After reading Daniel Apon's question, I started thinking that it might be useful (especially to junior researchers and graduate students like me) to ask a broader and more general question so we can learn from the experience of more senior researchers.

So here is the question:

What practices have you found most useful in your research?

I don't want to restrict it to any particular type of advice, so any advice on research practice is welcome.

13 Answers 13

up vote 94 down vote accepted
+150

One thing I found useful is to allocate time and designate a space for doing specific research activities.

When I was at Princeton U, I loved sitting at the Engineering library that is well lit, bright and spacious, to read and to think of new ideas. When I verified my 139 pages paper, I used to do it in a room in the biology library at Weizmann that had no computers and no other people, only a desk, chairs and a window to an inner garden. When I go over introductions or notes, I like doing it in coffee shops.

There are several reasons why I found this to be a good practice for me:

(1) Just pondering about a good environment for me for an activity fills me with anticipation for this activity, or at least somewhat prepares me for it.

(2) The fact that I decide to do something specific at this time, and I have the space I need for doing that, induces simplicity, clarity and good order.

(3) Knowing what I like, what I care about, and also what distracts me and what is not good for me, I create environments that make it is easier for me to do what I need to do.

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    This is actually pretty useful. It never dawned on me until I read this, but I really do perform certain tasks better at certain places (and I think I've unconsciously gravitated into a habit of going to those places for those specific tasks more often). Now I can do it intentionally. :) – Daniel Apon Nov 13 '10 at 13:47
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    Moving away from the computer (and internet) certainly helps a lot. – Dave Clarke Nov 13 '10 at 15:13
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    I like this idea. I have also experienced the phenomenon of greater powers of concentration when there is no internet. I also often work better at coffee shops than at home/office, but I haven't managed to work that into a systematic system. – Mugizi Rwebangira Nov 13 '10 at 19:36
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    couldn't agree more. And as faculty, the distractions are even more severe, making this 'carved-out-space' even more important. – Suresh Venkat Nov 13 '10 at 23:44

Manuel Blum has this extraordinary page on advice to a beginning Ph.D student. Read it slowly though, for there is much to absorb.

Update: Let me add this piece of advice by Dijkstra, his Third Golden Rule for successful scientific research:

"Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you."

He presents this interesting zen-ish inference: A corollary of the third rule is that one should never compete with one's colleagues.

This inference had an huge influence on me; but it took me some time to dig out this reference.

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    There's one particular comment in Blum's list that I wish I could give +10 to: "Consider writing what you read as you read it. This is especially true if you're intent on reading something hard." It won't work for everyone, or in every circumstance, but the first couple of times I sat down to tackle truly difficult papers, I did this. I was really surprised how dramatically much more information it helped me retain. – Daniel Apon Nov 13 '10 at 17:49
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    the only difference between a FA and a TM is that the TM, unlike the FA, has paper and pencil. Think about it. Without writing, you are reduced to a finite automaton. With writing you have the extraordinary power of a Turing machine. – gabgoh Nov 13 '10 at 22:55
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    Dijkstra's comment only works for people whose egos are the size of Dijkstra's. For most people, students especially, no matter what problem you're working on, it is very easy to "be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you", even when it's not true. No, work on it anyway. If you make progress, there's no need to compete with your colleagues—instead, write them and ask to collaborate! – Jeffε Nov 16 '10 at 1:14
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    JeffE, I was not bothered so much about his "golden rules" as I was by the corollary that <i>researchers need to collaborate, not compete.</i> We both agree on this and this site itself stands testimony to this spirit. However it is easy to overlook or forget this fact if one is not conscious of it. – V Vinay Nov 16 '10 at 2:34
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    My interpretation is this: you should try to tackle an open problem if you feel you have an edge in solving it. If you have some creative, bright idea, or if you feel you might have one if you think more about it. Work on problems that your unique inclinations/interests/knowledge/ lead you to. – Dana Moshkovitz Nov 16 '10 at 12:46

For every question that you can't solve there's an easier variant that you can solve; for every question that you've just solved, there's a harder variant that you still can't solve. Going back and forth across the "boundary of solvability" is extremely useful as it (1) allows you to progress in baby steps (2) gives you a clearer picture of the landscape.

