<p>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.</p>

CC BY-SA 2.5
2010-11-21T02:38:34.597Z
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
CC BY-SA 2.5
2010-11-20T21:16:50.837Z
2010-11-20T21:16:50.837Z
Noam
<p>Manuel Blum has this <a href="http://www.cs.cmu.edu/~mblum/research/pdf/grad.html">extraordinary page</a> on advice to a beginning Ph.D student. Read it <em>slowly</em> though, for there is much to absorb. </p>

<p><strong>Update:</strong> Let me add this <a href="http://www.cs.utexas.edu/~EWD/transcriptions/EWD06xx/EWD637.html">piece of advice</a> by Dijkstra, his Third Golden Rule for successful scientific research:</p>

<p>"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."</p>

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

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

CC BY-SA 3.0
2013-03-24T13:21:20.713Z
@JɛﬀE: Sorry if this seems naive, but it's a sincere question. Is Dijkstra's ego supposed to be large or small?
C.E.Sally
CC BY-SA 3.0
2013-03-24T18:50:35.773Z
@C.E.Sally : Dijkstra implied (modulo hypocrisy) that for any problem he tackled, no other person, present or future, could have done it better than him.  So I'm gonna go with **large**.
Jeffε
CC BY-SA 3.0
2015-04-03T21:56:49.387Z
I'm finding myself more and more in the position where I am clearly _not_ the best person to be doing a specific piece of research.  But I also have a large and growing list of problems that I really want to see solved, yet no-one else seems interested in solving them.  So by default I seem to be tackling things that by Dijkstra's rules I should leave well alone.  It's quite annoying.
András Salamon
CC BY-SA 3.0
2015-08-29T03:44:24.577Z
@C.E.Sally Dijkstra is famous for having a massive ego and dishing out condescending comments. Take what he says with a pinch of salt.
xji
CC BY-SA 2.5
2010-11-16T01:14:08.757Z
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
CC BY-SA 2.5
2010-11-16T02:34:33.850Z
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
CC BY-SA 2.5
2010-11-16T12:46:21.307Z
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
CC BY-SA 2.5
2010-11-13T17:49:54.363Z
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
CC BY-SA 2.5
2010-11-13T22:55:28.803Z
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
CC BY-SA 2.5
2010-11-13T17:18:18.980Z
2010-11-15T18:21:54.887Z
2010-11-15T18:21:54.887Z
V Vinay
<p>There is plenty of things that can be given as advice, but I tell 3 things to all my students (in no specific order):</p>

<ol>
<li>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.</li>
<li>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.</li>
<li>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 <em>everything</em> (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.</li>
</ol>

CC BY-SA 2.5
2010-11-16T22:12:16.773Z
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
CC BY-SA 3.0
2010-11-13T11:05:11.863Z
2014-04-07T10:28:49.643Z
2014-04-07T10:28:49.643Z
Sylvain Peyronnet
<p>I'm sure many have already seen these, but so they are collected in one place:</p>

<p><a href="http://www.qinfo.org/people/nielsen/blog/archive/000120.html">Nielsen's Principles of Effective Research</a></p>

<p><a href="http://www.paulgraham.com/hamming.html">Richard Hamming: You and Your Research</a></p>

<p><a href="http://matt.might.net/articles/phd-school-in-pictures/">Matthew Might: The illustrated guide to a Pd.D</a></p>

<p><a href="http://terrytao.wordpress.com/career-advice/ask-yourself-dumb-questions-%E2%80%93-and-answer-them/">Tao: Ask Yourself Dumb Questions</a></p>

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

<p>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.</p>

CC BY-SA 2.5
2010-11-20T20:56:13.210Z
+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
CC BY-SA 2.5
2010-11-21T00:51:54.513Z
@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 (http://terrytao.wordpress.com/career-advice/). Although Matt Night's blog also contains more than one interesting post on the topic, for instance, http://matt.might.net/articles/ways-to-fail-a-phd/
Alessandro Cosentino
CC BY-SA 2.5
2010-11-21T13:25:10.507Z
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
CC BY-SA 2.5
2010-11-13T17:50:16.880Z
I hope you don't mind, but I added an additional link into your answer.
Dave Clarke
CC BY-SA 2.5
2010-11-13T17:55:57.933Z
I don't mind at all, @Dave, thanks.  My answer, and the whole question, seems like a community wiki.
Aaron Sterling
CC BY-SA 2.5
2010-11-13T17:36:36.093Z
2010-11-13T17:50:51.903Z
2010-11-13T17:50:51.903Z
Aaron Sterling
<p>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.</p>

<p>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.</p>

CC BY-SA 2.5
2010-11-15T17:27:22.010Z
+1 It's unbelievable how much easier it is to write a paper if you write as you go along.
Lev Reyzin
CC BY-SA 2.5
2010-11-16T22:16:59.203Z
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
CC BY-SA 2.5
2010-11-17T02:22:17.713Z
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
CC BY-SA 2.5
2010-11-15T16:15:21.820Z
2010-11-15T16:15:21.820Z
Derrick Stolee
<p>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.</p>

