How do editors of mathematical journals know that a submited paper is original, that is unpublished? I wondered many times how the editors of mathematical journals know that the content of a paper or article that was submited by an author is original, this is, that the main content of such calculations and reasonings is unpublished.


  Question. How do editors of mathematical journals know that a submited paper is original, that is unpublished? Many thanks.


I would like to know it as curiosity, because I imagine that professors working in mathematical journals are experts in a field of mathematics. Then a day they receive a writing, a paper or a remark, with perhaps several results, and they have to evaluate if this was not published or known previously. 
Additionally I imagine that these professors or editors have tools to search information for this purpose, and maybe they have contact with other colleagues who have historical memory about what results, and of what kind, have been published. Am I wrong in these believes? How do they know and they note the originality of such mathematical content?
When submitting a paper for publication, it is not only the editor who looks at it. The editor will (usually) take a first look to determine if the paper looks to be suitable for the journal. If they see that the main results are already well-known this will likely make them reject the paper (especially if the authors have not made any remark on this themselves). 

If this is not the case and the paper generally looks fine (this also includes the results actually seeming to be interesting), then the paper will be sent to one or two experts in the field for review. These will (hopefully) take a much closer look at the paper and determine if they think it is suitable for the journal. Once again, this will include trying to determine whether the results are actually new, which is why it is important for the editor to choose reviewers who really are experts, as otherwise they will not be familiar enough with the field to determine this.

Finally, the reviewers will make a recommendation to the editor based on their reading, and using the editor will make a final decision on whether to accept the paper, possibly contingent on certain improvements.
Usually they have payed staff, some Prof. who are working in this field. So they send your paper to them, they review it. Based on their review it will be published or not. It depends on the quality of the journal, how well they check your work.