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I wonder if anyone else has noticed that the market for expository papers in mathematics is very narrow (more so than it used to be, perhaps).

Are there any journals which publish expository work, especially at the "intermediate" level? By intermediate, I mean neither (i) aimed at an audience of students, especially undergraduate students (e.g. Mathematics Magazine) nor (ii) surveys of entire fields of mathematics and/or descriptions of spectacular new results written by veteran experts in the field (e.g. the Bulletin, the Notices).

Let me give some examples from my own writing, mostly just to fix ideas. (I do not mean to complain.)

  1. About six years ago I submitted an expository paper "On the discrete geometry of Chicken McNuggets" to the American Mathematical Monthly. The point of the paper was to illustrate the utility of simple reasoning about lattices in Euclidean space to give a proof of Schur's Theorem on the number of representations of an integer by a linear form in positive integers. The paper was rejected; one reviewer said something like (I paraphrase) "I have the feeling that this would be a rather routine result for someone versed in the geometry of numbers." This shows that the paper was not being viewed as expository -- i.e., a work whose goal is the presentation of a known result in a way which will make it accessible and appealing to a broader audience. I shared the news with my officemate at the time, Dr. Gil Alon, and he found the topic interesting. Together we "researchized" the paper by working a little harder and proving some (apparently) new exact formulas for representation numbers. This new version was accepted by the Journal of Integer Sequences:

https://cs.uwaterloo.ca/journals/JIS/VOL8/Clark/clark80.html

This is not a sad story for me overall because I learned more about the problem ("The Diophantine Problem of Frobenius") in writing the second version with Gil. But still, something is lost: the first version was a writeup of a talk that I have given to advanced undergraduate / basic graduate audiences at several places. For a long time, this was my "general audience" talk, and it worked at getting people involved and interested: people always came up to me afterward with further questions and suggested improvements, much more so than any arithmetic geometry talk I have ever given. The main result in our JIS paper is unfortunately a little technical [not deep, not sophisticated; just technical: lots of gcd's and inverses modulo various things] to state, and although I have recommended to several students to read this paper, so far nothing has come of it.

  1. A few years ago I managed to reprove a theorem of Luther Claborn (every abelian group is isomorphic to the class group of some Dedekind domain) by using elliptic curves along the lines of a suggestion by Michael Rosen (who reproved the result in the countable case). I asked around and was advised to submit the paper to L'Enseignement Mathematique. In my writeup, I made the conscious decision to write the paper in an expository way: that is, I included a lot of background material and explained connections between the various results, even things which were not directly related to the theorem in question. The paper was accepted; but the referee made it clear that s/he would have preferred a more streamlined, research oriented approach. Thus EM, despite its name ("Mathematical Education"), seems to be primarily a research journal (which likes papers taking new looks at old or easily stated problems: it's certainly a good journal and I'm proud to be published in it), and I was able to smuggle in some exposition under the cover of a new research result.

  2. I have an expository paper on factorization in integral domains:

http://alpha.math.uga.edu/~pete/factorization.pdf

[Added: And a newer version: http://alpha.math.uga.edu/~pete/factorization2010.pdf. ]

It is not finished and not completely polished, but it has been circulating around the internet for about a year now. Again, this completely expository paper has attracted more attention than most of my research papers. Sometimes people talk about it as though it were a preprint or an actual paper, but it isn't: I do not know of any journal that would publish a 30 page paper giving an intermediate-level exposition of the theory of factorization in integral domains. Is there such a journal?

Added: In my factorization paper, I build on similar expositions by the leading algebraists P. Samuel and P.M. Cohn. I think these two papers, published in 1968 and 1973, are both excellent examples of the sort of "intermediate exposition" I have in mind (closer to the high end of the range, but still intermediate: one of the main results Samuel discusses, Nagata's Theorem, was published in 1957 so was not exactly hot off the presses when Samuel wrote his article). Both articles were published by the American Mathematical Monthly! I don't think the Monthly would publish either of them nowadays.

Added: I have recently submitted a paper to the Monthly:

http://alpha.math.uga.edu/~pete/coveringnumbersv2.pdf

(By another coincidence, this paper is a mildly souped up answer to MO question #26. But I did the "research" on this paper in the lonely pre-MO days of 2008.)

