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For my dissertation research, I feel like I was unproductive a lot of times because I didn’t have a good intuition about approaches to even try. I felt as if a whole year was wasted trying ideas that went nowhere. I think the reason for this is because there weren’t many related papers on my dissertation topic so when I’d read papers, I only had a few potential approaches I could think of.

Has anyone else had this problem? I also wish I had another easier/more tractable problem to work on, but my advisor wanted me to focus on this one (generalization bounds based on optimal transport theory).

Now I have some progress, but even now I’m stuck trying to make sense of a function that comes up in my generalization bound. And even that, I’m having a tough time making sense of that even for simple cases. Sometimes I think I’m being unproductive but it’s more because I lack enough relevant ideas than it is sheer laziness. And I also talked about my problem to other professors/researchers but most didn’t have much insight.

closed as unclear what you're asking by Thomas, Buzz, scaaahu, user3209815, Peter Jansson Dec 17 '18 at 8:36

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Some problems are just hard, and insight can't be scheduled. So, yes, others have had similar problems. Good problems, by the way, are hard to find. They can be too easy and have no real significance. You don't gain much by solving them. Others are just impossible, possibly theoretically, or possibly just at the current state of knowledge.

My field is different, but one thing I'd probably think of trying if I didn't understand a function would be to model it computationally. Another thing I'd probably want to think about is my partial results. Are they meaningful? Can the be used for other things?

But the best help will probably come from your advisor. If you can explain what is blocking you, maybe the two of you can find a crack to exploit. Just trying to explain your problem and your issue can sometimes free a block, if that is what it is.

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I am not in math/stats, but I understand the feeling of being stuck. I don't have a satisfactory "solution", but there are a few ideas that you can try:

  • With your supervisor, try to explain as concretely as possible where the problem is. Create a small concept note listing all the things you tried, why each one failed, and the remaining options ahead. Sometimes people underestimate the difficulty of the problem, or don't understand why you are stuck. Hopefully, you will either

    1. Succeed in proving that the problem is hard, and convince him/her that you can't realistically solve it;
    2. Get more precise advice on where to direct your efforts; or
    3. Find out that the supervisor actually does have a solution to suggest.
  • Try writing about what you've learned so far. You might be able to come up with a publishable review paper or a tutorial, and maybe putting things in print will help you organize your thoughts, understand the problem, and think of a new approach. This will also help you remember how much you have already done.

  • Pick a second "side" project and start working on that for fun. This will help hedge against the risk of not coming up with anything on your main topic, and on the other hand, you can use that to take short breaks when you are feeling too frustrated with your main work. Sometimes when you move onto something else you will be inspired with a solution to your original problem.

  • Try to find other students who are working on something similar. For example, is there a conference or summer school that you can attend where others in your field will be? They may have more time to think about your problem than other "professors/researchers", or they may be working on novel approaches themselves and be able to point you to recent literature. You might even build a new collaboration.

(I should add from my own experience that I don't think it's uncommon for students to be stuck on a problem for a year or more. I don't think even experienced researchers can always anticipate the difficulty of problems, and you have to remember that they got where they are by being incredibly persistent. However, it is really unfortunate and demotivating to go through this as a student.)

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