Mathematical results are published in journals. These mathematical journals have independent editorial boards that establish procedures on how to submit a completed manuscript for consideration and how they make their decisions concerning whether a submission will be published. A journal editor may get advice concerning a particular manuscript from one or more referees. An editor may explain to an author the reasoning behind the acceptance or rejection of a particular submission, but there is no steadfast rule that an editor must do so.
An article may be submitted to only one journal at a time. An author needs to choose an appropriate journal and contact its editorial board. The range of times that a particular journal needs to reach a decision is large. Some decisions may be made quickly, while others may drag out over many months or even years. Procedures for preparation of an article and for submission differ from journal to journal. Most journals prefer that manuscripts be prepared with TeX or LaTeX.
The editor of a journal will expect a complete and final version of a manuscript (possibly more than one copy), written in such a way that is clear and verifiable. With papers on classic problems that have been worked on by experts for years, clarity is particularly important. It is standard for an article to be accompanied by a letter stating that the author is not submitting the paper to other journals. In many cases, the journal asks an author to contact directly the member of the editorial board who handles the subject area covered by the paper. The specialties of the editors are often listed on the web site for the journal as well as in the printed journal. The specific guidelines for submissions will also be available from these sources.
It is up to the author to decide which journal to contact. The American Mathematical Society has no list of recommended journals, nor will it make specific recommendations to authors concerning their manuscripts, but see this list of mathematics journals. While this compilation provides a valuable resource, it undoubtedly does not include all mathematics journals and authors should be aware that this list contains many journals that are inappropriate for articles solving unusually challenging problems.
The AMS thanks the Clay Mathematics Institute for permission to post these publication guidelines.