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    Incidentally, this wise advice originates (I believe) with Pólya: "If you can't solve a problem, then there is an easier problem you can solve: find it." – Joseph O'Rourke Nov 21 '10 at 2:38

There is plenty of things that can be given as advice, but I tell 3 things to all my students (in no specific order):

  1. Be a (wo)man of scientific integrity. This is clearly harder in those days where we have to publish or perish, but trust if the basis of scientific relationship, and if we lose it we lose everything.
  2. Tenacity and hard work are the only mandatory things to succeed in research. OK, being smart is a big plus, but it is nothing without work.
  3. Keep track of what you have done, of why you have done it and of what is not working. It is indeed amazing how fast we lose our memory, since a few years I started writing everything (from the dumbest to smartest ideas) in notebooks. I added some extra shelves in my office specially for that, but it is worth the carpentering effort.
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    I agree especially with the third item. I haven't done that to the same extent, but I do keep track of ideas that might work and others that did not (and why), which comes in very handy, especially when going back a few months later to that hard problem you shelved because you got stuck. – Anthony Labarre Nov 16 '10 at 22:12

I'm sure many have already seen these, but so they are collected in one place:

Nielsen's Principles of Effective Research

Richard Hamming: You and Your Research

Matthew Might: The illustrated guide to a Pd.D

Tao: Ask Yourself Dumb Questions

The last one has multiple links that click through to other blog entries about research advice.

One thing I think I can offer, from myself, is this: Don't take rejections, or acceptances, personally. A sense of self-worth should come from far more important things than the temporary disposition of a mathematical result.

  • I hope you don't mind, but I added an additional link into your answer. – Dave Clarke Nov 13 '10 at 17:50
  • I don't mind at all, @Dave, thanks. My answer, and the whole question, seems like a community wiki. – Aaron Sterling Nov 13 '10 at 17:55
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    +1 for asking dumb questions, AND for not taking acceptance/rejection personally. One of the best ways to undermine your ability to be persistent is to become too personally involved in the validation of any given piece of work! – Daniel Apon Nov 20 '10 at 20:56
  • @Dave, when you added the last link, I guess you didn't modify the sentence that follows. It still makes sense because of Prof. Tao's insightful page on career advice (terrytao.wordpress.com/career-advice). Although Matt Night's blog also contains more than one interesting post on the topic, for instance, matt.might.net/articles/ways-to-fail-a-phd – Alessandro Cosentino Nov 21 '10 at 0:51
  • Just to clarify, Dave Clarke added the link to Matt Might's Illustrated Guide. My "multiple links" comment was about the Terence Tao blog entry. – Aaron Sterling Nov 21 '10 at 13:25

Write everything, all the time. In TeX, preferably. Whether you are considering a question or proving a lemma, put it in a digital format as soon as possible. Write the necessary background. Try to keep the thoughts organized in a narrative.

Having all of these things in a digital form makes paper-writing much easier, but still a lot of work. In my experience, it helps a lot to start again from scratch. This allows for a clean start to find an improved organization. Also, proofs are always easier the second or third time around.

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    +1 It's unbelievable how much easier it is to write a paper if you write as you go along. – Lev Reyzin Nov 15 '10 at 17:27
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    I agree, although I usually keep my figures hand-drawn until I'm very confident they will be useful. As much as I like and am comfortable with TikZ, an awful lot of time can be wasted drawing with it. – Anthony Labarre Nov 16 '10 at 22:16
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    I use Inkscape for figures, and frequently draw them early. Usually it's because I'm stuck and frustrated, and the drawing calms me down while my brain still works. – Derrick Stolee Nov 17 '10 at 2:22

I'll start with some advice my advisor Amit Chakrabarti gave that I found quite useful:

(1) Keep a research journal and write in it every day.

Its easy to forget about the details of what I was thinking about 2 weeks ago. Revisiting previous thoughts/problems/miniresults enables me to avoid reinventing the wheel. Also, I found it especially useful to write down places where I was getting stuck and not making progress. Revisiting later often let me break through whatever I was trying to solve. In a different way, writing in a journal forced me to spend those extra ten minutes at the end of the day to follow through and finish up whatever task I had left that day. Otherwise, I probably would've just put it off until the next day.

(2) Set aside time to read research papers, even if they're not directly related to your current research.

I get tunnel-visioned, so if I don't do this I tend not to keep up with current research.

Finally, it's been very useful to me to think about my research right before going to sleep/in the shower/while exercising/on the subway/etc. Some of the other commenters seem to disagree here, especially with the right-before-bed part, but I've found it to be very useful. I tend to look at the problem from different directions in these kinds of situations, and I might spot some insight I wouldn't have at work.

This may sound a very trivial thing, but I would recommend trying to take a break before you go to bed. Try to take a break from research and clear your head. It's very tempting to decide to take a few minutes to work on some pet problem in the comfort of your bed before you go to sleep, but in my experience it absolutely guarantees insomnia and leaves you totally unfit for proper thinking the next day.

This is more of a do as I say not do as I do thing, because I find myself drawn to working late at night far too often, and I can say from experience that it is a practice best avoided.