Looking at this paper helps me to see that the line between research and exposition can be blurry. I think it is primarily an expository paper -- in that the emphasis is on the presentation of the results rather than the results themselves -- but I didn't have the guts to submit it anywhere without claiming some small research novelty: "The computation of the irredundant linear covering number appears to be new." I'll let you know what happens to it.

(Added: it was accepted by the Monthly.)

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    $\begingroup$ Me too. I have to admit I am actually more interested in doing expository work in the future than research work, so I would really like to know where to get started. $\endgroup$
    – Qiaochu Yuan
    Commented Feb 15, 2010 at 22:03
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    $\begingroup$ +1. I am also interested in doing some sort of expository work. $\endgroup$
    – Akhil Mathew
    Commented Feb 15, 2010 at 22:32
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    $\begingroup$ @Pete: You're right. A refereed expository journal article is definitely worth more than a posting on a wiki for, say, a tenure dossier. (It's off-topic, but I can't help but add that in a research-oriented department neither carries much weight at all. I would advise any tenure-track person in a research math department to avoid devoting much effort to expository articles. Writing too many expository articles can actually harm your case, because it looks like you're diverting too much energy away from your research.) $\endgroup$
    – Deane Yang
    Commented Feb 16, 2010 at 18:44
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    $\begingroup$ Some Famous Person (was it Gian-Carlo Rota?) said you're remembered more for your expository work than for your research. $\endgroup$
    – Michael Hardy
    Commented Nov 10, 2010 at 18:40
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    $\begingroup$ In his introduction to Stanley's Enumerative Combinatorics II, Rota said, "The mathematical community professes a snobbish distaste for expository writing, but the facts are at variance with the words. In actual reality, the names of authors of a handful of successful textbooks written in this century are included in the list of most celebrated mathematicians of our time". Hardy (who took exposisiton quiote seriously) had written in his apology "Exposition, criticism, appreciation, is work for second-rate minds." $\endgroup$
    – Amritanshu Prasad
    Commented Mar 10, 2011 at 4:09

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I'm not too familiar with Expositiones Mathematicae, but have you given them a look?

EDIT: The article I happened to have seen, which made me think that Expo Math might be along the lines Pete Clark was looking for, is this paper of T. Bühler - it modestly claims to no originality save for assembling disparate parts of the literature and writing down what's old news to connoisseurs (I'm paraphrasing here!) but of course this is, in a sense, precisely its originality & worth.

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    $\begingroup$ Hmm, looks quite nice, but if only it weren't Elsevier. $\endgroup$
    – Tom Leinster
    Commented Feb 15, 2010 at 21:49
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    $\begingroup$ ...From their website: "Our aim is to publish papers of interest to a wide mathematical audience, such as expository articles that make research results more widely accessible, and papers on topics with fairly broad appeal. Main articles must be written in such a way that a research student interested in the topic of the paper can read them profitably. Mathematical notes can be at a slightly higher level. Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication." $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 21:53
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    $\begingroup$ (It is the "such as" which is worrisome to me.) $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 22:12
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    $\begingroup$ Thank you for mentioning this journal -- I went to their website and immediately found two very interesting papers. That never happened to me before. $\endgroup$
    – Ilya Grigoriev
    Commented Mar 14, 2010 at 4:56
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    $\begingroup$ The main problem with Expo. Math., as I see it, is that nobody knows about it. I've written two expository articles that I consider to be quite good (A beginner's guide to forcing, You could have invented spectral sequences), and I avoided Expo. Math. because I figured that nobody would ever see my work if I published it there. I think what's needed is for some bigshot to throw his or her weight behind a journal of expository work, either Expo. Math. or a brand-new journal. I've chatted informally with Gowers about this but at the time he had too many other commitments. $\endgroup$
    – Timothy Chow
    Commented May 31, 2010 at 16:48
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I too have thought that there should be such a journal, and found that Expositiones Mathematicae somehow doesn't stop me thinking that.

I think that if one were founding a new expository journal, then a very important feature that it should have would be that getting an article into the journal should be prestigious. And for that it should be difficult to do.

What makes it difficult to write an expository article? One obvious thing is if the mathematics you are writing about is very hard to understand. Sometimes, writing a good clear expository article involves digging deep into the thought processes of another mathematician who has not taken the trouble to say what they were, or of finding a clever way of presenting something that makes it much clearer where the ideas came from. Writing an expository article of this kind is pretty similar to research, in that it involves solving difficult problems. And one could argue that the value to other mathematicians of a good expository article is usually greater than the value of a good research article. (Perhaps I ought to change that "usually" to "often".)