<p>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.</p>

CC BY-SA 2.5
2010-11-16T18:26:54.830Z
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
CC BY-SA 2.5
2010-11-13T19:45:16.350Z
2010-11-13T19:45:16.350Z
Joe Fitzsimons
<p>I'll start with some advice my advisor Amit Chakrabarti gave that I found quite useful:</p>

<p>(1) Keep a research journal and write in it every day.</p>

<p>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.</p>

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

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

<p>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.</p>

CC BY-SA 2.5
2010-11-21T03:23:44.177Z
2010-11-21T03:23:44.177Z
Joshua Brody
<p>There is <em>envisioning</em>: 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.</p>

<p>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. </p>

<ul>
<li><p>It decreases dramatically the chances to miss something. </p></li>
<li><p>It makes you think about the right <em>order</em> to do things. </p></li>
<li><p>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.</p></li>
</ul>

<p>So things just go more smoothly when you plan.</p>

CC BY-SA 2.5
2010-12-09T16:16:21.827Z
I think that I also heard Guy Kindler giving this advice once
Dana Moshkovitz
CC BY-SA 2.5
2010-11-20T19:00:03.763Z
2010-11-20T19:00:03.763Z
Dana Moshkovitz
<p>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. </p>

<p>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.</p>

CC BY-SA 2.5
2010-11-14T06:12:21.263Z
2010-11-14T06:12:21.263Z
Justin
<p>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, <a href="http://rads.stackoverflow.com/amzn/click/1594487715">"Where Good Ideas Come From"</a>.  (One version of the talk can be found <a href="http://www.ted.com/talks/steven_johnson_where_good_ideas_come_from.html">at TED</a>.)  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.</p>

<p>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.</p>

CC BY-SA 2.5
2010-11-15T16:33:54.580Z
2010-11-15T16:33:54.580Z
Kurt
<p>Sylvain's already mentioned as much, but I think it's worth emphasizing how important hard work and persistence are. Also, I can add:</p>

<ol>
<li>Drink coffee. (It's honestly helped me!)
As Alfréd Rényi put it,
<blockquote>A mathematician is a machine for turning coffee into theorems.</blockquote>
<b>Addendum:</b> 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:<br><br>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!<br> <br>
<li>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.
<li>When you take breaks, make sure it's a <i>full</i> 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!)
</ol>

CC BY-SA 2.5
2011-02-14T00:12:54.663Z
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
CC BY-SA 2.5
2010-11-13T13:55:12.570Z
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
CC BY-SA 2.5
2010-11-13T16:33:19.440Z
I have to agree with @Dave here. I find too much caffeine makes me a little jumpy and very easily distracted.
Joe Fitzsimons
CC BY-SA 2.5
2010-11-13T17:15:38.637Z
@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
CC BY-SA 2.5
2010-11-13T19:33:26.810Z
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
CC BY-SA 2.5
2010-11-13T12:57:17.083Z
2010-11-20T20:53:00.637Z
2010-11-20T20:53:00.637Z
Daniel Apon
<p>Richard Feynman's must-read book <a href="https://en.wikipedia.org/wiki/Surely_You%27re_Joking,_Mr._Feynman!" rel="nofollow">"Surely You're Joking, Mr. Feynman!"</a> is a mine of good research practices. 
My favorite Feynman's advice is on how teaching helps to do good research, see <a href="http://www.pitt.edu/~druzdzel/feynman.html" rel="nofollow">these excerpts</a>. If nothing more, this is at least very motivating when you have TA/teaching duties that seem to "obstacle" your research. </p>

CC BY-SA 3.0
2010-11-23T23:12:32.967Z
2015-04-03T15:29:50.923Z
2015-04-03T15:29:50.923Z
Alessandro Cosentino
<p>One thing I found useful is to allocate time and designate a space for doing specific research activities. </p>

<p>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.</p>

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

<p>(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. </p>

<p>(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.</p>

<p>(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.</p>

CC BY-SA 2.5
2010-11-13T13:47:57.957Z
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
CC BY-SA 2.5
2010-11-13T15:13:44.500Z
Moving away from the computer (and internet) certainly helps a lot.
Dave Clarke
CC BY-SA 2.5
2010-11-13T19:36:43.267Z
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
CC BY-SA 2.5
2010-11-13T23:44:07.283Z
couldn't agree more. And as faculty, the distractions are even more severe, making this 'carved-out-space' even more important.
Suresh Venkat
CC BY-SA 2.5
2010-11-13T13:31:42.463Z
2010-11-13T13:31:42.463Z
Dana Moshkovitz
<p>After reading Daniel Apon's <a href="https://cstheory.stackexchange.com/questions/2924/choosing-a-research-topic-using-game-theory">question</a>, 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. </p>

<p>So here is the question:</p>

<blockquote>
  <p>What practices have you found most useful in your research?</p>
</blockquote>

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

CC BY-SA 2.5
2010-11-15T21:16:36.860Z
Thanks Kaveh for posing this very practical and informative question.
Mohammad Al-Turkistany
CC BY-SA 2.5
2010-11-16T02:32:22.637Z
@turkistany: :) thanks to Daniel for the idea and to the people for sharing their experience.
Kaveh
<soft-question><research-practice><advice-request>
Advice on good research practices
Kaveh
# Advice on good research practices

(Asked by: username_0 on 2010-11-13)

After reading Daniel Apon's [question](https://cstheory.stackexchange.com/questions/2924/choosing-a-research-topic-using-game-theory), 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.

