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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.

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    Important to clarify "mathematical folklore", not literally "proving folklore results", like "there is a ley line of unexplained deaths from Stonehenge to Giza". Be aware this is a HNQ so a vague title will attract lots of, ahem, contributions from other SE sites. – smci Dec 10 '20 at 0:39
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    maybe title should be "formalizing results that have been suggested previously" – aaaaa says reinstate Monica Dec 10 '20 at 4:19
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    Why did the recent edit turn this into an explicit shopping question? I think that was unfair to the OP. – Buffy Dec 10 '20 at 16:34
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    I vote to reopen. Personally, I don't consider answers opinion based. Regardless, this question has been viewed three thousand times since yesterday, there's clearly a lot of interest. – user2768 Dec 10 '20 at 17:31
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    @user2768 It's a question about whether the contents of the paper that warrant publication. That can only be decided by reading the paper. Hence, off-topic. None of the numbers you list have anything to do with topicality. – Azor Ahai -him- Dec 10 '20 at 17:32
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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.

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    Even in the case of Arxiv, you should still discuss your submission with other experts in the field. In some cases, Arxiv may require explicit endorsement from such an expert. – Brian Dec 9 '20 at 21:14
  • I've got a very harsh threatening warning for less (upluaded a technical report - a standalone chapter form my dissertation, requsted for sharing by a colleague). They are very tetchy at arxiv. They told me that all uploads must be original research publishable in a journal and that I will be banned if I do that again. It got some reads and a recommendation at RG instead... – Vladimir F Dec 10 '20 at 14:15
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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.

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  • I think my method does differ a lot from the published one. But what concerns me is that the idea that my method based on is folklore in the sense that it has been sketched in the conference report as mentioned, so the originality of my work might be discounted I think and might cause my paper less publishable. – unknownguy Dec 9 '20 at 13:28
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    Let the editor and reviewers decide that. It is their job to do so. I think there is no risk here. You will, of course, cite the earlier work. They will have complete information on which to make a decision. – Buffy Dec 9 '20 at 13:39
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    This is not bad advice in theory. In practice, it could lead to unpleasant circumstances. From personal experience: Journal's A referee report was "this should be published in journal B". Journal's B referee's report was "this does not belong here". To make it worse, it took a year from the first submission to the second report. – Martin Argerami Dec 9 '20 at 19:48
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    @MartinArgerami, perhaps, but any submission could lead to that same result. – Buffy Dec 9 '20 at 19:57
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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.

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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

* 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.

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  • @DanRomik I absolutely agree with the definition of folklore as a mathematical result [that] is an unpublished result with no clear originator, but which is well-circulated and believed to be true among the specialists. I'll tolerate the body of theorems, definitions, proofs, facts or techniques that circulate among mathematicians by word of mouth, but, for serious such results, word of mouth is insufficient, details matter. (That latter quote seems unsupported by the cited sources.) I'm clueless as to why you believe I know nothing about the matter. What exactly are you objecting to? – user2768 Dec 10 '20 at 17:09
  • Comments are not for extended discussion; please continue this discussion in the chat. – cag51♦ Dec 10 '20 at 17:36
  • @DanRomik I consider myself well-versed in mathematical folklore and the issues of publishing results in that arena: I've personally trodden the path, experienced the struggle. You've yet to highlight any specific lacking in my knowledge and seem to be merely gesturing. Do you have any concrete objections? You mention criticism expressed in the earlier comments, yet I see none. Perhaps you're confusing me with another user; I'd agree, from their comments, they don't seem knowledgeable. Community votes are divided, I've spit the vote, seven up, seven down. It seems I'm controversial. – user2768 Dec 11 '20 at 8:59
  • @user2768 I just gave you a bit of feedback, I’ll leave it at that. – Dan Romik Dec 11 '20 at 9:18
  • @DanRomik It wasn't in any way constructive, in my opinion. Hence, my questions, which you've ignored. I love discovering gaps in my knowledge. Unfortunately, you seem unwilling or unable to highlight deficiencies. You've now retracted your commentary. I wonder whether this is a case of mistaken identity. – user2768 Dec 11 '20 at 9:23

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