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Although in mathematics the letters, i.e., really short articles, just a few pages long, are perhaps less common than in the other fields (see e.g. the comments by Pete L. Clark under his answer to this question), sometimes such a letter really is the best way to communicate the result. It is also quite clear that for this very reason (that the letters are quite uncommon), such letters are not likely, save for some very exceptional situations, to be a good fit for the top pure math journals like the Annals, Inventiones, JAMS, etc.

Apparently in earlier times the best place for publishing letters in mathematics was the French journal Comptes Rendus. This journal still exists but I am not quite sure whether it is the place for letters in mathematics anymore.

Another option that comes to mind could perhaps be the math section of the PNAS but again I am not quite sure how this journal is actually standing with the pure math community, especially outside the US.

There should certainly be other worthy alternatives, so I look forward to the answers pointing them out as well as discussing the journals mentioned above.

QUESTION: What are the best (in terms of standing in the math community and being widely read by mathematicians) journals, or perhaps sections of mathematical or even multidisciplinary journals, for letters in mathematics nowadays?

P.S. I am specifically interested in the journals which would tolerate the papers which are on the border of mathematics and mathematical physics (just to clarify, this refers to the subject matter rather than, say, lacking in rigor). The Letters in Mathematical Physics and Nonlinearity appear to be a bit too niche, I would prefer more broad-scope alternatives.

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  • P.P.S. This question is an outgrow of the discussion in comments to the Pete L. Clark's answer to http://academia.stackexchange.com/questions/17050/acknowledging-the-discussion-with-someone-in-the-paper-but-excluding-this-person/17092 – just-learning Feb 18 '14 at 09:50
  • You have already named several options for publishing letters in mathematics, so what else do you expect as an answer? I am saying this because whatever a possible answer would be you can raise some doubt about it anyway, as you have already done about the abovementioned journals. –  Feb 18 '14 at 11:52
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    Why not just publish these on your blog+arXiv? Why is the journal necessary for short letters? – Artem Kaznatcheev Feb 18 '14 at 11:54
  • @Vahid: Quite the contrary: I hope that other experts in the field will make my doubts go away. It's also quite possible that there exists some community consensus on the math letter journals and I just happened to be unaware of it. – just-learning Feb 18 '14 at 14:15
  • @Kallus: would you please care to expand why do you think this is the journal for letters in math? – just-learning Feb 18 '14 at 14:22
  • Mathematical Research Letters is one option I have come across in my reading. A cursory look suggests it has a fair deal of mathematical physics. – Kallus Feb 18 '14 at 14:25
  • @Kallus: thanks, will check them out again. However, listing any further alternatives (ideally with some comments on them) is still very welcome. – just-learning Feb 18 '14 at 14:27
  • @Vahid: I have also asked some specific questions about PNAS and Comptes Rendus and I hope people will share their opinions on them. – just-learning Feb 18 '14 at 14:28
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    In my experience, mathematicians tend to call such short articles "notes" rather than "letters". Also, my impression is that Comptes Rendus, while it did publish some very short self-contained papers, was mostly intended for announcements of results for which complete proofs would later be published elsewhere. – Nate Eldredge Feb 18 '14 at 15:57
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    @Nate: Thanks, this trend explains a lot :) By the way, how about "communications"? Are they the same as letters or notes, or something in between the letters and the regular papers? – just-learning Feb 18 '14 at 21:51
  • @Kallus: how would you compare MRL vs PNAS vs CR? – just-learning Feb 18 '14 at 21:53
  • @just-learning: How would I compare them? I would browse some of their recent issues to get a feel for the kind of papers they publish. – Kallus Feb 18 '14 at 22:01
  • @Kallus: Sorry, I wasn't clear enough. By "compare" I meant "compare in terms of their standing in math community" (or "compare in your eyes", if you like). But anyway I'll use your advice too, thanks. – just-learning Feb 18 '14 at 22:06
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    @just-learning: I don't have a clear sense of what a "communication" would be. We don't use this word much. It may appear in some journal titles but I wouldn't have a clear sense of what such a journal expects without looking at its aims-and-scope and what they've published. – Nate Eldredge Feb 18 '14 at 23:39
  • The sense in which I've seen "communication" in math journals is that some journals have, after the byline, a "communicated by X" line, which means that X was the handling editor. – Pete L. Clark Feb 19 '14 at 00:38
  • @Nate and Pete: Thanks for the remarks on "communication". – just-learning Feb 19 '14 at 07:17
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    There are a few cases of pairs of companion journals, whose main difference is the length of the papers. For example, Proceedings of the AMS/Transactions of the AMS, or Electronic Journal of Probability/Electronic Communications in Probability. As those two examples illustrate, there's no universal way of signaling in the journal name which is which. – Mark Meckes Feb 19 '14 at 07:45

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As Pete L. Clark, I do not quite know what a letter is: short papers are usually quite similar to regular paper, only shorter and usually called notes.

