The differences between AMS research journals
If a mathematician wants to submit a paper to an AMS journal is the decision process for which one really as simple as "If my paper isn't good enough for JAMS I'll check its length and ship it off to the appropriate one of the other 3?"
Yes, more or less. Journal of the AMS is a special case (as you observed) because of its extremely high level, and Memoirs of the AMS because it will consider incredibly long papers. In both cases, there are only a small number of competing journals with these properties. On the other hand, Transactions and Proceedings have substantially more competitors. The primary distinction between them is length, but from my perspective there's also a difference in prestige. Proceedings of the AMS gets some great submissions, but the length cut-off is pretty short for mathematics papers and this means it gets fewer great submissions than Transactions does, so the prestige level is a little lower. Other than length and prestige, they are pretty much identical, for example in topics covered (a broad spectrum of pure mathematics, but limited coverage of applied mathematics).
So for Proceedings/Transactions papers, there's a four step decision procedure:
Is your paper on an appropriate topic? (To a first approximation: is it pure mathematics?)
How long is your paper?
Do you have a realistic shot at acceptance?
Is the journal prestigious enough that you would be happy publishing your paper there?
This is not an answer, but it is too long for a comment. I am not going to compare the quality and scope of the AMS journals, but I would like to share an experience. Once an editor of PAMS told me that he receives about 100 papers every year and he can only accept about 10 papers each year, so he has to reject so many of (good) submissions. My estimation is more than half of the submitted papers (to PAMS) contain some interesting results and deserve publication in a respectful journal, but most of them will be rejected, just because there are better papers.
Regarding this point of view, I think one should submit a paper to an AMS journal only if he is sure that his paper is among the top 10% papers submitted to the journal. Otherwise, he is wasting his time.
There are so many other nice mathematical journals which provide authors with professional services and have way less traffic.
I found a paper Mathematical Journals by A.J. Hildebrand
- Journal of the American Mathematical Society is one of the elite journals
- Proceedings of the AMS and Transactions of the AMS are society journals come in pairs that have a single editorial board, and which complement each other in that one specializes in shorter articles, whereas the other publishes mainly longer articles
There are interesting descriptions for other math journals in that paper as well.
According to the Wiki page
Memoirs of the American Mathematical Society (ISSN 0065-9266) is a mathematical journal published in six volumes per year, totalling approximately 25 to 30 individually bound numbers, by the American Mathematical Society. It is intended to carry papers on new mathematical research between 80 and 200 pages in length. Usually, a bound number consists of a single paper, i.e., it is a monograph.