I am an applied mathematician. A very simplified outline of my situation is as follows:

The leader of my research group is a "big wheel" in his specific research area. His contributions are considered both important and very demanding.

Recently I found a way to get a simplified access to one aspect of his work. I am very sure that no more than a few dozen people have ever made the effort to dig through this and understand it. The simplification is substantial, and even to my group leader it has not been known. Certainly it is not known to almost everybody else.

Other than an alternative simplified manner of setting up the theory, I can round out some things that have previously been done by hand-waving. That is only of theoretical interest.

So I wonder: finding this has been difficult, and it would help other researchers to know about it. But is it worth being published, with only a "sugar glaze" of actually -new- results? How can I determine this? How low for a journal should I aim?

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    I think this is so specific to your situation that you really have to ask several senior people whom you trust and who can appreciate the details. – Alexander Woo Nov 26 '15 at 4:10
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    It seems you are in discussion with your research group leader about this - wouldn't (s)he be able to judge well whether, and where, to publish this? – xLeitix Nov 26 '15 at 7:28
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    This sort of work is often publishable. I'd recommend making it obvious, even in the title of your paper, that its main contribution is simplification; for example, use a title like "A simplified proof of X". You don't want inattentive referees complaining that your main result is already known. – Andreas Blass Nov 26 '15 at 17:35
  • It sounds exciting, and I can understand your itch to get your streamlined derivation out there. The only thing that concerns me is the hand-waving part. Could you find some usefuly application of the result that you re-derived? This might give you a better way to package your theoretical work. – aparente001 Nov 26 '15 at 17:39

In general, this kind of result might be worth publishing, also in top journals. However, it is impossible to tell without knowing the specifics. It might well be something that has been known as a "folklore result" for long in your field.

Luckily, you say that the leader of your research group is the major expert on this. So, ask him and not a random bunch of people from other fields you found on the internet.

If you have already asked and he disagrees, chances are that he is right. But if you disagree and insist that it is a major breakthrough, you can still write everything up, put it on arXiv, and wait for feedback from other researchers.

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  • Very much agree with this statement - the group leader seems in the best position to judge on this statement, and as long as there is no valid reason not to talk to him.. – Olorun Nov 26 '15 at 7:57
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    Let me add to this good answer an explicit example: Kleiner gave a new proof of a famous theorem of Gromov (that any group of polynomial growth is virtually nilpotent, but it does not matter here what this means) and published it in one of the very best mathematical journal, Journal of the AMS (about the equivalent to Science in mathematics, except it is a serious journal rather than a magazine). So, in some cases new proofs of known results are highly regarded. What is important in a paper is how it improves the reader's understanding of its subject, and that can be achieved by new proofs. – Benoît Kloeckner Nov 26 '15 at 13:03
  • To avoid misunderstanding, I am not looking for a decision here on this site, but for "decision help", if you get what I mean. – Ambicion Nov 27 '15 at 17:02

You are not very specific in your question, so much of this is guesswork. However, since you say you are working in applied mathematics, there are two situations that would definitely lead to publishable results:

  1. If you have a simplified proof of a significant theorem, that is worth publishing.

  2. If you can find a simplified algorithm, especially with better complexity, that is of course also worth publishing.

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    The 'worth publishing' part is what the question is all about. – Ébe Isaac Nov 26 '15 at 7:01

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