Is my mathematics "folklore" paper worth publishing?

Question

I wrote a math paper a while ago which was initially mainly for my own attempt to understand a topic/theorem in algebraic geometry. The methods and results are kind of folklore (not well-documented in literature). Although the ideas presented in my write-up was sketched in a recent and well-known conference report, the details and the proof of the main theorem were not given. My write-up did the job to give a detailed treatment of the theory and gave a proof of the main theorem. So this is kind of something between expository and research (I think?).

Now I'm wondering if this paper is worth to be published?

P.S. The main result was also proved by someone using a different approach and got published in a good journal this year.

Answer 1

I would definitely put it on the arxiv because it could help other people.

Whether it is publishable in a journal is a question which you should probably discuss with other experts in the field.

Answer 2

I think the proper action is to submit it to an "appropriate" journal. The editors and reviewers will decide whether it is "worth it" to publish, as they will see what you have written.

Having a proof of a conjecture is valuable, but the nature of the proof is much more valuable. If your method differs sufficiently from the published proof and if it has potential to provide new insights, then it is certainly worth publishing.

Sorry, but I can't recommend any specific journals.

Answer 3

There are also some reputable (= not predatory) journals (but mostly with not very high impact factor), which are specialised also on publishing such results.

Exemplary (but not from your area), European Journal of Physics publishes, among others, "Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks." I can imagine that there are also mathematical journals which such a scope.

Answer 4

Folklore has no scientific basis.* The "recent and well-known conference report" does. You've taken that further by adding details and formally proving results. Congratulations, you've advanced science.

In parallel, "[t]he main result was also proved by someone using a different approach." You've been scooped. Some of your work's novelty has been lost.

Nonetheless, given that the published work appears in "a good journal," we can infer that the folklore (in this instance) was worthy of formally establishing in science. Whether an alternative approach is similarly worthy, we can't know for sure, only opinions can be offered. I suggest asking the journal's editor whether they'd consider publishing your alternative approach. E.g.,

Dear Prof X,

To my dismay, I discovered my work on ABC has been scooped by Prof Y et al. in their article (entitled "DEF"), published in volume N issue I of Journal Name, over which you preside.

Perhaps all isn't lost: Prof Y et al. use approach blah, whereas I use approach blah-blah. I wonder whether you'd consider publishing my work as an alternative approach (subject to peer-review, of course)?

If not, could you perhaps suggest an alternative venue?

Many thanks for your support,

Disheveled scoopee

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^{* Details matter. Yet, folklore (and, more generally, story telling) omits, looses, or never possessed details. Folklore has no scientific basis. If folklore sufficed, we'd have no need for science. "Nevertheless," Paul Taylor notes, "if some younger person is so presumptuous as to write out a proper proof and attempt to publish it, they will get shot down in flames." A theorem, by definition, demands proof, without such it is but an idea, a conjecture at best. "The ossification of a caste system – in which one group has the general ideas and vision while another toils to realize that vision – is no way for a subject to flourish," remarks Clark Barwick. Maybe I'm naive, perhaps ivory towers unassailable. That'll tarnish science. Building upon complaisant folklore will lead to failure, there's no rigor.}