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This is a question specific to mathematics.

• what is the status of the journal Proceedings of the American Mathematical Society (Proc. AMS)?

It seems to be a generalist journal that only publishes short papers, and has a massive output (in 2018: 12 issues on 5485 pages). The blurb says :

"To be published in the Proceedings, a paper must be correct, new, and
significant. Further, it must be well written and of interest to a
substantial number of mathematicians. Piecemeal results, such as an
inconclusive step toward an unproved major theorem or a minor
variation on a known result, are in general not acceptable for
publication".

Yet on Scimago it is ranked below most of the journals I have heard about (in their math/stats ranking it is #256, edit: in the subranking that lists mostly pure math journals, it is still lower than most I know edit ends). Nevertheless, I see that very well established researchers sometimes publish there (I won't give names obviously).

So to be more specific :

• do you always submit somewhere else first, and it the paper is rejected then consider Proc. AMS ?


• or maybe is publishing there an act of "giving back to the community by promoting the AMS" ?


• or is it mostly a journal for anybody who needs a quick publication (as the workflow seems quite fast) ?

do you always submit somewhere else first, and it the paper is rejected then consider Proc. AMS ?

I've never submitted to the journal. In general, it is true that in many respects the best math journals are the generalist journals, but if a paper was rejected for not being interesting enough, I'd likely be substantially more inclined to resubmit it to a more specialist journal, and not to a generalist journal like the Proc. AMS. That said, if one is building up a standard career, it is important to build up a CV that has at least some papers which are in journals which are generalist journals, so people don't feel like your work is so specialized that anyone outside one's own area won't be able to interact with you. This is important for hiring decisions for post-docs, VAPs and tenure-track positions.

or maybe is publishing there an act of "giving back to the community by promoting the AMS" ?

I don't know of anyone who publishes with the AMS to deliberately give back to them. Unless one is already tenured, having that sort of desire to give back influence where one publishes would be odd. There are a bunch of other ways mathematicians give back to the AMS, such as by writing reviews for MathSciNet, which is run by the AMS.

or is it mostly a journal for anybody who needs a quick publication (as the workflow seems quite fast) ?

In general in math, one rarely needs quick publication since one can put things up on the arXiv and math is very fond of preprints. There is a difference between a preprint that's been submitted to a journal and an accepted paper, and if one is at a particularly bureaucratic school, such a thing might even be a relevant distinction for tenure if one is borderline, but that would itself be weird. While issues with long publication time can be a problem (I have one personal horror story involving it), it is very rare to target a journal based on their review/publication time. I'm also not sure what makes you conclude that the workflow is quick. What gives you that impression?

Scimago is a clearly false, possibly semi-fake ranking. It is very easy to check this: for instance when I clicked on your link I got the following amusing result:

Vital and health statistics. Series 2, Data evaluation and methods research is considered of higher ranking for mathematicians (!) than the Annals of Mathematics.

There is no need to elaborate more.

Subjectively my impression is that Proceedings of the AMS is a very good journal for short papers. Having a paper there says two things: 1) The paper is short, and 2) For a short paper, it's a good paper. No one is going to mistake a Proceedings publication for one in the Annals, but no one is going to question whether it's good work.

As for the rankings, very short papers are rarely as substantial or influential as longer papers, so it's not really fair to compare a journal that only publishes short papers to a typical journal. It would be more fair to compare it only to the short papers in another journal, but this data is difficult to find. Nonetheless I expect that Proceedings would rank reasonably highly once you compare papers of similar length.

I tried an alternative measure that seems reasonable, but in the end the numbers are weird so I don't think it's a great measurement. But since I have the data here it is.

One could rate journals per page instead of per article. Eigenfactor gives a nice way to do this, since the un-normalized Eigenfactor is calculated at the level of all papers published in the journal. Their "article influence" is measured by dividing Eigenfactor by number of articles (and normalizing), so we can equally well calculate "page influence" by dividing 2010 Eigenfactor by 2010 number of pages published. Normalizing by multiplying by 10^6, this gives: JAMS 13.4, Acta Math. 8.6, Proc. AMS 7.1, Annals 5.9, Trans. AMS 4.9, J. Alg. 4.9, Adv. Math. 4.5. By that measurement Proc. AMS would be a very highly ranked journal! I think that naively just measuring per page unfairly advantages short papers relative to long ones so one shouldn't treat these numbers as too meaningful, but the numbers you were looking at unfairly penalize short papers, and the truth is somewhere in between.

Do you always submit somewhere else first, and if the paper is
rejected then consider Proc. AMS ?

What kind of journal selection algorithm is this? Surely at some point you're going to want to take into account the strength of your paper, right?

Speaking only for myself, I've had papers that I thought weren't strong enough to publish in PAMS and which I submitted to more specialized journals, have had papers which I felt were strong enough to be published in significantly more selective journals, and have had a paper published in PAMS. When I decided to submit the latter paper to PAMS, I did so because I thought the paper was of broad appeal (thus meriting publication in a generalist journal) and because there was an editor at the journal that I thought would like the paper and know of some good potential referees.

or maybe is publishing there an act of "giving back to the community
by promoting the AMS" ?

My own opinion of the AMS journals is that PAMS is a very good journal, TAMS is excellent and JAMS is one of the top two or three journals in all of pure math. In general people publish in the AMS journals because they're great journals. The only sense in which you might be correct would be if someone were to choose to publish in an AMS journal over a similarly ranked journal published by a giant company like Elsevier or Springer. This seems quite plausible.

or is it mostly a journal for anybody who needs a quick publication
(as the workflow seems quite fast) ?

I've only published one paper in PAMS, and I found the journal neither especially fast nor especially slow. It was about average, I would say. (I think I received a referee's report after approximately six months.)