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I am amateur mathematician with some formal training but am not a student and did not get some college degree, but, much of the time (really really too much) I think about mathematics and mathematical tasks and problems and I expand my knowledge of and about mathematics.

Sometimes I am solving some (mostly) undergraduate exercises, and sometimes I even do try to settle some unsolved problems.

Of course, if I dwell onto and into some mathematical theory, I try to understand basics and then the more general results.

Now, there are some ideas and a few results on the papers next to me, but I am extremely non-motivated to do the research in the future because of lack of support.

I can expect that even if I prove something of major interest, or if I prove something known by some other methods, that my work will hardly be published, because of lack of support.

So, if really I have written some results which could be published in some journal, or if I prove in the future something worthy of publishing, what are your general guidelines of what to do?

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Sorry to have to say it, but the first step is to assure yourself that you aren't a crank. You don't sound like someone trying to "square the circle", so the first comment was just for completeness. But if you aren't sure about the validity of your research then getting some feedback on it from a pro would be helpful. Perhaps you are close enough to some university to make contacts and talk about what value your ideas might have.

But in the final analysis, you publish in a journal by submitting your work to the journal. If you get desk-rejected by an editor you have some information that your work isn't up to the required standard. But otherwise your work will be given to experienced reviewers for comment.

You don't need any credential or affiliation to publish. Just quality work.

Longer term, however, forming some circle of collaboration can help get you in the game. It can help you up your game as well.


You don't say what you mean by "lack of support". If you edit the question to add more, I might have more to say as well.

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    it seems (at least to me) that i have proven elementarily that if k>1 and b>1 then n!+k=m^b has a finite number of solutions n_1,...n_a and this is already proven somewhere, but only by assuming abc-conjecture of which there is no proof (one, but controversial and largely unaccepted) and i think that this result could be published somewhere, this is just me giving you an example of some of my findings – user120709 Mar 20 at 15:58
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    I won't discourage you at all. But collaboration and feedback are good. Submit and learn. – Buffy Mar 20 at 16:01
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    I'll also note, as I have elsewhere here, that proofs are more "interesting" than theorems, especially if the give new insights. So an elementary proof of anything is a good thing. – Buffy Mar 20 at 16:06
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    @Ante: Especially in Number Theory, journals will often just ignore amareur mathematicians. So, please talk before to some mathematicians who you are on a friendly basis with (ie a friend who is phd or prof). Convince them first and pay them a glass of wine for their help. – user111388 Mar 20 at 19:49
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Perhaps you could 'practice' by submitting solutions to the venerable 'Problems and Solutions' in either the College Mathematics Journal or the American Mathematical Monthly. I submitted a solution to this in my student days (early Pleistocene...) and they published it. These journals are great for amateur mathematicians.

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