Concerning the venue suitable for short articles, there are quite a few. First, you should now that most journal could accept short papers, but certainly you have more chance to get accepted in a journal specifically targeted toward short paper (except if you solve a known problem or reprove a notoriously difficult theorem, in which case no reviewer can use the length of the paper to argue it does not have much merit). Let me give my impressions on the journal that come to mind (to remind that this is from a biased perspective, I will often refer to the French mathematical community), limiting to journals that to not claim being restricted to a subfield -so called generalist journals.

  • CRAS (Comptes-Rendus de l'Académie des Sciences, Paris): this journal publishes both research announcements and complete short papers. The announcement part is less and less relevant, but I do not know whether it is less present now. Sadly, while CRAS published top-notch papers, it cannot afford to be very selective anymore. It also suffers from the research announcement role: French hiring committees often blankly dismiss CRAS papers, partially because they may be only announcements.

  • PNAS (Proceedings of the National Academy of Science, USA): this journal is not very well-known from French mathematicians, but publishes some quite good papers. I think it has a particular taste, but I cannot find the word to describe it. Beware that even if it has a page limit, the format is very dense so articles are not necessarily that short overall.

  • PAMS (Proceedings of the American Mathematical society): this journal is explicitly for short papers, but the page limit recently moved from 10 to 15 (AMS format). As far as I can judge it is selective, and sometimes publishes excellent papers. It is reasonably well regarded, benefiting from the sisterhood of Transactions AMS.

  • Bul. LMS (Bulletin of the London Mathematical society): this journal is the LMS counterpart to PAMS, and is somewhat similar (although a little less known and considered, maybe). Since the LMS series has three journals (Bulletin, Journal and Proceedings in increasing order of paper size) instead of two for the AMS, I guess that the average Bulletin paper is somewhat shorter than the average PAMS paper, but the different format makes it difficult to judge.

  • AMM (American Mathematical Monthly): this journal is well-known and extremely selective. It publishes papers of general interest, of varying length. The notes are typically a few pages long. It is even possible to publish mathematical facts of a few lines, in a grayed box. Since it is considered somewhat recreational, publishing in the Monthly gives less weight to a CV than its harsh selectivity would do for any other journal.

  • Elemente Math. (Elemente der Mathematik): this is a Swiss cousin to AMM, much less known and much less selective.

  • MRL (Mathematical Research Letters): this does barely belong to the category of note-publishing journals: it does not usually published paper more than 30 pages, but the average paper there is not a note as far as I can judge.

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  • Could you please at least hint a bit (perhaps in the comments) on the taste of PNAS? That's very intriguing as after looking at their math section I was not able to figure this taste out. – just-learning Feb 19 '14 at 19:44
  • @just-learning: I do not know many PNAS papers, but I would expect PNAS to publish papers that could have been sent to Nature or Science, but would not because these journals are not very open to maths: papers with a link to other science, or some appeal to a wider audience. One example which makes me think that way (but I may be overweighting it) is http://www.pnas.org/content/109/19/7218.short – Benoît Kloeckner Feb 19 '14 at 21:23
  • Thanks again. This rings very true to me as the appeal to a broader audience is certainly characteristic of PNAS (I think it can be found in their Aims and Scope), and they do not shy away from the multidisciplinary papers too. – just-learning Feb 19 '14 at 21:40
  • @Benoit: I did a little copyediting in your answer. If that is unwelcome, please feel free to roll it back and let me know. – Pete L. Clark Feb 19 '14 at 23:37
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I think this is a good question because I don't really know what "letters" means in the world of mathematical publishing. While I have a paper published in Math Research Letters, I am having trouble pointing to a single way in which that paper is different from any of my other papers: it is slightly short (12 pages) but I have several other papers which are shorter, it contains complete proofs, the syle is not especially conversational or different from the norm...

With regard to Comptes Rendus: it still exists, and it is still a very high quality journal, so far as I know. I do not have a CR paper, and I wish I did, but setting aside the limitations of my own research achievements I am not sure exactly what papers to submit to this excellent and highly French journal. My understanding though is that it is roughly analogous to Proceedings of the AMS but of higher quality (or better taste?). For instance I have a PAMS paper and think that would be in the right ballpark of CR but that I would be lucky to get it published there.

