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I'm in the following situation: currently I'm finishing my Master's in (mathematical) Logic in Amsterdam. I'm interested in doing a PhD (preferably in the US), either in something more applied or in continuation of my current research (set theory/proof theory). I've understood this logic department has excellent placement for PhDs (many go on to places like CMU, Oxbridge, Berkeley, Stanford) and the study program is considered fairly intensive. However, I have significant chronic health issues preventing me to study much beyond 70% of what is considered ordinary full time studies here, without it affecting my mental health (although I should add that in this program around 25-40% of the people don't fully reach the 100% rate). The illness does not affect my ability to do mathematics, just how much I can do effectively of it in a day. Therefore, in all likelihood I would need more time, or at least the possibility of more time, to finish a PhD successfully. Say the average time of some PhD program X to finish is 5 years, I might need 6.5-7 years. I've read many questions on this site related to my situation, but I get very mixed signals in the answers.

So:

  1. Given the situation is it even reasonable to attempt a PhD?

  2. Suppose I were to apply for a PhD in (say) the US, and I am honest and upfront about the situation to my potential supervisor, would such extensions be possible? Or would it just mean an instant rejection?

  3. If I'm open to pursue more applied avenues (logic in computer science perhaps) would this change the answer to the above two questions? The reason I ask is that I've gotten the strong impression that such programs are in general somewhat less intensive than those in pure mathematics. But this can also just be a symptom of superiority feeling that floats around in many pure math departments ;)

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    The median time to complete a PhD in math in the US is 5.7 years. 7 years would not be unusual. ncses.nsf.gov/pubs/nsf20301/assets/data-tables/tables/… – Anonymous Physicist Jun 11 '20 at 13:23
  • I think you need to be honest and upfront about your intended working schedule. I'm not sure I can answer the rest of the question, though. I think the real question is, how would you survive on 70% of a PhD stipend? Can you have another job 30% of the time or do you need to use that time exclusively to take care of yourself? – Anonymous Physicist Jun 11 '20 at 13:26
  • @AnonymousPhysicist Thanks for your comment! Well, that of course depends on the situation and the size of the PhD stipend. But in first instance my question would be whether such an arrangement is possible. I might be able to get some external support. Are PhD stipends in the US absolutely bare minimal for survival? – Ibrahim Jun 11 '20 at 13:39
  • @Buffy Yes (anywhere), and I have a green card, if that matters. – Ibrahim Jun 11 '20 at 13:40
  • Stipends vary. You won't find many above $35,000 USD, and most will be much lower. High stipends are only found in very expensive locations. – Anonymous Physicist Jun 11 '20 at 22:46
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My advice, for the US, is to share your medical condition as narrowly as possible. Most US universities will have an office for student support in such things and they may need to know so that they can provide some services that will help you. But I, personally, probably wouldn't share it even with an advisor unless and until it proves to be an actual issue. I don't know whether this is a purely US view, but there are rules about discrimination for medical conditions here.

I also wouldn't try to work out in advance some "part time" degree. Just take as long as you need to take (caveat below).

I'm guessing a bit here, but also suggest that you are better off in pure math than applied math here, since the former seldom has deadlines to worry about. Research takes as long as it takes. And you are probably better off in a subfield that you already know pretty well to help you get through any coursework and comprehensive exams.

Don't worry about or suggest "partial stipends". Most doctoral students in the US serve as TAs, working with students in elementary classes, grading or running study sessions. Stipends without duties, as such, are pretty rare, though you seem to be writing about a pretty high level place where they may be a bit less rare. But they are likely funded by grants, even then. If you can put in the time for that, then it doesn't need to end since you are providing a service that the university vitally needs.

Caveat: Some universities have a quite firm maximum number of years of study. Make sure you know about that before you begin, but also that you know what accommodation can be made in your case. And many students take seven years to complete for other reasons. You don't have to hit the median to be successful.

Again, the student support office can be your friend.

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    @AnonymousPhysicist, there are variables here neither of us can measure. But going in assuming a priori that 70 percent will be an absolute requirement is suboptimal. What the OP "wants" with little knowledge of the US system and what is best may not align well. I'm suggesting maximum flexibility. And in math "spending" 50% on teaching and 50% on research is unmeasurable. I wonder if you are in the US. Grad students don't punch a clock here - most especially math students. Physics may be different if you are in a lab. – Buffy Jun 11 '20 at 23:16
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    @AnonymousPhysicist: Actually it is the OP's job to judge this. And, for the record, I can read. I can also think. If you have better advice, by all means, give it. – Buffy Jun 11 '20 at 23:31
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    I don't think anyone would be concerned if you took, say, seven years to complete. It is actually fairly common and for lots of reasons. But I still suggest not making making decisions early (money especially) that you may regret. Making big decisions as late as possible can be an advantage. If people already have a chance to measure your worth it will be easier to make accommodations than if they don't know you at all. First, get accepted. And the only times I pulled all nighters I failed the exam. Not worth it even for the healthy. – Buffy Jun 12 '20 at 22:02
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    "ideally have some guarantee that I won't be immediately kicked from the program if a throttle back a bit." You should only join a PhD program that has a good completion rate. This advice applies to all prospective PhD students. A good program will not kick you out for anything except serious misconduct. At top universities kicking a student out is considered a very bad thing that needs to be avoided. – Anonymous Physicist Jun 13 '20 at 1:38
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    You need to pass comprehensives. Often (usually?) you get two tries only. You may have most of the knowledge (from your MS) to do that already as the early coursework in US is intended to enable that. Afterwards, in math, your proposed 40 hour schedule should e fine. Especially if your research doesn't have to be closely coordinated with that of others as it might in a lab science. And the 60 hours per week is partly (mostly?) driven by students desire to finish quickly. But working longer hours is different from working smart. Don't push through frustration with longer hours. – Buffy Jun 13 '20 at 12:41
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I think a PhD is possible, but I am not sure whether you have maximised your opportunities. Your main focus is understandably on health restrictions, but from the supervisors and institutions point of view, funding, ability for you to support yourself, ability for you to access appropriate health care etc etc would be the major considerations, before the usual issues of competency, skill etc. I think a green card does help with the application and visa process. But I do not think that the usual and even the more expensive stipends would be enough unfortunately Ibrahim, sad to say, despite your interest, competence and skill.

