Advice to a new PhD student
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.bak files 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 :-)