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I work in abstract mathematics and I'm currently in the mid stage of my PhD. I try to get bounds on computational aspects of mathematics. I have been working on one problem for almost half a year and I have got four/five really challenging questions in this way. I am trying to solve these new questions but some of them seem to be very tough. I have been able to solve some of these new questions partially, but did not obtain the optimal results.

Question: Is it good to publish a research paper with many partially answered questions with sub-optimal results?

  • Just go for it. Best of luck – old Jul 18 '18 at 17:13
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    In your other question here you describe yourself as a post-doc. Here as a pre-doc. I've seemed to answer both questions in different ways, but largely on what you have said about yourself. Different things are more appropriate at different stages of your career. If you were a junior professor, up for tenure, I'd think publishing a lot would help. Don't misinterpret the two answers. – Buffy Jul 18 '18 at 17:19
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    This is a good question for your advisor, because it's impossible to answer without knowing the specifics of the problems you're working. – user37208 Jul 18 '18 at 17:29
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This depends on many things. Most important is the significance of the questions themselves and whether the partial solutions add anything beyond standard techniques. The questions can be "challenging" without being significant, of course. Do they lead to other things, for example.

If your solution techniques are standard, then they won't add much either, but if you have developed a new way of looking at such problems, then it could be very important.

"Almost half a year" doesn't sound very long, actually, for the stage you are at.

Your advisor should give you good advice here. He or she is more familiar with your problem and your attack and degree of attainment.

However, I come down a bit on the side of waiting to publish. For one thing, if you publish partial results it may lead others to join the search for solutions in competition with you, perhaps denying you a more significant publication (or even a dissertation) in the future.

If it makes sense to separate them, having four or five papers, each with a complete solution would be much better for you than rushing now. The publishing venue is likely to be more prestigious, and also more likely to accept complete results.

Carry on.

  • @sade, yes, that makes a difference. However, a full year on the research leading up to writing the dissertation is not excessive. I earned the doctorate in the (very) old days where it was uncommon for students to publish before finishing. I agree that the world has changed. If your research problem is significant it may just be in the nature of things that solutions are hard to find. This is true in maths certainly. – Buffy Jul 19 '18 at 12:57

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