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I am a PhD student mid stage, working on computational aspects of mathematics. I am working on a research problem with my supervisor. I am at a stage where I can't take much help from the supervisor because I am in the fourth year. I can't do something like going to supervisors office to verify my answers. I did these things in the initial years of my PhD, but now I can't poke my supervisor that often.

I am facing a difficulty that how to come with something non-trivial on myself. The problem with me is that I go into wrong directions many times, and in the past I have spent many days, weeks, or longer on these wrong directions. I want to minimise the number of these trials and failures. Does it come with age?

Question: Is there any way to pick a right direction (which yields a paper) in research while solving a problem? I can take the help of my research supervisor once in two weeks. However, many times a day or week, I also need to discard some of the possible directions of research.

  • ** I can't do something like going to supervisors office to verify my answers. ** Why??? When I work on something, I do not hesitate to walk into my colleague's office and say "LIsten, I have this problem and this idea. Let's discuss it a bit" and I can no longer count the number of times somebody else played this game on me. Of course, this requires decently good relationships, but I hope you haven't seriously quarreled with your adviser yet. – fedja Jun 15 '18 at 4:33
  • You show your independence by leading a meaningful discussion, coming with your own ideas, figuring out answers, clearly understanding where you are stuck, etc., not by avoiding regular communication. The latter is neither necessary, nor sufficient for demonstrating maturity and independence, IMHO. So, if you feel like you want to discuss anything and have to say something more meaningful than "I need help figuring out what I need help with", I would say, by all means, go ahead and talk! – fedja Jun 15 '18 at 5:33
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Short version: no.

Long version: absolutely no. Having experience in the field helps (and experienced people are those that have already taken lots of wrong directions in their life), but ultimately encountering road blocks is a part of research. It happens all the time. You take lots of wrong directions, you waste time.

What you read in the papers is the road that works and gives the best and shortest solution to the problem, but the people who wrote them typically have also tried several approaches that didn't work, or were a lot more cumbersome.

If it is already clear from the beginning what will work, it's not research anymore, it's just an exercise. :)

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    And usually the best approach to be written up is recognized in hindsight after getting there a more painful way... – Jon Custer Jun 14 '18 at 13:45
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The only way to pick the right direction in research inevitably leading to a research paper is knowledge of your field. There is no set way to do this. However, you can certainly, make educated guesses based off previous results and your knowledge of the literature.

Regarding your supervisor, I think it is very reasonable request that you ask for guidance as to whether you are working in the right direction. After all, he/she is probably an expert in this field and will have a better hunch about your chosen direction.

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