**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.

14more comments