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I was recently delighted to receive an email from someone saying that he'd just started a PhD with my old supervisor, and did I have any advice for him? You'll be unsurprised to learn that I did; I thought I'd post it here in the hope that someone else might find it useful. Some of what follows is specific to my supervisor, my field, or my discipline; most is more general. Your mileage may vary.
- Your main problem for the next 3/4 years will be maintaining morale. Don't beat yourself up for slow/no progress. Do make sure you're eating, sleeping and exercising properly. Consider doing some reading about cognitive behavioural therapy so you can spot negative thought-patterns before they start to paralyse you.
- Try to get some structure in your life. Weekly meetings are a minimum. Set yourself small deadlines. Don't worry overly if you miss them: if this stuff were easy to schedule, they wouldn't call it "research".
- Sooner or later you'll discover that something you're working on has already been done, probably by Kelly. Do not panic. Chances are that one of the following is true:
- his technique applies in some different domain (actually check this, because folklore often assigns greater utility to theorems than they actually possess)
- your technique is obviously different (so there's an equivalence theorem to prove - or maybe not...)
- your technique can be generalised or specialised or reapplied in some way that his can't.
- Start writing now. I know everyone says this, but it's still good advice. It doesn't matter if you don't think you've got anything worth writing up yet. Write up background material. Write up rough notes. The very act of writing things up will suggest new ideas. And it will get you familiar with TeX, which is never a bad thing. As a category theorist, you will probably need to become more familiar with TeX than the average mathematician. And writing is mostly easier than doing mathematics - important, since you'll need something to do on those days when you just don't have enough energy for actual research.
- Even if you don't start writing, you should certainly start maintaining a bibliography file, with your own notes in comments.
- Speaking of fluctuating energy, you should read Terry Tao's advice on time management for mathematicians.
- Keep your TeX source in version control. It's occasionally very helpful to be able to refer back and find out what changed when and why, and using a properly-designed system avoids the usual mess of
thesis.old.tex.bakfiles lying around in your filesystem. I like Git, but other systems exist. Mercurial is meant to be especially nice if you haven't used version control before. - Make sure you have up-to-date backups (perhaps via a source-code hosting site like GitHub or BitBucket). And try to ensure you have access to a spare machine. You don't want to be futzing around with screwdrivers and hard drive enclosures when you've got a deadline.
- Tom's a big fan of using rough sheets of paper to write on in supervision meetings [and perhaps your supervisor will be too, O reader]. You'll need to find a way of filing these or otherwise distilling them so that they can be referred to later. I never managed this.
- For my own rough working, I like paper notebooks, which I try to carry around with me at all times. Your mileage may vary. Some people swear by a personal wiki, and in particular the TiddlyWiki/Dropbox combo.
- Speaking of filing: the book Getting Things Done (which I recommend, even if I don't manage to follow most of its advice myself) recommends a simple alphabetical filing system for paper documents, with those fold-over cardboard folders (so you can pick up your whole file for a given topic and cart it around with you). I find this works pretty well. Make sure you have some spare folders around so you can easily spin up new files as needed.
- Don't be afraid to read around your field, even if your supervisor advises you not to. I really wish I'd ignored mine and read more about rewriting systems, for instance.
- Try to seize that surge of post-conference inspiration. My major theorem was proved in the airport on the way back from a conference. Also, airports make great working environments at 2am when hardly anybody's around :-)
- Don't forget that if things get too bad, you can quit. Sometimes that's the best choice. I know several people who've dropped out of PhD programmes and gone on to happy lives.
- The supply of newly-minted PhDs now outstrips the number of academic jobs available to them, and category theory's a niche and somewhat unfashionable field (in maths, at least - you may well have more luck applying to computer science departments. Bone up on some type theory). When you get to the end of your studies, expect finding an academic job to take a long time and many iterations. Try to have a backup plan in case nothing comes up. Let's hope the economy's picked up by then :-)
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My friend Mike (who was finishing off his PhD as I was starting mine) once said "start writing up your thesis - even if you've got nothing to write up, write it up anyway" and I found that quite helpful, because it's often when you try to write something down in rigorous detail that you find out what the problems are. Also, studies have shown (see "How to Write a Lot" by Paul J Silvia) that the more often you sit down and write, whether or not you think you've got anything worth writing, the more ideas you tend to get.
