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I am an amateur mathematician, and have written my first paper. How would I go about getting it reviewed / published? I have absolutely experience of what journals might expect, and do not know any mathematicians. I do not know which journals are respected, what is the correct procedure for submission, nor any academics who might look at it. Neither am I affiliated with any college / university.

martin
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    Go to the homepage of a journal and read the instructions to authors. Fo example http://www.elsevier.com/journals/acta-mathematica-scientia/0252-9602/guide-for-authors – Claude Leibovici Jan 04 '14 at 13:49
  • See also http://math.stackexchange.com/questions/181210/how-to-write-a-good-mathematical-paper. – lhf Jan 04 '14 at 14:14

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The arxiv is not a peer-reviewed journal, but a pre-print arxiv. Most people my age find it indispensable to make their work visible by putting it on the arxiv and you should certainly aspire to do so as well. However, this is an issue independent from publication in a journal.

Furthermore, you should first answer these questions (maybe just to yourself): What makes you think that your paper merits a publication in a mathematics journal? What do you want to gain from publication?

For example, if the answer to the first question is that your paper seems similar in scope and subject to papers you read in journal X by author Y, then a natural next step would be to politely contact author Y and ask for their opinion on your paper and/or invitation to the arxiv.

However, it is easier to get in contact with people if it is not all about yourself. You might want to listen to mathematics talks in a nearby university and ask questions or email an author of an article you liked.

Whatever you do, do not sign a contract that makes YOU pay for publication.

Phira
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Read these guides:

lhf
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  • I have written it - just wondering about the submission / review process. – martin Jan 04 '14 at 14:21
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    @martin, Krantz's article talks about this. – lhf Jan 04 '14 at 14:22
  • Great, ok - thanks - will take a look now :) – martin Jan 04 '14 at 14:23
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    I understand that I cannot submit to Arxiv as I need to be 'invited' by a pre-existing member. I have also heard some rather dubious things about it - such as questionable 'proofs' of the RH being published on it, on account of there being no peer review system. Would I be correct in believing what I have heard as regards this issue? On the other hand, I have read some excellent papers from this site. – martin Jan 04 '14 at 14:26
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    @martin Whatever you do, do not sign a contract that makes YOU pay for publication. – Phira Jan 05 '14 at 18:40
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    ok, thanks - I will be wary of that! Just out of interest, and being completely naive in these matters, at what stage of the process might this issue arise? – martin Jan 05 '14 at 18:56
  • @Phira, perhaps you could turn your comments into an answer. – lhf Jan 05 '14 at 19:41
  • @lhf Done. ${}{}$ – Phira Jan 05 '14 at 21:47
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    @martin I have never signed anything before an article was accepted, but my experience is only with respected math journals. It is hard to predict what can happen with a bad editor. For example, there is a predatory "mathematicians handbook" editor out there who spam-mails mathematicians with demands for clarification of biographical details including some fine print that they agreed to pay some money for the publication of said biographical details. This is not a special math problem, but the fact that you are inexperienced puts you at higher risk, so I wanted to mention it. – Phira Jan 05 '14 at 21:52
  • @ Phira Thank you for the warnings, and your encouragement - your comments have been really helpful - especially valid for someone in my position. I agree with your suggestion that I should really ask these questions to myself. Again, well said, and thanks :) – martin Jan 05 '14 at 23:38
  • @ lhf - thanks again for the links - they have made interesting and informative reading :) – martin Jan 05 '14 at 23:40