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I am currently in a little dilemma about publishing a result related to general matching.
The dilemma is, that I am not associated to any research institute and thus do not have contact to professional mathematicians, which I could ask for checking a fairly simple proof for correctness.

So my question is, how and where I could find an expert, who is willing to take a look at my result and proof. Another question is, what convinces professional mathematicians, that a claimed finding is promising enough to volunteer for reviewing despite limited time and some chance to find a fly in the ointment?

(Alternatives might be to either ask the MO community for counter examples or, to boldly publish on ArxiV and awaiting the reaction of readers; but it seems to me that neither of these two alternatives is a nice way of getting a review.)

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    $\begingroup$ Why not take the conventional route and submit to a journal? $\endgroup$
    – Alex Degtyarev
    Commented Jun 14, 2016 at 19:01
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    $\begingroup$ If you have a nearby maths department, and someone there looks like they might be suitable, just email them and invite them for a coffee (you pay), you never know ... $\endgroup$
    – J.J. Green
    Commented Jun 14, 2016 at 19:04
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    $\begingroup$ I'd follow @J.J.Green's suggestion if possible. If this is impossible, I would look for approachable people doing related work (either through contacts who are in research institutions or through the web - people's web sites give some indications of approachability or otherwise), explain the situation and ask if they are willing to read your manuscript. You may well have to ask more than 1 person (but do this in series rather than parallel). $\endgroup$
    – Anthony Quas
    Commented Jun 14, 2016 at 20:02
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    $\begingroup$ There is good advice on various points at research.microsoft.com/en-us/um/people/cohn/Thoughts/… $\endgroup$
    – Neil Strickland
    Commented Jun 14, 2016 at 22:01
  • $\begingroup$ @AlexDegtyarev: simply because I don't trust myself enough to believe I can't be wrong. $\endgroup$
    – Manfred Weis
    Commented Jun 17, 2016 at 6:22

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This is not an answer to your question, but rather a short relevant observation that is too long for a comment. I occasionally see math papers with non-standard formatting and am immediately discouraged from reading them. For example, I might see a paper typeset in Word and will more likely dismiss it than if the identical words were typeset in Latex. In some respect it's crazy that something as silly as formatting would make a difference as to whether I choose to read a paper. At the same time, however, use of non-standard formatting can communicate to a reader that the author is an "outsider", unfamiliar with professional mathematics and its norms, raising red flags immediately upon sight. The reader might never get beyond the title, and the beautiful Word-typeset mathematics might never receive serious consideration. Although no one in the beginning of the 20th century was using either Word or Latex, I'm sure that the unconventional presentation of Ramanujan's mathematical work likely discouraged many from giving it the proper attention it deserved.

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Answer 1: In universities, research institutions, and the Internet. Answer 2: nothing does for those professionals who are not interested in the area or specific results, while a well-written abstract and introduction often works for those few who are.

I think you should post your paper in two or more places, so that those who have their own interests in the subject can find it quickly, look it over, and give you their comments. Nowadays there are many nonprofessionals who are able to provide useful critiques: even if they can't find bugs in your proof, they can find bugs in your exposition, and put pressure on you to improve your presentation.

Regarding MathOverflow, you should be able to review your paper, find the two or three points that are most questionable, and for each point, generate a question for MathOverflow. Ideally the points will require little technical background and each can form a self-contained question. If necessary, you can link the questions together to form a mathematical narrative. You can briefly state your motivations and provide a link to the paper. This way you can get several professionals and amateurs to spend the time where it is needed most (hopefully).

Writing a good question for MathOverflow addressing one of these points is hard. The benefit from doing such is showing the essence of (that part of) the result. It can make the rest of the paper easier to write so that it can be easier to read.

Gerhard "Fast, Cheap, Good: Pick Two" Paseman,2016.06.14.

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    $\begingroup$ There are lots of bits advice I have regarding this. The first bit is to post a version on meta, referencing this question. If you do a good job, you can set the standard for other non-academics to follow. Gerhard "Too Many For One Posting" Paseman, 2016.06.14. $\endgroup$
    – Gerhard Paseman
    Commented Jun 14, 2016 at 23:13
  • $\begingroup$ thanks for encouraging me to post on Mathoverflow/Meta; it seems to me the lowest hanging fruit to get first feedback. I only hope that other MO users will not see such post as "self advertising" $\endgroup$
    – Manfred Weis
    Commented Jun 15, 2016 at 6:06
  • $\begingroup$ So don't self-advertise. You are working on a paper (handy link provided), you are working through an argument in the paper, and one of the steps you are unsure of is (fill in the blank). Is the step correct, and is there a better way to communicate it? Provide enough but not too much background to keep the question self-contained. Rewrite the paper to acknowledge the help you get from MathOverflow. Gerhard "Make It About The Math" Paseman, 2016.06.15. $\endgroup$
    – Gerhard Paseman
    Commented Jun 15, 2016 at 16:53

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