Other features of a journal that I think would make good sense are that it should be online and open access (with plenty of links to other internet resources such as blogs and wikis), and that writing about one's own work should be forbidden. Also, referees should not necessarily be experts in the area being written about, and should be encouraged to be completely honest if there are parts of the article they do not understand.

The advantage of an online journal is that with no pressure to produce issues on a regular basis one could keep the standard of acceptance very high. Perhaps one could even make it so high that the appearance of a new article would be something of an event. But the main thing is that it should be a significant contribution to a CV, or else the motivation for writing such an article would not be high enough.

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    $\begingroup$ Another push for an online journal is that it eliminates the pressure to shorten articles at the expense of readability. $\endgroup$
    – Kevin O'Bryant
    Commented Feb 2, 2011 at 15:11
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    $\begingroup$ Historically, there are cases when the original article is difficult to read and a later article explains the work more clearly, often adding an epsilon of progress (in order to be published?). As a result, the latter paper is read (and cited?) more often than the original. $\endgroup$
    – user2529
    Commented Jan 5, 2014 at 14:45
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These journals say that they publish expository and/or survey papers...

Bulletin of the London Mathematical Society
DOCUMENTA MATHEMATICA
Global Journal of Pure and Applied Mathematics
International Journal of Modern Mathematics
INTERNATIONAL MATHEMATICAL FORUM
Journal of Analysis and Applications
Journal of Interdisciplinary Mathematics
Lobachevskii Journal of Mathematics
Logic and Analysis
Journal of Mathematical Sciences: Advances and Applications
Surveys in Mathematics and its Applications

Another possibility: Lecture Notes in Mathematics (Springer) or similar. But only for longer expository pieces: Lecture Notes has a minimum of 100 pages.

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    $\begingroup$ The Bulletin of the London Mathematical Society claims at lms.ac.uk/publications/blms to publish surveys. I have been an editorial advisor for this journal for over 4 years and haven't seen a single survey submitted to it through me though. $\endgroup$
    – Kevin Buzzard
    Commented Feb 21, 2010 at 22:41
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    $\begingroup$ The current (as of January 2016) editors of BLMS are quite interested in publishing more surveys, and the journal has published three survey articles in 2015. I have therefore added BLMS to the list above - I hope nobody minds. $\endgroup$
    – Arend Bayer
    Commented Jan 26, 2016 at 19:26
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On placing the expository paper "Transseries for Beginners"
(too long for a comment)

Transseries arise when we complete things in a certain way by including formal series, exponentials, and logarithms. But they have come up in non-trivial ways in many parts of mathematics: real analysis, model theory, computer algebra, dynamical systems, surreal numbers. So it seemed that an exposition NOT using the special knowledge or jargon of one area but accessible to all would be good. That is what this paper tries to be.

I tried at first to place it in a general-mathematics journal. Starting with the Monthly. But did not succeed. So in fact it will appear in the Real Analysis Exchange. (One of the three types of papers they publish are "survey" papers.) And interested people in other areas (who don't regularly scan the contents of that journal) will have to find out about it somehow.

For the Monthly: The paper was 30 pages then, but still on the borderline of being too long and on the borderline of being too technical. Journals I tried averaged 8 months to reach a decision. In all, from first submission (August 1, 2007) to acceptance (January 31, 2010) was exactly two and a half years.

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    $\begingroup$ Thank you for sharing this, Gerald. It's a somewhat sobering story. (For those who don't know: Prof. Edgar is a famous expositor of mathematics: he has written or edited five books, including "Measure, Topology and Fractal Geometry", which I read and enjoyed towards the beginning of my undergraduate career.) Of course your post here will at least somewhat improve the problem, since it will inspire some MOers to read your paper on transseries. (I will!) $\endgroup$
    – Pete L. Clark
    Commented Feb 17, 2010 at 16:43
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From their website:

"Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles."

A search in Math Reviews shows many articles in RMJM described as expository, either by the authors or by the reviewer. Often there is disagreement as to whether a paper is expository, which indicates the utility of having a journal that publishes both research and expository articles.