On one occasion I'd written up a few pages of stuff, put it in my supervisor's pigeonhole, realised halfway back to my desk what was glaringly wrong with it this time, went back and retrieved it from the pigeonhole and dejectedly traipsed back to my desk again. A little while later I saw Jack Cohen (reproductive biologist, SF fan, honorary professor in my department, and all-round splendid chap) in the common room, and mentioned what had happened. "Ah, very good," he said. "That means you're pushing back the boundaries of what you can do." I'd not quite thought of it that way, but it resonated with something various people told me when I was learning to juggle: a drop is a sign of progress.
My supervisor was very hands-off, which suited me fine (I was a part-time student and preferred thinking about stuff for long periods and then going to see him when I'd got something to talk about) but occasionally irked some of his other students. If you find that your supervisor's supervision style isn't quite what you were expecting, then try to figure out how to work around that, rather than trying to get your supervisor to change (which they probably won't).
(Hello, by the way - I don't think we've met, but
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This is very true, and extends beyond your doctoral studies. My PhD advisor had sufficiently little else on his plate that I was able to get a LOT of attention from him (as I wanted to); but once I got to my first postdoc, the difference between being a doctoral student with an attentive advisor to being a postdoc with a PI who was hands-off even to his doctoral students turned out to be a larger step than I had entirely expected.
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Susanne gave me a photo-shoot for my birthday. This is the result.
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[It is a good post. Oh, if only I'd had it before I'd failed mine... ;-) ]
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Of course it's OK - in fact, it's exactly what I was hoping for :-)
start writing up your thesis - even if you've got nothing to write up, write it up anyway
Yes, that's exactly what I was driving at. It's nice to know that my observations about writing causing you to get more ideas have been demonstrated more formally!
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What they did was take three groups of academics, instruct the first group only to write when it became absolutely necessary, the second group to schedule 50 writing sessions but only write when they felt particularly inspired to do so, and the third group also to schedule 50 writing sessions, and make sure they wrote something, anything, every time. (As an incentive, members of the third group had to make a donation to a disliked organisation every time they missed a session.)
They then measured the pages per day output of the subjects, and the results were what you'd expect: group 1 produced typically a fraction of a page per day, group 2 about one page per day, and group 3 about 3-3.5 pages a day.
More interestingly, though, they asked the participants to record when they had a good creative idea. The first group averaged about one idea every five days, the second group averaged about one idea every two days, and the third group (the ones who were forced to write regularly) averaged one decent, creative idea a day.
This tallies with a couple of things I've heard writers say about "writer's block". Philip Pullman famously writes three (handwritten, A4) pages every day when he's working on a book - sometimes it takes him an hour, sometimes all day, but he makes himself do it anyway, and consequently says he's never suffered from writer's block. I remember Iain Banks once saying something like "yes, I did once have writer's block - it was terrible, it lasted for almost an entire afternoon", and I suspect he has an analogous writing regime.
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Not that things went that bad anyway - I did successfully complete the PhD, but there was definitely a year early on where I didn't really get anything useful done, because I was juggling my programming job and an absurd number of undergraduate supervisions, and found that this left me with little time or energy for my own studies and research.
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This was the result. Feel free to share far and wide.
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1) For most people it's just impossible to do pure mathematical research for 8-10 hours per day - hell, Terry Tao says he can't, and he has a Fields Medal. This is where lower-concentration activities like writing, coding, sending emails, filling in expenses forms and so on come in - though writing and coding both require a fair degree of concentration too.
2) A very very small number of people do manage to change their fields with their PhD theses. You're right, though, about them best being ignored for our purposes.
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As for 1), I tend to count my days in Achievements these days. If I get one in, the day is a win. And the achievements I measure are things like “actually read that one reference I've identified I will need”, “Write down the E2-page for my toy spectral sequence example”, things like that. It accumulates, and before I know what's happened, I'm in the middle of frantic paper writing for my next submission.
Then again, I've always been surprised at the regular occurrence of actual work in the middle of all my procrastination.
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Interesting Links for 18-10-2011
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When choosing a supervisor, don't think in terms of how smart or prestigious or knowledgeable they are or seem to be. Pretty much anyone who's got a job in a university is intellectually capable of mentoring you. But a lot of academics are emotional basket cases who are incapable of forming a healthy long-term student-teacher relationship. If you're being supervised by one of these... you are going to have a lot of trouble, no matter how resilient you think you are. Pay attention to your personal intuitions about the person who is going to be the most powerful figure in your life for the next 3+ years.
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