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I submitted a paper in math/cs/economics to a top-level journal. The paper involves a new variant of a well-known problem. All reviewers agreed that the results are interesting and non-trivial, but they rejected the paper as not being general enough for their journal.

Encouraged by the positive feedback, I submitted an improved version of the paper to a medium-level conference. The improvements include simplifications of some of the proofs and additions of stronger results about the same problem. Now the reviewers rejected the paper claiming that the results are too weak and unsurprising!

What should I do in the next time I submit (to a different journal), in order to make the reviewers believe that the results are indeed surprising and non-trivial? I don't want to write the proofs in their more complicated version, as in the first revision, because this is unscientific. But writing it in a simple way seems that doing so creates a false impression that the results are too simple. What do you suggest?

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    Why on earth would you want to convince the reviewers that the results were difficult? I think the word you're really looking for is significant or perhaps surprising. – JeffE Oct 20 '14 at 20:54
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    @JeffE - Or the results were difficult to attain. I wonder if difficult here is intended as a synonym for "not trivial." – J.R. Oct 21 '14 at 0:04
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    Sorry, I still think this one is a dup. After reading both questions, I have a thought. If you can write this question to distinguish it from the other question, you can write your paper to convey why yours is not too weak and unsurprising. I think the answers to the other one (including yours) did not really solve the problem. The answers just told you why it is a difficult task. – scaaahu Oct 21 '14 at 7:00
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    @JeffE: The "significance" of a result is often subjective and/or difficult to evaluate. To perform this evaluation, it's natural to take into account the "depth" or "difficulty" of the arguments. If when refereeing a paper you meet a result that you had never thought to establish, it is very natural to stop and see if you know how to establish it, or have a sense of what would be needed to establish it. You are also of course looking for "new ideas" and "new techniques", but it's a similar story; such things are much more convincing when there is no other easy way to solve the problem. – Pete L. Clark Oct 21 '14 at 15:39
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    That said, I take the point that difficulty ought not to be valuable for its own sake. In my experience, prestigious journals can lean too heavily on wanting to publish things that look hard and/or showcase exceptional technical skill (versus a more novel approach that doesn't look as hard). My very first referee report, a rejection, contained the passage: "Admittedly, Theorem X is a nice result. The proof, however, is not overly cumbersome." To which I always react: "Wait! Give me another chance: I can make the proof much harder." – Pete L. Clark Oct 21 '14 at 15:44
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In the end, the significance of a scientific advance is determined not by how complicated it is or how much hard work was put in, but by comparison with what was known / possible before.

It sounds to me like you need to have a much clearer and stronger comparison with the prior state of the art, particularly emphasizing why the new result makes a difference to larger or deeper issues. Depending on the nature of your work, this might mean anything from a little improvement on the prior work section to introducing new sections with explicit comparisons.

For example, if you were able to mathematically compute the Nash equilibrium for preference of donuts vs. muffins, that's a nifty little result, but it might seem obvious or insignificant. If you can explain that this was something impossible with prior methods, because nobody had previously been able to deal with the breakfast uncertainty principle, then that is surprising and interesting. If you can show that your result accurately predicts sales in major chain stores, then that is also surprising and interesting. In either case, you are showing how your result has implications outside of just being a result.

Now, you could probably also make your work appear harder and more significant by obfuscating the mathematics, and that might "work" for purposes of getting this paper accepted. I personally, however, consider that to be scientifically dishonest, and would strongly recommend against that. Remember, that your colleagues are not stupid, and sooner or later, people will realize that you are fluffing up your results, to your detriment.

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    "In the end, the significance of a scientific advance is determined not by how complicated it is or how much hard work was put in, but by comparison with what was known / possible before." I wish this was an universally accepted fact, but it is not. – xLeitix Oct 20 '14 at 15:27
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    (there are still plenty of people that state that it ain't science if it ain't complicated - and yes, I am saying "complicated" instead of "complex" on purpose ... this is a huge pet peeve of mine) – xLeitix Oct 20 '14 at 15:28
  • @xLeitix I absolutely agree with you, and I think it's an ongoing frustration for many of us. Scientists are, after all, human. I do think, though, that in the long term, significance does tend to sort out. – jakebeal Oct 20 '14 at 16:13
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    The reviewers agree that the results themselves are new, important, and were not known before, but they claim that the techniques we used are not new. In other words, although no one asked this question before, anyone asking this question would come up with the same answers easily. – Erel Segal-Halevi Oct 21 '14 at 6:39

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