I am on the board of the Rocky Mountain Mathematics Consortium.

I have found it nearly impossible to write an expository paper that stays that expository. New results have a way of being found by authors who are trying to clean up proofs of existing results.

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The AMS Bulletin publishes very high quality expository papers.

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    $\begingroup$ Yes, I referred to this above. To me, this is sort of like pointing out that the New Yorker publishes excellent short stories, so the market for fiction can't be so bad. $\endgroup$
    – Pete L. Clark
    Commented Feb 16, 2010 at 8:02
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The Electronic Journal of Combinatorics have these "Dynamic Surveys" which are allowed to be updated -- some of which are quite massive.

EDIT: It has been pointed out to me that there is another category, called "articles", in the Electronic Journal of Combinatorics which include non-dynamic surveys and exposition papers. At the moment, there are not many such articles, but there are some (I counted 14 in total).

Research articles as well as surveys and articles of more general interest are welcome.

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    $\begingroup$ @DSS: +1. That's very close to what I'm asking for. Now why are the combinatorialists so enlightened about this? $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 23:17
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    $\begingroup$ I don't really think of the dynamic surveys at EJC to be the kind of expository paper you're talking about, though---while all (most?) surveys are expository, not all expository articles are surveys. (And some of those surveys hardly count as articles: 219 pages (the survey on Graph Labelling) is a lot!) $\endgroup$
    – Leah Wrenn Berman
    Commented Mar 12, 2010 at 4:56
  • $\begingroup$ @LWB: I agree that what EJC publishes is not the most general kind of expository paper, but I think that it is at least an example of the type of thing I had in mind. $\endgroup$
    – Pete L. Clark
    Commented Mar 13, 2010 at 23:55
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L'enseignement mathématique: http://www.unige.ch/math/EnsMath/

For longer papers: Ensaios Matemáticos.

Disclaimer/shameless plug: I was an editor of the latter.

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  • $\begingroup$ @FV: I'm not quite buying that L'Enseignement is an expository journal. See my #2) above. Can you point to some purely expository papers that EM has published? $\endgroup$
    – Pete L. Clark
    Commented Feb 16, 2010 at 8:05
  • $\begingroup$ @Pete Sorry, I missed the reference to L'Enseignement Math. in the body of your question. You might be right about it. I recall seeing new proofs of old results but perhaps not something that is purely expository. (BTW EM, in the context of my answer, is ambiguous) $\endgroup$
    – Felipe Voloch
    Commented Feb 16, 2010 at 13:42
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    $\begingroup$ (@FV: Good point: I meant L'Enseignement both times. I am more than willing to believe you about Ensaios.) $\endgroup$
    – Pete L. Clark
    Commented Feb 16, 2010 at 14:06
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    $\begingroup$ FYI, I have a paper in L'Enseignement that (at least to "experts") is fairly expository (for sufficiently contrived meaning of the word "experts"). IMO although it's largely expository, I think this material is not very well known in the low-dimensional topology world and that's likely what it was accepted for publication. There's bits and pieces scattered all over the literature, but to anyone who needs to know something specific the literature appeared to be a maze. $\endgroup$
    – Ryan Budney
    Commented Mar 16, 2010 at 3:47
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    $\begingroup$ L'Enseignement publishes expository monographs; see unige.ch/math/EnsMath/EM_en/welcome.html and click on "Monographs". $\endgroup$
    – Richard Stanley
    Commented Oct 26, 2013 at 1:49
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It may seem to you like the market for expository papers has narrowed, but I think it has increased tenfold. Personal blogs appear to be the medium of choice for exposition these days. I am sure you are aware of this (in part because many high-profile Mathoverflow users have popular blogs), but I just wanted to remind you that blogs can reach a wide and interested audience. Perhaps not everything belongs in a journal.

EDIT (Douglas S. Stones): Adding to the "alternative to journals" answer -- authors could consider writing a book instead.

