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I'm struggling to find a home for a certain paper of mine. The problem is that the mathematical content of it is extremely easy: a couple definitions and a theorem with a five-line proof, invoking the Recursion Theorem and the Smn Theorem. It's not really appropriate for a logic journal, because it's too easy (are there any logic journal equivalents to "Mathematics Magazine")? But every easy math journal I send it to rejects it saying that the Recursion Theorem and Smn Theorem are too obscure for mathematicians!

Due to its easiness, it might even be more appropriate as a "Problem", in a place like AMM's monthly list of problems, except it definitely requires Recursion Theorem and Smn theorem. Are there any places where such a problem would be welcome?

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I think we all keep a few papers like that in the drawer, sometimes for years, before they are included in lecture notes, books, or more substantial papers. Is it on the ArXiv? As you describe it, the paper will not add much to your reputation so why go through the hassle of submission, rejection/acceptance, editing, etc.? – alvarezpaiva Jan 7 '14 at 15:47
To silence my conscience, let me add that if you think the result is important (who cares if a proof is simple, the importance of a result is not measured by the difficulty of its proof but by how well it fits into the mosaic mathematics), then maybe you should try to publish it or make it widely known sooner than later. – alvarezpaiva Jan 7 '14 at 16:56
Might adding an expository account of the two theorems make it both acceptable to the journals in question and valuable to a broad audience? Besides, maybe you shouldn't think of a journal as "easy" merely because following the math involved in the papers is easy and elementary. – Michael Hardy Jan 7 '14 at 20:07
I agree with alvarezpaiva that it matters less how easy the result is than how important/interesting it is. But if you're considering the AMM problem section, I don't think that recursion/smn necessarily disqualify it. What would disqualify it is an uninteresting statement. If the statement of the result is interesting and short then I'd go ahead and submit it to the AMM. – Timothy Chow Jan 7 '14 at 21:13

You should look beyond the standard outlets. The so-called "micropublishing revolution" is slowly emerging in mathematics and science in general. Original research ideas and results that aren't necessarily suitable for journal publication regularly find their way here on MathOverflow and in a variety of alternative outlets such as blog posts, social networks and whatnot.

The idea is not new, Doron Zeilberger's 39th Opinion was posted in 1999 and Michael Nielsen has already written several books and essays on the topic. Though these new outlets don't have the notoriety of journals and other traditional outlets, they all achieve the basic goal of disseminating research ideas. (A five-line proof doesn't need any peer review or any other "added value" that journals provide.)

Look around until you see something that fits your result. Don't worry about community acceptance and similar illusions, the people who are interested in your result will eventually find it and use it. News travels much farther and faster than it used to!

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Let somebody else who is currently finishing up a related paper include it in their paper (with attribution). This will be good karma, if it should happen to be possible in your situation.

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Find an appropriate conference and send your paper there. If it will be not rejected then you can put it in conference proceedings.

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