I think I may be on the verge of solving a previously unsolved problem. It is not a hugely interesting or revolutionary problem. However, I was wondering if there would be something I should do after having solved it? What is the process for publishing a solution, and does a problem have to be sufficiently "interesting" or "useful" for it to be published?
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1This is very vague. Why not just submit it to a relevant journal? May be worth noting: most publications contain neither "hugely interesting" nor "revolutionary" results, just good hard work. All progress is progress. – lulu Apr 26 '22 at 11:13
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The very first thing you should do after having solved it is very carefully and firmly shove it aside and do not even think about it for at least a week. Maybe two. Then go back, read it with as critical an eye as you possibly can - trying your best to look at it as if you had never heard of it before - and make sure it makes sense. Fill out carefully those details that you skimmed over. Then, set it aside for another week or two. Repeat. If you can't find anything to improve, then start editing it to be presentable to an audience that is familiar to the field, and figuring out how to submit. – Paul Sinclair Apr 27 '22 at 01:59