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Actually I'm proving that ∀n∃p∈P|n<p<en. Which is a result similar to Bertrand's Postulate, but with a shorter proof. Should I publish my result? If so, as I'm not affiliated with any Research Institute how do I do that?

Edit

Since yesterday I've improved my proof: ∀n∃p∈P|n<p<2n. This means I'm proving Bertrand's Postulate with a simpler and shorter proof. So, which is the most appropriate Journal to publish this result?

user1582006
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    Probably start by posting it on arXiv (to establish priority) with a public key (to establish identity). – Nat Feb 08 '18 at 15:10
  • How significant would you say that this result is? I mean, is it primarily just a shorter proof for an accepted principle, or does it reveal some actionable insight to real-world problems? – Nat Feb 08 '18 at 15:13
  • @Nat: The result itself isn't more significant than those stated by Bertrand's Postulate, but the proof is simpler and shorter. – user1582006 Feb 08 '18 at 15:20
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    It sounds like you might not (yet) have a doctorate? In principle shorter proofs can be interesting and, in my field at least, it is possible to submit to journals and conferences without an affiliation. However, your problem is determining the significance of your result and for that, you need another mathematician. I don't think we can answer your question, but you should try and find a number theorist at an institute who can, it may even lead somewhere. – Dr. Thomas C. King Feb 08 '18 at 15:32
  • have you asked on Math stack exchange? – aaaaa says reinstate Monica Feb 08 '18 at 15:46
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    @aaaaaa https://mathoverflow.net/questions/292477/should-i-publish-my-result-if-so-where-and-how – user1582006 Feb 08 '18 at 16:02
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    I noticed you didn't use TeX in the MathOverflow post despite them having it enabled (SE.Academia doesn't, sadly); was that an oversight because you're new to StackExchange? In any case, if you go to post this proof, you'll definitely want to ensure that it's typeset well. Poorly formatted work is a huge red flag that'll drive a lot of readers off at first glance while well-formatted work is far more likely to receive attention and understanding. – Nat Feb 08 '18 at 16:28
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    Any alternate proof is potentially interesting, regardless of length. Well I suppose an extremely long proof of something that can be proved more concisely would be less interesting. But alternate proofs are very helpful in understanding the theorem better as well as connecting it to other areas of Mathematics. – Todd Wilcox Feb 08 '18 at 18:13
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    To those who voted to close: how is this even remotely a duplicate of the cited question? OP does not "believe they have solved a famous open problem", since Bertrand's postulate is not an open problem. OP also is not asking anything at all similar to "how do I convince people in the field that I am not a crank?", in fact there is no indication that OP has any concerns about being perceived as a crank - their question is entirely different. Voted to reopen. – Dan Romik Feb 10 '18 at 08:16
  • @DanRomik Claiming to have a big improvement over a known proof doesn't seem very different from claiming to have a proof of an open problem. Similar pitfalls would seem to apply, e.g., it not being a correct proof, reformulating the problem to something much simpler, etc. In any case, "should I publish" is opinion-based, "how should I do that?" is a duplicate of other questions on the site and "which is the most appropriate journal?" is shopping. So, even if this was closed for the wrong reason, I still think it should be closed. – David Richerby Feb 11 '18 at 19:27
  • @DanRomik Based on questions the OP has posted on MathOverflow and MSE (e.g. https://mathoverflow.net/questions/292577/is-my-proof-a-notable-result-if-so-where-and-how-do-i-publish-it ), I think that reopening the question here may not be so constructive. I also agree with the last sentence of David Richerby's comment above – Yemon Choi Feb 13 '18 at 02:55
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    @YemonChoi I’d say the question (or, at least the parts of it that I was addressing in my answer) is a valid question by itself. What facts may be inferred about OP from their other questions seems irrelevant to me. But anyway, all I was saying is that logically, the question is not a duplicate. I don’t have an opinion about whether opening or would be constructive or not. – Dan Romik Feb 13 '18 at 03:04

2 Answers2

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As @Nat says, do post in on arXiv. Many journals have a "Notes" section for short results like yours, which people would find interesting, especially if they were teaching similar results. The MAA Monthly does this, e.g. After you have the proof up on arXiv, submit it to the "Notes" section of an appropriate journal, following the specific directions for that section. At least one professional mathematician will look at it, so you'll get some vetting. Have a look at the Missouri Journal of Mathematical Sciences.

B. Goddard
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  • Thanks for your answer. But what would be the best journal to publish for as a non-academic? – user1582006 Feb 08 '18 at 16:23
  • "Best" is hard to say. I mentioned the MJMS because, while it has a good reputation, it's one of the easier journals to get published in, and it has a "short notes" section. – B. Goddard Feb 08 '18 at 16:32
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    I would hardly say MJMS has a "good" reputation; rather I would say it has a "non-junk" reputation. – Alexander Woo Feb 08 '18 at 16:48
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    It is easy for people with institutional email addresses to say "oh, just post it on arXiv" and incorrectly assume that their interlocutor will be able to do that. To be clear: posting on arXiv can be a significant challenge for people without an institutional affiliation. Unless you're able and willing to personally endorse the OP, the initial advice needs to be tempered quite a bit. – E.P. Feb 08 '18 at 19:08
  • @E.P. I had no idea. Good point. But perhaps a solution: I know that UT Austin will give almost anyone some e-access. The public gets to have access to the libraries and such, so it's possible for a citizen to get a UT e-id and library card, and perhaps an e-mail address. Maybe the OP's local state-supported school has such a service. – B. Goddard Feb 08 '18 at 19:39
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    @B.Goddard If that works, then I'd be disappointed with arXiv's filtering scheme (or at least, I'd hope they're ready to turn it off the minute it starts getting abused). The restrictions on submitting to the arXiv are there for a reason (note e.g. that arXiv had been running for 13 years when they instituted them), because there's a lot of content (much of which now makes its way to viXra) that we don't want to end up on arXiv. – E.P. Feb 08 '18 at 20:18
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Can such results be published and how?

“Such results” certainly can be published, if by “such results” you mean genuinely new proofs of well-known theorems, especially if they contain a new and interesting idea (rather than being a trivial modification or variant of an existing proof), and especially if they are shorter than existing proofs, although that is not a necessary condition for a new proof to be publishable.

Such new proofs are published quite frequently. For example, when I was a graduate student I published a new proof of Stirling’s formula. It was published in the American Mathematical Monthly, a respectable journal that often publishes papers in this category.

Should I publish my result?

As others have said, you can at the very least write up your proof as a paper and submit it to arXiv to make it available to the community. And you can try to publish it in a journal - if it’s interesting, well-written and novel, I think you have a good chance of getting it published somewhere.

If so, as I'm not affiliated with any Research Institute how do I do that?

See this question for some suggestions.

Dan Romik
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    Thanks for your answer. I just revisited my proof and I realised I can also prove Bertrand's Postulate with a minimal change. Maybe it's worthwhile publishing it. – user1582006 Feb 08 '18 at 17:15