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I am a PhD student working in theory (computer science). I am confused about one thing, and I am only the researcher in my group. I work on 2-3 small problems which I am trying to combine and publish. Although my results on these 2-3 problems are not big (the idea is also not big), I have tried to solve 2-3 small problems and have gotten a result that makes a paper, according my colleagues in the university. I have seen researchers (very senior) whose work seems to be very non-trivial to me (as compared to me). I am confused about this: should I work on one particular problem for a year and get a result (there is a high risk with this thing) or should I work on 2-3 small problems and combine them to make a result?

Question: For a PhD student, what is good about working on a few small problems vs solving a big problem? I have heard and have seen the profile of some professors in which they say/write that PhD students (mostly) do survey kind of things. I don't know this is true or not.

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    You probably need your supervisor(s) opinion on this. If it was me, I would say, your goal is to learn how to do research rather than aim for big breakthroughs. Once you have sufficient materials to graduate, which can consist of multiple small problems, then go for bigger problems. Usually, big problems require experience and time and no small risk. At the very minimum, make sure you will still get your PhD even if you come up empty handed. – Prof. Santa Claus Apr 14 '18 at 11:12
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    Alternatively, if your supervisor is experienced, he/she can cut up the big problem into smaller chunks; say A-->B-->....-->Z. Say you fail at Step-N. Then you should still be able to graduate using the work you have done for chunks A to M. – Prof. Santa Claus Apr 14 '18 at 11:15
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    Often times, to solve big problems, you need to solve many small problems. Instead of thinking in terms of small and big problems, focus on working on and solving the right problems. – 101010111100 Apr 14 '18 at 14:04
  • @101010111100 I am agree with you but the problems is at the end of PhD I should also have something non-trivial. – ffffref54 Apr 14 '18 at 15:20
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[I'm an American theoretical computer scientist; some of this advice will not translate well to other fields and countries.]

I am confused about this: should I work on one particular problem for a year and get a result (there is a high risk with this thing) or should I work on 2-3 small problems and combine them to make a result?

Neither. You should work on problems if and only if

  1. You find them interesting.
  2. You enjoy being frustrated by them.
  3. You have time and energy to work on them.
  4. You (and your advisor) believe you can make progress on them.
  5. You (and your advisor) believe you can convince your target community to care about them.

As a beginning PhD student, your first goal should be to publish something. Don't worry about whether it's big or small. It doesn't have to be important. It doesn't have to have anything to do with your later thesis research. It doesn't have to be in a top venue, although it does have to be in a venue that people actually care about. Your only goal here is to successfully walk through the process of writing, submitting, revising, publishing, and presenting a research result, so that later, when your much harder research isn't going well—and that will happen—you have direct evidence that you can do publishable research.

Once you have that, your next two goals are (1) publish something at a top conference in your field, and (2) have something rejected from a top conference in your field, and then later publish it anyway. Note that these two goals can be met by the same paper. Satisfying these goals requires understanding the expectations/standards/style/taste of the community you're aiming for; this understanding is far more important than (but related to) whether the result is "big" or "small". Again, both of these goals are important bulwarks against Impostor Syndrome.

If you've gotten this far, whether your realize it or not, you've built up some significant expertise and intuition that is unique to yourself. Exploit it. Your next goal is to exploit that and publish two or three papers on some common theme — similar tools, or similar problems, or at least similar venues. You don't have to fix the theme in advance; you may not even understand what the theme is until you're done, and that's fine. Your earlier papers can be used as part of this body of work, but they don't have to be.

In parallel, you absolutely must publish something without your advisor. That can be part of your coherent body of work, but it doesn't have to be. It can be a solo paper or with other collaborators; that doesn't matter so much. But it is absolutely vital that your advisor is not a coauthor. In particular, your advisor must not contribute enough to the paper to deserve to be a coauthor—gift non-authorship is just as unethical as gift authorship.

On the other hand, your advisor must be fully aware and supportive of your independent work, while they keep their hands off. If your advisor is likely to object to you working independently, you need a new advisor. (If your advisor's objections are dictated by your university, you need a new university.)

Once you have a coherent body of work, all that's left to do unify the presentation (especially the terminology and notation), write a coherent introduction/literature survey/conclusion, cram everything into the horrible thesis style dictated by your university, and convince your thesis committee that you're done. Congratulations, it's a thesis! This is the easiest of all the steps listed so far, and by far the least important.

Over time, as you gain experience and confidence, your results will naturally get "bigger" (at least on average). Don't worry about making it happen; as long as you keep working on things that you enjoy being frustrated by, it'll happen on its own.

  • If I read this correctly, you're saying a PhD student should publish at least 5-7 papers in TCS. Out of curiosity, this amount of publication typical for students in your areas? (In pure math, as you probably know, the typical number is much much smaller, possibly 0.) – Kimball Apr 29 '18 at 1:52
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    @Kimball I think of a PhD thesis in theoretical computer science as roughly 3 or 4 papers, and it's rare for every result that a student publishes to go into their thesis. So, yeah, 5-7 papers doesn't sound unreasonable. That also seems consistent with recent and upcoming graduates from my department. – JeffE Apr 29 '18 at 4:52

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