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I am new to meta, and I am editing my question in response to comments. First, I want to thank the many users who commented for their time and effort, it has been useful.

What if I discover something interesting, and I am pretty sure it is right, although a second opinion would be nice. The real questions are : is this right? this strikes me as interesting, but does anyone else care? Is this previously known? How can I find out more about this? etc.

Is there a place for such "discoveries" on MSE. If so, advice on putting such things into the question-answer format would be appreciated.

I would like to clarify, what I mean by "discoveries". I mean things like a polynomial with an unusual Galois group, which helped me understand Galois theory or a simple derivation of a known result, when the literature proofs are hard to find or hard to understand. These are things which would help students learning math, in the unlikely event that I do discover something "revolutionary", I would try to publish. My motives are altruistic, not personal gain.

As to my situation, I am not presently not a student, so ask a mentor is not a good option.

I strongly feel that allowing such posts would benefit many MSE users.

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    $\begingroup$ math.se is NOT for vetting claims. It's OK to post something to ask whether it's already in the literature. For a second opinion, send it to a journal, or talk to a math prof. $\endgroup$ – Gerry Myerson Aug 28 '20 at 10:41
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    $\begingroup$ I agree with @GerryMyerson that this is not the place, but I think how to get a second opinion depends on your background. For example, if you are currently learning maths (high school, university, college) then in the first instance you should ask your teacher/lecturer/professor or other mentor for their opinion. However, I am unsure I agree with GerryMyerson's point about submitting to a journal - finding the "correct" journal can be hard without a good mentor. $\endgroup$ – user1729 Aug 28 '20 at 11:45
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    $\begingroup$ (Also, you might find this question on Main interesting, although it is slightly tangential.) $\endgroup$ – user1729 Aug 28 '20 at 11:47
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    $\begingroup$ @user you are surely correct about the difficulty of finding an appropriate journal without a mentor – but if OP doesn't have a teacher/mentor to ask, then what do you suggest OP do? $\endgroup$ – Gerry Myerson Aug 28 '20 at 12:31
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    $\begingroup$ @GerryMyerson I don't know. It also depends on their motivation (fame/fortune/job prospect/they just find it interesting). Possibly they could ask on here about ideas of journals to send it to? (Of course this has to be done carefully, but I suspect such a question would be better received than a "check my 10-page proof" question.) $\endgroup$ – user1729 Aug 28 '20 at 12:40
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    $\begingroup$ Just make sure you have a solid foundation in the relevant field, and get feedback from a professional in that field, or at least someone you trust who has academic experience in that field. It almost surely doesn't apply to you, but note that every crank thinks [s]he is right, so thinking you are right doesn't actually lend weight to actually being right. Fortunately, in mathematics there is a way of making sure of that; write a formal rigorous proof using FOL reasoning and nothing else. $\endgroup$ – user21820 Aug 28 '20 at 17:38
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    $\begingroup$ And if you want informal feedback on Math SE, you could try chat. $\endgroup$ – user21820 Aug 28 '20 at 17:39
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    $\begingroup$ If you are doing just for the sake of interest (no material gains like fame, fortune, job as mentioned by @user1729) then you may as well publish it on your blog. There is vixra and arxiv also. Sending to a renowned journal may require help of others and if it gets published it restricts access. $\endgroup$ – Paramanand Singh Aug 29 '20 at 3:31
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    $\begingroup$ However if there is some minor stumbling block in your way of discovery (eg getting a closed form of a series or integral which you are unable to handle yourself) then you may well ask that here (main site). In that case do give credit to the user who helped you out when you publish your discovery. $\endgroup$ – Paramanand Singh Aug 29 '20 at 3:39
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    $\begingroup$ Surely, I would as well wish for such a place (MSE isn't such a place as mentioned in the comments) . One prominent place for such a forum is possibly the usenet-newsgroup "sci.math". While I liked that group (and its german sister newsgroup) much in the 1990ies up to say, 2004 or a bit longer, that group had many serious problems with trolling and too often falling down in personal attacks. I've managed this for a certain time using filters on names & subjects, but even this became ineffective over the time. (...) $\endgroup$ – Gottfried Helms Aug 29 '20 at 7:12
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    $\begingroup$ (...) A big promise was then the MSE-model, providing mathjax for true formula-display. The including of mathjax into the newsgroup-mechanics would have been a real relief over the ascii-art writing & reading. But surely the trolling would increase, but even then overfeeding of the forum with long exposés, spam, commercial advertizing etc would occur: so such a forum must be curated. SE and MSE cannot (in my view) provide the likely needed amount of care for such a forum and real (and provoked) conflicts could only be resolved or kept low (...) $\endgroup$ – Gottfried Helms Aug 29 '20 at 7:19
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    $\begingroup$ (...) by much more effort than the SE-network or even a small specific solution (private or from some institution) could implement. Always, from time to time, I was considering the same as your question, tempting to create a sufficient working model, but without any real perspective. The vixra-platform exists, and possibly something is existent or creatable with discourse. Conclusion: it is really regrettable that no such platform "for interesting findings" exist in the "open space" ... $\endgroup$ – Gottfried Helms Aug 29 '20 at 7:25
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    $\begingroup$ @Paramanand Journal publication doesn't restrict access any more than not publishing in a journal does! Journals are happy for you to distribute your paper in other ways e.g. the arxiv (but read their conditions carefully). It is only the journal version which is restricted, which doesn't exist if you didn't publish in a journal. Also, there are high quality open-access journals (New York J. Math., Documenta, Discrete Analysis, etc.). $\endgroup$ – user1729 Aug 29 '20 at 7:50
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    $\begingroup$ @GottfriedHelms There was once a Math.SE blog. It ran out of steam (officially closed in 2016), but maybe with a new core set of users it could live again. I encountered someone on main yesterday who would probably be interested, and I am sure there are others. So maybe there is potential to resurrect this? $\endgroup$ – user1729 Aug 29 '20 at 8:02
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    $\begingroup$ @user1729: the problem is that most of the interesting math papers which I can understand are from old days and the only way to get them is through journals. I sometimes take help from friends who have access to these. I have an account on jstor which helps me read a few limited number of papers online at a time (the limit was increased to 100 due to covid recently). And there is obviously Google which can give access to preprints from the author webpage (if they are listed there). But it still takes time and effort. $\endgroup$ – Paramanand Singh Aug 29 '20 at 9:09

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