It was suggested in the comments that the publications in CR are more like research announcements. I don't think that's true. They're short, punchy and written in a somewhat telegraphic style, but they certainly do include proofs. Quite recently I had the occasion to go to the actual library and pull off the shelf a CR paper. It was lovely, and short enough so that I transcribed (and translated, but big whoop: mathematical French is so easy that I can do it) it in its entirety on my notepad. (If you're interested, it is Guy Terjanian's first paper, referred to here...and as I learned slightly to my chagrin, one could regard the research contribution of this note of mine as being a fleshing out of a mild Alon-style generalization of Terjanian's argument. Actually there is another theorem he proves in that paper as well which is more interesting. To me this is a CR paper par excellence: a small but perfectly polished gem.)

I also think that Enseignement Mathematique is somewhere in this constellation of journals: more apparently elementary than CR, less laconic, but still high quality work which is somehow in "good taste". And note that the title of the journal would lead you to think that it publishes expository papers, but I don't think that's really the case.

After all this, let me come back to where I started:I am not sure what a "letter" is in this context, other than a short paper which is high quality and is written in a relatively laconic way. I have, unfortunately, zero expertise with physics, including the substantial portions of mathematics that overlap with physics. Maybe the concept of a letter is better understood by that portion of the mathematical community?

Added at the end: okay, let's see how MRL describes itself:

Dedicated to rapid publication of complete papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.

Thus there is some kind of vestigial connection with abbreviated papers, expository work and research announcements, but by and large it is no longer what that journal is about. I think this is rather typical.

Added: Since I was specifically asked to comment on PNAS, and I am a little gun-shy about leaving things in comments at the moment (see the meta site for more on this...), I will add the following non-answer answer: I have very little direct experience with PNAS. I tried to think of a single paper that was published in that journal and I came up with Milnor's "Eigenvalues of the Laplace operator on certain manifolds", a famous one page note. Based on that one paper (!!) I will guess that PNAS is like CR but for laconic treatments of even more important results. (I will also guess that most of their papers are more than one page long...)

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  • Thanks a lot for a very informative answer. If possible, I'd be happy to learn how'd you compare CR vs pure math section of PNAS. Many thanks in advance. – just-learning Feb 18 '14 at 22:59
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    Browsing a few of CR's recent papers, I stand by my comment: some papers are self-contained with short elegant proofs, some give proof sketches but omit details that would normally be expected in a full paper, and some just have a sentence or two giving the main idea of the proof. The latter are more in the way of announcements, and in those cases one usually expects a complete proof to be published later in another journal. – Nate Eldredge Feb 18 '14 at 23:35
  • @Nate: Okay, thanks, that's good to know. I should say that I have probably read on the order of a dozen CR papers. It does happen to be the case that none of these have been research announcements though. I wonder if this is field-dependent. Since you already looked, I wonder if you could tell me whether you found any research announcements in the areas of algebra and number theory? – Pete L. Clark Feb 19 '14 at 00:27
  • See for example http://dx.doi.org/10.1016/j.crma.2013.07.016, whose last line is "The proofs of the results of this Note will be published in detail elsewhere." But it does seem like there may be fewer than in, say, analysis. (Actually, a brief skim seemed to show disproportionately few total papers in either area.) – Nate Eldredge Feb 19 '14 at 03:52
  • @Nate: thanks again for your time. This type of information is rarely definitive but always interesting. – Pete L. Clark Feb 19 '14 at 04:28
  • By the way: I just realized that the way I come across CR papers almost certainly biases me against seeing research announcements. I don't have a subscription or page through whole issues: I get directed there from other papers. It's much less likely that I would get directed to a research announcement. Actually, I'm not sure I understand the point of a research announcement in 2014 (or 2013). Maybe there's a question there as well... – Pete L. Clark Feb 19 '14 at 04:34
  • @PeteL.Clark: Thanks for the comment on PNAS. – just-learning Feb 19 '14 at 07:20
  • My experience of CR agrees with Nate's. In functional analysis CR has published quite a few research announcements in recent years. (I suspect this is a result of others following the practice of a couple field leaders.) I also agree with Pete, though, in saying I'm not sure I understand the point of a research announcement in the modern world. – Mark Meckes Feb 19 '14 at 07:52
  • FWIW, I had to look through more than a year's worth of CR papers to find a number theory paper that only sketched a proof (it was roughly the 20th such paper I looked at). Finally I found this one:http://www.sciencedirect.com.proxy-remote.galib.uga.edu/science/article/pii/S1631073X11003578. – Pete L. Clark Feb 19 '14 at 08:32
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    @PeteL.Clark: Just in case, here is the direct link to the paper you mention in the last comment (your link appears to ask one one for some Galileo password): http://www.sciencedirect.com/science/article/pii/S1631073X11003578 – just-learning Feb 19 '14 at 16:05