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Background

I am a mathematician with two published papers. The first is based on my PhD thesis and generalised a tool to a more general setting. The thesis was cited a number of times by the time the paper was submitted and I think that helped get it published in a top journal. The citing papers solved many of the open problems in the thesis but one eluded the experts but I managed to solve it in my second paper.

What I did in the thesis could probably have been done by any expert in the field if they found the time, but the elusive open problem had been open for a few decades, and a number of experts clearly attacked the problem without success. I was delighted to solve the problem and submitted to a top journal. The referee took particular issue with the length of the paper and felt that I elaborated too much and included too much elementary material.

This is kind of a side issue but an expert in the field warned me that the paper might fall down on these grounds. I found this quite deflating - I am no expert nor star, and struggle sometimes with the brevity employed in papers. I find authors could be allowed explain a lot more in papers and find far too much is in the minds of the experts and not committed to paper. I never have any issue with overly long papers, any parts that are familiar can easily be skimmed.

So the background is that I find myself at odds with convention in terms of what I consider to be the good mathematical writing. The second paper did get published by a good journal. Now I have written a third paper which I love but I am worried it is moving further away from what journals might want. Or indeed mathematicians.

The Paper under Discussion

I work in a field that has a level of abstraction inbuilt it where intuitions are very difficult to come by. For a mere mortal like me it provided a ferocious learning curve. Last year I emailed an expert on a technical point and they included in the reply a little bit of intuition that they use.

I was not satisfied one bit with the intuition - it did not capture at all the nature of the objects we study. Since then I have developed what I consider to be an comprehensive and consistent interpretation rather than mere intuition.

I have a paper explaining the background to the area, the motivations, the conventional interpretations, and have presented this new interpretation.

In terms of theorems and proofs I have some rather elementary but most of the paper is dealing with examples explaining how the interpretation works. It has inspired easier proofs of known results and I have some new counterexamples. What the paper possibly does is make the whole subject far more accessible to even undergrads where formerly it is a subject that is firmly of the grad level.

The paper touches on heavy technical machinery but mostly works in easier examples.

The interpretation brings forth streams of conjectures, etc and I have included a number of these ideas in the paper. The second half of the paper as such comprises a miscellany of ideas and conjectures and I believe can help people understand these mathematics better than before.

I think it makes the whole area easier to understand but because it doesn't really contain any new big results I am worried whether or not it actually comprises mathematics.

It is of an expository nature but not traditionally because it does not quite survey known results (although naturally there is an element of survey to it).

It is a paper I wish I could have read at the start of my PhD but I am worried it is inappropriate for publication.

Question

I intend to put it on the arXiv and send it to some correspondents for feedback. However I am a little bit nervous of doing even that.

I really would like advice here but need to ask a concrete question.

Is a paper whose purpose is to introduce a new interpretation of given results mathematics fit for publication.

PS: The irony about the second paper is that after the negative review I trimmed the elaboration and elementary material. The referee who approved it for another journal asked me to elaborate further in spots.

EDIT: I have suggested in comments that I would submit the paper as is to the arXiv and then spawn a note and an article. On reflection I have decided to host the long version on my website and liberally edit down to one solid expository article for the arXiv and submission to a journal. Thanks for your help.

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    $\begingroup$ I think more papers like this would be great, but I agree the reality is that it probably would be hard to get it accepted. But not impossible --- if you're willing to swallow your pride and be prepared for several rejections before it's accepted (probably to a lower quality journal than you would like) then it could be doable. The other route would be to expand the paper into a book. Have you considered this? Maybe consult with a senior person in your field who you know admires your work; they might be able to open some doors. $\endgroup$ – Nik Weaver Mar 17 at 21:38
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    $\begingroup$ One problem with this post is that it is so vague, that it is impossible for us to give an answer other than vague. Why the secrecy? You don't even mention what field you are working in. Furthermore, I have never seen articles about the "interpretation" of results. This may happen in the philosophy of physics (or mathematics), but not in mathematics proper. $\endgroup$ – Alex M. Mar 17 at 21:46
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    $\begingroup$ Hard to say just based on your hints, but maybe Expositiones Mathematicae is a possible way to go. $\endgroup$ – Fred Rohrer Mar 18 at 5:48
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    $\begingroup$ What is stopping you from publishing the full paper on the arXiv? If I were you, I would follow the referee's instructions for getting the paper accepted into the journal but with a line in the introduction explaining that a fuller account of the "minor expositional" details can be found on the arXiv for the interested reader. There is absolutely nothing wrong with publishing both versions of the paper on the arXiv. $\endgroup$ – Zorawar Mar 18 at 10:14
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    $\begingroup$ Good. Publish in a journal for your career and follow the orthodoxy of what they regard as an acceptable paper, but don't be afraid of publishing whatever you think is acceptable on the arXiv. The point of publication is only to allow peers to see your work. And I think of the arXiv as a no-nonsense mode of publication for people who know what they are doing. Of course, this does lead to a fair few bad papers being uploaded, but it is part of your job as an academic to write good papers, here as everywhere else. If you think the full paper serves a purpose, then publish it. Good luck. $\endgroup$ – Zorawar Mar 18 at 11:08
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Why don't you make it a book? I know of several quite good books based on theses which were not really teeming with groundbreaking results. It does not even have to be that long as there is a niche now (absent until fairly recently) for something in the range of 80-100 pages (too long for an article and too short for a "real" book). Books are much easier to publish than papers, and no one will be picking on you for indulging in "interpretation" and "philosophy" (alas, there is a lot of people who think that there is no place for them in what they call "mathematics").

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    $\begingroup$ Thank you. I think I will commit the long version to the Arxiv. I don't think it is a book but thanks for the suggestion. $\endgroup$ – Newbie Mar 18 at 16:11

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