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    $\begingroup$ PS. Depending on the content, the Tricki may also be an appropriate medium. $\endgroup$
    – aorq
    Commented Feb 15, 2010 at 22:27
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    $\begingroup$ I don't agree that blogs are the new journals. I would need to write an entire response to explain this, but briefly: blogs are neither refereed nor reviewed. The blog format imposes length requirements and discourages repeated, substantial revision. Blog-writing receives no academic credit. And so forth. $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 22:41
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    $\begingroup$ Not that mathblogs are a bad thing: they are a very positive recent addition to the mathematical community. But I feel strongly that they are not the answer to my question. $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 22:49
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    $\begingroup$ Here's why blogs and wikis are great for expository writing: Even if you publish an expository article in a refereed journal (like BAMS), you don't gain much professional status from it. So most people are not likely to devote much time and effort to writing such articles. Blogs and wikis allow people to write and disseminate expository articles and thoughts with a minimum of effort and fuss, making it much more likely that they will actually do it. Even Math Overflow gives me a nice outlet for expository thoughts that I would never publish formally. $\endgroup$
    – Deane Yang
    Commented Feb 16, 2010 at 18:50
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There is a new journal of the European Mathematical Society that seems perfect for these articles: EMS Surveys in Mathematical Sciences. The description at the link reads:

The EMS Surveys in Mathematical Sciences is dedicated to publishing authoritative surveys and high-level expositions in all areas of mathematical sciences. It is a peer-reviewed periodical which communicates advances of mathematical knowledge to give rise to greater progress and cross-fertilization of ideas. Surveys should be written in a style accessible to a broad audience, and might include ideas on conceivable applications or conceptual problems posed by the contents of the survey.

I am actually quite excited about this, as there are some notes I've been sitting on trying to find an appropriate place for them. This may be the solution.

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    $\begingroup$ This journal is not open access. $\endgroup$
    – Dmitri Zaitsev
    Commented Nov 7, 2017 at 0:04
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In probability, there's Probability Surveys. From their web site:

Probability Surveys publishes survey articles in theoretical and applied probability. The style of articles may range from reviews of recent research to graduate textbook exposition. Articles may be broad or narrow in scope. The essential requirements are a well specified topic and target audience, together with clear exposition.
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This used to be a post about the Central European Journal of Mathematics which has changed quite a bit since the writing of the original post.

I no longer endorse that journal.

The true successor of the original spirit is the European Journal of Mathematics, whose Editorial Board is essentially what used to be the CEJM editorial board which resigned in its entirety as a group in protest of the publisher's actions with regard to the journal.

Here is some more explanation in response to the comments:

Keith and Darij: Perhaps calling the journal evil was too much, I meant that for the publisher. Here is what happened. De Gruyter acquired the journal a few years ago and immediately decided to change its philosophy. They call it "open access", which means that you can access the published articles free of charge, but in order to publish an article you have to pay €1000 (see https://www.degruyter.com/view/supplement/s23915455_Article_Processing_Charges.pdf). At the time of enacting this policy they even decided to charge those authors whose paper had already been accepted, but had not yet appeared in print. The Editorial Board protested this action, but De Gruyter ignored us. In addition, it seemed that the emphasis was on charging the authors not on the quality of the publication. I cannot speak for the current Editorial Board, but back then we felt that the publisher's model would potentially lead to a journal where people can simply pay to get published which would naturally lower the quality of the publication. The fact that the publisher decided to charge those whose articles had been accepted within the free-to-publish model was a bad sign and did not reflect well for the resolution of potential future issues. I do not claim anything about the current state of the journal, I simply wanted to withdraw my endorsement.

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  • $\begingroup$ This is currently known as Open Mathematics, but is it (still) expository? The titles at least don't suggest so. $\endgroup$
    – darij grinberg
    Commented Feb 14, 2019 at 19:58
  • $\begingroup$ Uh, this post is now totally outdated. I'll update it.... $\endgroup$
    – Sándor Kovács
    Commented Feb 14, 2019 at 20:49
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    $\begingroup$ What does "gone evil" mean? $\endgroup$
    – KConrad
    Commented Feb 14, 2019 at 21:15
  • $\begingroup$ I am not getting it either. Open Mathematics, at least, is OA, which the other journal is not. $\endgroup$
    – darij grinberg
    Commented Feb 14, 2019 at 21:58
  • $\begingroup$ @KConrad: I edited my answer as a response to that... $\endgroup$
    – Sándor Kovács
    Commented Feb 16, 2019 at 2:30
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In fact, many journals give this option, but very few people use it. For example, Discrete Mathematics has something they call "perspectives paper" which is basically high quality survey paper on a novel topic or a novel technique: http://tinyurl.com/yh9swnn My understanding is that these perspectives paper undergo the usual refereeing process.

