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    I guess the second PhD is self-funded, so not what OP has in mind.
    – henning
    Jun 11, 2019 at 8:37
  • Having two Bachelor's degrees is also a possible outcome of simultaneous double-majoring at (some?) colleges.
    – Daniel R. Collins
    Jun 12, 2019 at 5:34
  • It's possible, I have two Bachelor's degrees myself but I did the second time simultaneously whilst working full-time, so I am sure it would be possible to simultaneously do two at the same time depending on the college.
    – Tom
    Jun 12, 2019 at 14:16
  • @henning then there's Really no point. Why pay out of your own pocket to let others decide what you should use your time for when you already have "stamp of approval" saying you have learned to decide that stuff independently on your own now.
    – mathreadler
    Jun 12, 2019 at 15:06
  • @mathreadler exactly.
    – henning
    Jun 12, 2019 at 16:02
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To improve your chances, I would suggest you to move to a country where multiple doctorates (and titles) are seen as a positive. As far as I can tell, this is the case in my country, Austria (and especially in the humanities). I know a few people with two PhDs and also a few people with three. It's also not uncommon to see signs from lawyers or (medical doctors) displaying two PhDs. And, there is this guy: https://www.nachrichten.at/oberoesterreich/Das-ist-Doktor-Doktor-Doktor-Doktor-Doktor-Doktor-Norbert-Heinel;art4,843952 (article from 2011 in German, professor with 6 PhDs, two more are planned).

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  • Austrians love their titles, but the Austrian Doctorate is often self-funded. Certainly the chances of getting a second funded PhD position are not better than elsewhere.
    – henning
    Jun 11, 2019 at 8:36
  • @henning: Sure, but as I read the question, OP does not specify that they want to be funded by the PhD position (and not by, say, a side job).
    – user109737
    Jun 11, 2019 at 9:06
  • Don't enable OP's inappropriate academic and life choices.
    – einpoklum
    Jun 11, 2019 at 21:53
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    @einpoklum: I don't see what's innappropriate about that. As said before, there are people here doing exactly that. For inappropriatness, that's in the eye of the viewer. I, for one, see OP's plans as much more ethical than working for a big company and helping them making profits as most people do.
    – user109737
    Jun 11, 2019 at 21:58
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    @user109737: I may write my own answer to explain. But in a nutshell: Those people are 1. preventing others from being PhD candidates, and 2. Are making available post-PhD-trained researches at PhD salaries, undercutting the rest of us. I think it's probably a bad place to be personally and psychologically but that's a minor and speculative point.
    – einpoklum
    Jun 11, 2019 at 22:20

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