**Tags:** soft-question, research-practice, advice-request
> **Comments:**
> **username_1**: Thanks Kaveh for posing this very practical and informative question.  
> **username_0**: @turkistany: :) thanks to Daniel for the idea and to the people for sharing their experience.  

---

## 13 answers

### Answer by username_9 on 2010-11-13. Score: 110 | Accepted answer

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.

> **Comments:**
> **username_10**: 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. :)  
> **username_16**: Moving away from the computer (and internet) certainly helps a lot.  
> **username_25**: 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.  
> **username_26**: couldn't agree more. And as faculty, the distractions are even more severe, making this 'carved-out-space' even more important.  

---

### Answer by username_2 on 2010-11-20. Score: 73

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.

> **Comments:**
> **username_3**: 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."  

---

### Answer by username_4 on 2010-11-13. Score: 70

Manuel Blum has this [extraordinary page](http://www.cs.cmu.edu/~mblum/research/pdf/grad.html) 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](http://www.cs.utexas.edu/~EWD/transcriptions/EWD06xx/EWD637.html) 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.

> **Comments:**
> **username_10**: 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.  
> **username_11**: 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.  
> **username_6**: 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*!  
> **username_4**: 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.  
> **username_9**: 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.  
> **username_5**: @JɛﬀE: Sorry if this seems naive, but it's a sincere question. Is Dijkstra's ego supposed to be large or small?  
> **username_6**: @C.E.Sally : Dijkstra implied (modulo hypocrisy) that for any problem he tackled, no other person, present or future, could have done it better than him.  So I'm gonna go with **large**.  
> **username_7**: I'm finding myself more and more in the position where I am clearly _not_ the best person to be doing a specific piece of research.  But I also have a large and growing list of problems that I really want to see solved, yet no-one else seems interested in solving them.  So by default I seem to be tackling things that by Dijkstra's rules I should leave well alone.  It's quite annoying.  
> **username_8**: @C.E.Sally Dijkstra is famous for having a massive ego and dishing out condescending comments. Take what he says with a pinch of salt.  

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### Answer by username_12 on 2010-11-13. Score: 49

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.

> **Comments:**
> **username_13**: 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.  

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### Answer by username_14 on 2010-11-13. Score: 42

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

[Nielsen's Principles of Effective Research](http://www.qinfo.org/people/nielsen/blog/archive/000120.html)

[Richard Hamming: You and Your Research](http://www.paulgraham.com/hamming.html)

[Matthew Might: The illustrated guide to a Pd.D](http://matt.might.net/articles/phd-school-in-pictures/)

[Tao: Ask Yourself Dumb Questions](http://terrytao.wordpress.com/career-advice/ask-yourself-dumb-questions-%E2%80%93-and-answer-them/)

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.

> **Comments:**
> **username_16**: I hope you don't mind, but I added an additional link into your answer.  
> **username_14**: I don't mind at all, @Dave, thanks.  My answer, and the whole question, seems like a community wiki.  
> **username_10**: +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!  
> **username_15**: @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 (http://terrytao.wordpress.com/career-advice/). Although Matt Night's blog also contains more than one interesting post on the topic, for instance, http://matt.might.net/articles/ways-to-fail-a-phd/  
> **username_14**: 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.  

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### Answer by username_17 on 2010-11-15. Score: 34

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.

> **Comments:**
> **username_18**: +1 It's unbelievable how much easier it is to write a paper if you write as you go along.  
> **username_13**: 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.  
> **username_17**: 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.  

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### Answer by username_19 on 2010-11-13. Score: 30

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.

> **Comments:**
> **username_20**: 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...  

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### Answer by username_21 on 2010-11-21. Score: 30

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.


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### Answer by username_10 on 2010-11-13. Score: 24

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!  
      
   - 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.- 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!)

> **Comments:**
> **username_16**: 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.  
> **username_19**: I have to agree with @Dave here. I find too much caffeine makes me a little jumpy and very easily distracted.  
> **username_10**: @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!  
> **username_25**: 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.  
> **username_24**: 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  

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### Answer by username_9 on 2010-11-20. Score: 23

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.

> **Comments:**
> **username_9**: I think that I also heard Guy Kindler giving this advice once  

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### Answer by username_22 on 2010-11-14. Score: 23

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.


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### Answer by username_23 on 2010-11-15. Score: 21

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"](http://rads.stackoverflow.com/amzn/click/1594487715). (One version of the talk can be found [at TED](http://www.ted.com/talks/steven_johnson_where_good_ideas_come_from.html).) 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.


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### Answer by username_15 on 2010-11-23. Score: 15

Richard Feynman's must-read book ["Surely You're Joking, Mr. Feynman!"](https://en.wikipedia.org/wiki/Surely_You%27re_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](http://www.pitt.edu/~druzdzel/feynman.html). 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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