P.S. Full disclosure - I am an editor of DM.

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    $\begingroup$ My (purely anecdotal) understanding is that in fact journals which primarily publish original research typically apply much higher quality standards in refereeing such survey papers. $\endgroup$
    – Mark Meckes
    Commented Feb 16, 2010 at 19:02
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Apparently the Japanese Journal of Mathematics is focused on survey/exposition papers:

The official journal of the Mathematical Society of Japan, the Japanese Journal of Mathematics is devoted to authoritative research survey articles that will promote future progress in mathematics. It encourages advanced and clear expositions, giving new insights on topics of current interest from broad perspectives and/or reviewing all major developments in an important area over many years.

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You can certainly find such journals if you are not too career-minded. Although there are not many examples in recent issues, Rendiconti Torino has open access and a tradition of publishing occasional expository articles, though typically less than 30 pages. It will effectively referee such papers provided that they appear to have a novel approach (as is the case of yours) thta cannot be found elsewhere. Publishing in such a journal may be more satisfying than simply leaving a paper on a homepage or the arXiv (which you can still do anyway). [I am its director, but it's a non-profit concern and I feel that such publicity is in the community's interest.]

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    $\begingroup$ Since there are essentially infinitely many journals which publish research papers and not expository papers, it would be nice to find at least one journal which publishes entirely expository papers (otherwise expository papers "compete" in some sense with the research papers, which is not a good situation when research is valued much more than exposition). $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 22:28
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The Moscow Journal of Math says they publish "research-expository articles."

"An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists."

I'm not sure exactly how that plays out in practice, I haven't submitted any articles there. But it looks like it's worth a try for certain sorts of articles with significant expository content.

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    $\begingroup$ A paper which contains "important new results" is not what I would call an expository paper. My reading of this passage is that they want to be a serious research journal in which they allow/encourage authors to take time and space to motivate and explain what they are doing. That sounds great (and indeed I have seen some very fine papers published there), but it's not an expository journal. $\endgroup$
    – Pete L. Clark
    Commented Mar 13, 2010 at 23:42
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Just in case, as it seems that nobody has already mentioned this above: Russian Mathematical Surveys (the English translation of Uspekhi Matematichekikh Nauk) also publish quite a number of high-quality survey papers which usually occupy most of the issue but these papers are almost always written by Russian authors (and, I guess, at least some of them are just solicited by the Editorial Board).

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  • $\begingroup$ Notice is is not an American journal,mathphysicist. Other,civilized countries value education far more then ours. $\endgroup$
    – The Mathemagician
    Commented Apr 18, 2010 at 21:27
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    $\begingroup$ Andrew, I don't quite see which point you are trying to make. Could you make yourself (more) clear? $\endgroup$
    – mathphysicist
    Commented Apr 19, 2010 at 1:30
  • $\begingroup$ I'm saying that the lack of expository articles for relative beginners in mathematics is due to a larger problem of the percieved unimportance of educational value for such articles.This is why not only is the art of writing such articles dying out,it's being encouraged to do so very strongly. $\endgroup$
    – The Mathemagician
    Commented Apr 21, 2010 at 7:53
  • $\begingroup$ @Andrew L: I would tend to disagree with you. It is certainly true that there are fewer journals that publish expository/survey work, but this is natural, as the volume of such work coming from research mathematicians is much lower than the volume of research articles (as to why this is - that's a different story; but I wouldn't infer from this a poor state of higher education in the US). $\endgroup$
    – user39719
    Commented Mar 30, 2013 at 0:07
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There's an online Mexican journal Morfismos that seems to specialize mainly in surveys. It seems to be a small-ish operation, but they've published expository papers by well-known authors such as Snaith, Landweber, Kontsevich, and Kervaire. Unfortunately they are not listed on Math Reviews yet, but I understand this may be in their future.

