Advice on getting first paper reviewed 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.
 A: 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.
A: Read these guides:

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*How to Write Your First Paper by Steven G. Krantz.


*How to Write Mathematics by Paul Halmos.