Even with all that lined up, bigger issues would need to be considered. All the various visas and checks, would you fail those due to the health condition? Are there more health checks required after obtaining a Green card? Australia demands that its international students are able to obtain appropriate health insurance before any offers can be made, for example. Many students can not come here due to inadequate health insurance coverage unfortunately. It is likely that your health issues would be covered by the university insurance, but details that like that, you would need to deep dive and clarify due to your condition(s).

Once you have your head around all that, then approaching supervisors and networking is key. Hopefully people from your Masters can help, and you can find a great team that is understanding and flexible enough for your needs.

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You can consider applying for fellowships instead of PhD programs. There are accommodations for people with medical conditions in applications for fellowships. I know for instance UCLA fellowship programs have such accommodations. Try to reach out to Office of Research in the target university and let them know about your condition.

Some fellowship applications require you to find a professor who can sponsor you beforehand and some do not. Your research plan (proposal) can be as short as two pages as one of the application materials. The whole process can take up to one year and you can apply for multiple fellowships to increase your chances.

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It sounds like what you need (subject to consideration of some issues that I will discuss soon) is to seek a part-time PhD candidature. It is not impossible to get this, but some universities are reluctant to grant entry to the program because of the long period it takes, and the risk of non-completion. Some candidates enrol in a part-time candidature because they have a full-time job (one of my past PhD candidates was a part-timer and graduated successfully) but there is no inherent reason you could not seek a part-time workload for other reasons, including health issues.

  1. Given the situation is it even reasonable to attempt a PhD?

This is a matter of opportunity cost and it depends on many factors (e.g., how old you are, your ultimate career goal, etc.). Don't kid yourself --- seven years is a long investment of your time and is a substantial opportunity cost. You will also need to consider how you will sustain yourself financially for this time. Nevertheless, if you really want to develop further in this research field, and you are still pretty young, you might find that seven years of study is a worthwhile investment of your time.

  1. Suppose I were to apply for a PhD in (say) the US, and I am honest and upfront about the situation to my potential supervisor, would such extensions be possible? Or would it just mean an instant rejection?

I can't really say whether being open about your circumstance will hurt your chances of entry. That really depends on the views of the particular academics that scrutinise your application. All I can say is that if I were the potential supervisor looking at your application, I would appreciate knowing up-front that you want to do the program part-time, and it would not bother me to have a student do this. So long as the other aspects of an application are good (i.e., strong skills, good previous education, etc.) there would be no issue for me in accepting a PhD candidate on a part-time basis. Probably the only issue would be interviewing the student to make sure they are confident that they can sustain interest in the topic for such a long period of time. Other academics may have a different view, but that is my own view.

The other important thing to bear in mind here is that there is an existence after acceptance in the program that you want to think about. It is best to get accepted under an explicit agreement that you will work part-time, and with work expectations diminished accordingly. A PhD candidature can be quite stressful, and it will compound that stress if you put yourself in a position where your supervisors expect a higher workload from you than you are able to give. Contrarily, if you have this conversation up-front, and you are accepted, you will be able to start on the right foot, knowing that the work expectation of your supervisors accords with what you are able to give.

  1. If I'm open to pursue more applied avenues (logic in computer science perhaps) would this change the answer to the above two questions? The reason I ask is that I've gotten the strong impression that such programs are in general somewhat less intensive than those in pure mathematics. But this can also just be a symptom of superiority feeling that floats around in many pure math departments ;)

The entry requirements may indeed be different for different programs, but I do not think it changes any of the previous advice.

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  • Thanks for your answer! Would 70% be considered part time? Where does this limit lie? Does part time status mean you won't get any funding/tuition waiver? Because part time status sounds interesting: I could test the waters and adjust my speed accordingly. The main thing I'm trying to avoid is a situation in which my potential supervisor expects a work rate that I cannot durably maintain and this in turn further reducing work output. – Ibrahim Jun 11 '20 at 13:46
  • I'm 24, by the way. – Ibrahim Jun 11 '20 at 13:49
  • RE part-time rules: that will depend on individual university policy, but I would think that anything less than a 100% load is part-time. If you are 24 now then you will only be 31 in seven years, so there is plenty of time post-PhD. That fact militates in favour of the feasibility of the candidature. – Ben Jun 11 '20 at 13:54
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    Is this an Australian perspective? I question a lot of it for the US. – Buffy Jun 11 '20 at 14:24
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    Yeah, I agree with Buffy, part-time US PhDs are not as common as here in Australia. In Australia, many people work and self-fund their PhDs or have a university position and do their PhDs part-time. That seems much less common in the US. – Poidah Jun 14 '20 at 0:55

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