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    $\begingroup$ From editorial guidelines: "MORFISMOS is the journal of the students of the Mathematics Department of CINVESTAV... Publication of papers is not restricted to students of CINVESTAV... Mathematics research reports or summaries of bachelor, master and Ph.D. theses will be considered for publication, as well as invited contributed papers by researchers. Papers submitted should be original, either in the results or in the methods." 3 of the 4 big names you mention had their articles published in the last few years, I think, so perhaps their focus has shifted from the original mission statement $\endgroup$
    – Yemon Choi
    Commented Jul 9, 2010 at 3:23
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I just wanted to comment on Pete's answer to Felipe Voloch but it seems I can't so I'll write an answer instead. I think that L'Enseignement Mathématique does publish purely expository papers. I have two examples in mind (hope I'm not mistaken):

  • L. Illusie "Catégories dérivées et dualité: travaux de J.-L. Verdier" Enseign. Math. (2) 36 (1990), no. 3-4, 369--391
  • J. Nicaise "Formal and rigid geometry: an intuitive introduction and some applications." Enseign. Math. (2) 54 (2008), no. 3-4, 213--249
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  • $\begingroup$ @JP: OK, I take your point. I am even slightly familiar with the second paper: it is a good example of "intermediate exposition" of the sort I was describing above. Are we agreed, though, that it is not a journal devoted entirely to expository papers? Or even primarily? $\endgroup$
    – Pete L. Clark
    Commented Feb 18, 2010 at 8:10
  • $\begingroup$ @Pete: Sure. I don't think that L'Enseignement Mathématique publishes primarily expository papers. I'm just saying they sometimes do (and answering your question to Felipe Voloch I guess). $\endgroup$
    – Jérôme Poineau
    Commented Feb 18, 2010 at 9:28
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I just came across the following new publication. SpringerBriefs in Mathematics. (Somewhere between a paper and a book; 50-125.) I think It is not what was originally asked for, but might be close to some things that came up in the discussion.

Since it is new, and I only know what is written on the webpage, the relevance of this to the subject at hand is not yet completely clear to me. Still, I hope it is close enough to be on-topic. [Some of the text below is the same for all Briefs in different fields, which might explain some possibly surprising formulations.]

From https://www.springer.com/series/10030

Excerpts from the page.

SpringerBriefs present concise summaries of cutting-edge research and practical applications across a wide spectrum of fields. Featuring compact volumes of 50 to 125 pages, the series covers a range of content from professional to academic. [...]

Typical topics might include:

.) A timely report of state-of-the art techniques .) A bridge between new research results, as published in journal articles, and a contextual literature review .) A snapshot of a hot or emerging topic .) An in-depth case study .) A presentation of core concepts that students must understand in order to make independent contributions

SpringerBriefs in Mathematics showcase expositions in all areas of mathematics and applied mathematics. Manuscripts presenting new results or a single new result in a classical field, new field, or an emerging topic, applications, or bridges between new results and already published works, are encouraged. The series is intended for mathematicians, applied mathematicians.

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  • $\begingroup$ @unknown: I hadn't heard of this either. Thanks for bringing it up. $\endgroup$
    – Pete L. Clark
    Commented Mar 25, 2011 at 17:14
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The Journal of Commutative Algebra publishes expository/survey papers. Your article on factorization might be appropriate, though I have not looked at it. Disclosure: I am an editor for JCA.

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The front page of the Notices (Jan 2011) is an advertisement for the "Bulletin of Mathematical Sciences". The "Aims and Scope" are:

The Bulletin of Mathematical Sciences, a peer-reviewed free access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (about 10 pages) containing significant results of wider interest. Most of the expository articles will be invited.

One of the executive editors is Efim Zelmanov, so that certainly counts as a "big-shot" getting behind the effort.

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    $\begingroup$ "Most of the expository articles will be invited"? Does it mean a higher bar for people not related to the editorial board than for people who are? $\endgroup$
    – Dmitri Zaitsev
    Commented Nov 7, 2017 at 10:34
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[Obsolete, see comments below.]

I have published a few expository pieces in The Australian Mathematical Society Gazette in recent years.

