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What can be recommended for contacting journals with the purpose of checking whether they would be interested in an publishing an article if one is not affiliated to a research institution and still is unknown to the professional math community?

Specifically I would like to know whether it is acceptable to initially only state the problem whose solution is claimed and give some indication that there is strong evidence for the correctness of that solution, e.g. by providing experimental results, proving acquaintance with the problem and attempts to solve it.

Are such initial contacts tolerated by journals or do they insist on the availability of a mature document when they are initially contacted?

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  • $\begingroup$ Based on your description, it does not seem like you solved any particular problem that would be of interest to some part of the mathematical community but rather found some numerical evidence that something is true. There are journals who publish experimental results, as long as the computations are interesting (Mathematics of Computation comes to mind). You can try emailing one of the editors of a journal like this and see if they are interested. $\endgroup$ – Stanley Yao Xiao Jun 14 '20 at 16:24
  • $\begingroup$ @StanleyYaoXiao I am very sure that I have found the solution to an interesting problem, specifically an algorithm to find a solution; the experimental evidence would be to run it on test instances and document its performance. $\endgroup$ – Manfred Weis Jun 14 '20 at 16:36
  • $\begingroup$ @StanleyYaoXiao I wouldn't have a problem to provide details on that algorithm on MO, but that would be self advertising, which is deprecated. If however someone asked for it the situation may be a different one. $\endgroup$ – Manfred Weis Jun 14 '20 at 16:40
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    $\begingroup$ If you believe you have solved a problem that would be of interest to some mathematical community, then your best bet is to prepare a manuscript carefully and submit to a journal. Your manuscript should 'look like' a math paper: i.e., preferably in LaTeX, demonstrate a good knowledge of existing literature, and has good exposition. $\endgroup$ – Stanley Yao Xiao Jun 14 '20 at 17:20
  • $\begingroup$ @ManfredWeis it sounds like you are an independent researcher with little involvement in the mathematical "community". In that case you are really to be commended for having the wherewithal to pursue research on your own. Good for you! $\endgroup$ – Nik Weaver Jun 14 '20 at 19:29
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Sending an editor an outline like you describe won't have much of an effect. All an editor will do, if they respond at all, is say "why don't you submit the paper, and then we will decide whether to send it for peer review and to accept it". They couldn't possibly be any more committal based on just an email.

Writing mathematical papers is hard! Graduate students and early postdocs struggle a lot with that, and typically rely on considerable input from their advisors or other more senior colleagues to produce a paper that is submittable.

What I would recommend is that you first find a professional mathematician who is interested in your problem, and contact them with the questions that you would ask an editor. If you cannot find a mathematician who is interested in your problem, then that does not bode well for your journal submission (since if the editor cannot find anybody interested in it, they will reject the paper).

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If the point is to get published in a journal, you need to do it their way. Their job is to take mature papers, have them vetted to make sure they are mature enough to commit to the literature, and then publish them with the stamp of their reputation. If you are unsure whether your paper merits their approval, you probably should not ask. (This is different from trying to determine publishability. If you contact an editor or two, they might give you their opinion if it does not take much time. I think Alex B. has a correct and charitable reading of the situation here.)

If the goal instead is to gauge interest in the problem, there are better ways. Probably the best is to look up conference proceedings of the area and see how much play the problem is given. Use these to get names and addresses of experts who can probably tell you how and when to approach journals, if you still want to go that route. There is less barrier to self publishing, and you can use your MathOverflow user page to talk up about yourself and your work. The user page can serve as a big business card should you wish to contact these experts.

Gerhard "Don't Need No Stinkin' Journals" Paseman, 2020.06.14.

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  • $\begingroup$ Gauging interest in the problem wouldn't be hard as it is of some fame; that is also the reason why I am careful not to claim that I have solved it but only that I am very convinced to have solved it. The situation is like riding a tiger and not knowing how to get off graciously. $\endgroup$ – Manfred Weis Jun 14 '20 at 18:56

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