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    I completely agree with this one. Even worse is the phenomenon of working on a problem late at night, being certain you've solved it, and waking in the morning to find that your solution is complete gibberish... – Ashley Montanaro Nov 16 '10 at 18:26

Sylvain's already mentioned as much, but I think it's worth emphasizing how important hard work and persistence are. Also, I can add:

  1. Drink coffee. (It's honestly helped me!) As Alfréd Rényi put it,
    A mathematician is a machine for turning coffee into theorems.
    Addendum: Since considering the comments of others about coffee, I have discovered the wonders of a fresh cup of hot tea. :) Allow me amend this comment by saying:

    Try identifying the things that get you "in the mood" to work. It might be a cup of coffee, a cup of tea, the right type of music, or whatever. Some things will make you perform BETTER, some things will make you perform WORSE (coffee putting you on edge/giving you the jitters, the wrong type of music distracting you, etc). Importantly, these can be very personalized types of triggers, but it is DEFINITELY worthwhile to find the things that work for you!

  2. Practice discipline. Having a regular time set aside to work on research, and absolutely never missing it can work wonders. You can then consciously tweak the frequency and duration of these regular times to suit yourself.
  3. When you take breaks, make sure it's a full break. Some people are naturally better at this than others, but I believe it's important to find periodic times to completely forget about TCS/research/work/school/etc for a full day and go do something completely recreational. (Of course, do this in moderation, or you won't get anything done!)
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    Actually, after giving up coffee I feel much calmer and less prone to be stressed. Much as I love it, coffee may not be the universal solve all. – Dave Clarke Nov 13 '10 at 13:55
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    I have to agree with @Dave here. I find too much caffeine makes me a little jumpy and very easily distracted. – Joe Fitzsimons Nov 13 '10 at 16:33
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    @Dave and @Joe make a good point here. Caffeine consumption is definitely something worth considering, and making a conscious choice about; it can really go either way. For some people, it does wonders; for others, it does more harm than good! – Daniel Apon Nov 13 '10 at 17:15
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    Erdős was famously addicted to amphetamines. I feel somewhat more productive for 1-2 hours after taking coffee, but after that I get very jumpy and distracted. Also I can't drink it after 4pm or I can't sleep. So basically YMMV. – Mugizi Rwebangira Nov 13 '10 at 19:33
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    if you're feeling too jittery from coffee, a strong cup of tea will actually smooth that out. This is because along with caffeine, tea contains some related stimulates that interact synergistically with caffeine but also mildly relax the very same muscles that feel jittery – Carter Tazio Schonwald Feb 14 '11 at 0:12

Get up and talk to colleagues and fellow grad students, take breaks and lunches together and talk about that interesting problem you're exploring. Most research benefits from multiple points of view, and most researchers are happy to discuss intriguing and knotty thought experiments.

Some people dislike (or fear) to talk about their projects, perhaps out of concerns for poaching, but most people when I was in grad school were pretty open. Unless the door was closed, in which case either I or they were hard at work without wanting interruptions.

There is envisioning: describing to yourself in a detailed way what you are going to do, before you start doing it. It works extremely well when you have a complicated task ahead of you, like writing a paper, preparing a presentation, planning a class, etc.

I found that when I have a very clear vision in my head of what I'm going to do, actually doing it becomes easier and faster and the outcome is better.

  • It decreases dramatically the chances to miss something.

  • It makes you think about the right order to do things.

  • It helps simplifying: we can't hold in our heads too many things at once, so it makes you concentrate on what's important, and modularize.

So things just go more smoothly when you plan.

  • I think that I also heard Guy Kindler giving this advice once – Dana Moshkovitz Dec 9 '10 at 16:16

I would like to second the advice given by Justin. There are a lot of great suggestions in the replies, but many of them are just about effective work habits and don't specifically have anything to do with research. I was thinking about this recently after viewing a talk by Steven Johnson on the subject of his latest book, "Where Good Ideas Come From". (One version of the talk can be found at TED.) His basic premise is that there are certain environments which act as natural incubators for new ideas. He gives the example of the coffee house in Renaissance England, which aside from the effects of the coffee itself, brought people of varied backgrounds together and encouraged the exchange of ideas. It is this cross-pollination of ideas which gives rise to new, novel ideas.

Now quite possibly this hasn't been mentioned in most of the other responses because it is just assumed that everyone is already going to be doing this, but I thought it would be worth emphasizing the point.

Richard Feynman's must-read book "Surely You're Joking, Mr. Feynman!" is a mine of good research practices. My favorite Feynman's advice is on how teaching helps to do good research, see these excerpts. If nothing more, this is at least very motivating when you have TA/teaching duties that seem to "obstacle" your research.

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