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  • $\begingroup$ Would you care to tell us who you are, so we might look these up? $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 23:18
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    $\begingroup$ @fpqc, Leonid: I believe it's considered bad netiquette to try to guess the identities of pseudonymous users. (I made this mistake here once.) I do think it's also a little silly to be pseudonymous and make statements about your own work, but that's up to the user. $\endgroup$
    – Pete L. Clark
    Commented Feb 15, 2010 at 23:39
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    $\begingroup$ I think what's particularly bad netiquette is to post their names online as a guess. For example, several pseudonymous posters here have links to their homepages from their userpages. So figuring out who they are is certainly fine. But the reason they're pseudonymous is to control what comes up when you google their name. Hence what's bad netiquette is to actually type out their full name online. $\endgroup$
    – Noah Snyder
    Commented Feb 16, 2010 at 1:18
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    $\begingroup$ Yes, I'm Gerry Myerson. The papers were, Irrationality via well-ordering, 35 (2008) 121-125; Trifectas in geometric progression, 35 (2008) 189-194; and Crime investigation: an introduction to error-correcting codes, 36 (2009) 119-126. $\endgroup$
    – Gerry Myerson
    Commented Feb 16, 2010 at 3:10
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    $\begingroup$ I really enjoyed the 'Irrationality via well-ordering' paper. However, on the Gazette web site the following message can be found: "Please note that following the AustMS Council meeting in September 2009, the Gazette will no longer accept technical, peer reviewed papers. Technical papers submitted before October 2009 will be processed as usual and undergo peer review". So, it seems that it is no longer possible to use the Australian Mathematical Society Gazette as a venue to publish such articles. Why this is so, I do not know. $\endgroup$
    – Philip Brooker
    Commented Feb 16, 2010 at 5:28
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Dear Prof Clark,

I had a good experience a few years ago with Expositiones Mathematicae (an article on bump functions), and it seems that a fair number of colleagues happened upon it - so it is not obscure. This may be a good venue for you. I quite enjoy expository work, and lament the fact that many departments (and granting agencies) do not value them highly. Good Luck.

R. Fry

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A new journal which could be better known and which publishes expository work is The Graduate Journal of Mathematics.

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  • $\begingroup$ Very nice to know it, personally. $\endgroup$
    – Fei Cao
    Commented Apr 21, 2021 at 6:43
  • $\begingroup$ There haven't been any issues in 2024. Hopefully it is not defunct. $\endgroup$
    – Cameron Williams
    Commented Jun 22 at 6:49
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As it has not been cited before, there is also a recent journal devoted exactly to what you suggest, Confluentes Mathematici (originally published by World Scientific, but now OA).

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And here is another journal that publishes long papers of "utility for a broad readership of specialists in the domain": Dissertationes Mathematicae. Apparently they quite often publish entire Ph.D. theses.

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  • $\begingroup$ I get the impression Dissertationes is not meant for expository work per se. "Utility for a broad readership" just means that one is allowed a more leisurely style, I think. $\endgroup$
    – Yemon Choi
    Commented Mar 16, 2010 at 1:33
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    $\begingroup$ For instance, the paper journals.impan.gov.pl/dm/PDF/dm457-0-00.pdf is a survey. So they do publish review papers but apparently indeed not too often :( $\endgroup$
    – mathphysicist
    Commented Mar 16, 2010 at 1:47
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I want to second Deane's comment on the usefulness of blogs (wikis). We can TeX, meanwhile, anywhere, anyhow. There could be a very fruitful symbiosis between blog and journal. The blog symbiont is the garden where expositions grow, perhaps fertilized if not seeded by commenters. Each symbiont consists of two poles: medium vs. reader. The journal symbiont faces the problem that its reader can not always write in it (or the marginals get closed away in one library somewhere). So, blogs (wikis) can also serve the marginals, something the medieval libraries knew to value.

This might hint at a new internet gadget. Which reminds me of another gadget: The user-sorted printout shelves, to be set up in and moderated by the library.

...Ooh, could amount to an extremely worthwhile internets programming project, including organizing real paper work, sort, and storage.

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You could even try "Mathematics Student" published by the Indian Mathematical Society or "RMS Newsletter" published by Ramanujan Mathematics Society.

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I am quite (quite, indeed) late on this one. A "good" journal which has probably gone unnoticed (didn't see any references in the answers provided) is the Milan Journal of Mathematics. Aims and scope:

Milan Journal of Mathematics (MJM) publishes high quality articles from all areas of Mathematics and the Mathematical Sciences. The authors are invited to submit "articles with background", presenting a problem of current research with its history and its developments, the current state and possible future directions. The presentation should render the article of interest to a wider audience than just specialists.

I remembered seeing an expository article of Heineken on complete groups published in its predecessor, Rendiconti del Seminario Matemàtico e Fisico di Milano. That is quite old though and I haven't recently perused Milan's contents to know if it indeed does what it claims.

I guess Astérisque falls into category ii).

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