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As the title suggests, I am interested to know the chances of a middle-ranking journal's acceptance of a paper by an unknown author, detailing comparatively elementary results. By elementary, I mean results which are simply stated and simply proven: requiring knowledge only up to perhaps undergraduate year 3 or 4 courses. The results are new but do not have any obvious implications, nor are they usually considered as well-known interesting questions (not like open questions posed by previous authors). The "interestingness" of the results are mediocre at best. The methodology involved is new, but there is nothing to show that it is applicable in other related problems in the field, nor that it is significant in any way beyond the paper. Note that the field I am interested in is mathematics.

So, what are the chances of a journal accepting such a paper? My initial reaction is that perhaps this kind of papers would seem too trivial, given that often papers published in journals consider material from the PhD level or beyond. But then again, it is novel research with results interesting to some, so perhaps they are worth publishing.

(You can assume that the results and methodology given in the paper are truly novel and correct.)

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    What's the "story" behind the paper? That is, what makes your paper worth reading? – user2768 Aug 30 '18 at 12:14
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    The quality of a mathematical result is certainly not proportional to the sophistication of the techniques used to prove it. On the contrary, an elementary proof of a worthwhile result is typically viewed as much better than a proof that uses more advanced techniques. What matters more is how interesting your results are, and you haven't provided enough information here to determine that. Why not show them to an expert or two and ask for their opinions? In any case, it sounds like something that is worth putting on arXiv to start with. – David Ketcheson Aug 30 '18 at 12:21
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From your description it sounds like the results have no implications, no relation to other problems, and is not significant in any way beyond that paper. In that case, chances are journals will not accept the paper. A paper needs to convince the editors & reviewers that its results are actually interesting.

Check out Steven Gubkin's answer to another question:

Here is a brand new mathematical theory I have invented just now (in the last 30 seconds):

A Gobleflump is a set together with a ternary operation Star(a,b,c), and a binary operation Spade(a,b) satisfying Star(Spade(a,b),Spade(c,d),Spade(e,f)) = Spade(Star(a,b,c),Star(d,e,f)).

I could now devote my life to the study of Gobleflumps. I could publish papers about extremely regular gobleflumps, and the equivalence between hyperconvex gobleflumps and hypoconvex grendleflops. This might all be legitimate, correct mathematics.

No one will ever care about my lifes work, or probably even read it, unless it makes some connection to existing mathematical theory, illuminates why something disconnected from the theory works the way it does, or solves some existing problem.

... and if no one will ever care about the results, most reputable journals will not publish them, either.

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    Can I say that the main thing now determining the success of the paper is it's connections to existing theories, their impacts, etc. (i.e. how interesting the results are) and the sophistication or "level of math" involved in the paper is not as important? – YiFan Aug 30 '18 at 12:30
  • @user496634 That's certainly part of it. – user2768 Aug 30 '18 at 13:05
  • @Allure I think it is a little premature to speculate that the "results have no implications, no relation to other problems, and is not significant in any way beyond that paper." Perhaps you can elaborate on how the OP can determine whether this is the case? (I like your reference to Steven Gubkin!) – user2768 Aug 30 '18 at 13:08
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In general, mathematical results need to be interesting in some way to some subset of practitioners to be publishable. You haven't pressented them in that way so you need to think about who wants to know this.

But it isn't the quality of the journal here that will matter, but the kind of thing they want to publish. For example, if the results are accessible to beginners, say undergraduates, then you might find acceptance in a journal devoted to teaching at that level, rather than a more research oriented journal. The MAA, Mathematical Association of America, for example, could possibly be interested. But it still needs to be interesting.

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Stash the paper for now. Talk to people that you trust about it. Chances are, in a few years you'll discover a connection to something completely unexpected, making it interesting. At that point you have a good chance it gets published, regardless of how 'advanced' the required foundations are.

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