The Journal of Number Theory has been (for some time) the standard “specialist” journal for number theory papers. By that, I mean it was a home for reasonably good number theory papers which were not (necessarily) good enough for some of the top general journals. Of course, like every journal, there are better and worse papers. At least several papers in this journal have been referenced on this blog at some point, including those discussed here and here.

However, a number of recent changes have been taken place. JNT has introduced “JNT Prime” which seeks to publish

a small number of exceptional papers of high quality (at the level of Compositio or Duke).

(I’m not sure if free two-day delivery is also included in this package.) My question is: why bother?

I have several points of confusion.

**It’s easier to start from scratch**. It is much easier (as far as developing a reputation goes) to start a new journal and set the standards from the beginning, than to steer a massive oil tanker like the Journal of Number Theory with its own firmly established brand. Consider the Journal of the Institute of Mathematics of Jussieu. This early paper (maybe in the very first issue) by Richard Taylor set the tone early on that this was a serious journal. Similarly, Algebra & Number Theory in a very few number of years became a reasonably prestigious journal and certainly more prestigious than the Journal of Number theory has ever been during my career.**The previous standards of JNT served the community well**. Not every journal can be the Annals. Not every journal can be “better than all but the best one or two journals” either, although it is pretty much a running joke at this point that every referee request nowadays comes with such a description. There is plenty of interesting research in number theory that deserves to be published in a strong reputable journal but which is better suited to a specialist journal rather than Inventiones. Journal of Number Theory: it does what it says on the tin. Before the boutique A&NT came along, it was arguably the most prestigious specialist journal in the area. It is true that it was*less*prestigious than some specialist journals in other fields, but that reflects the reality that number theory papers make up a regular proportion of papers in almost all of the top journals, which is not true of all fields. So where do those papers go if JNT becomes all fancy?**Elsevier**. Changing the Journal of Number Theory is going to take a lot of work, and that work is going to be done (more or less) by mathematicians. So why bother making all that effort on behalf of Elsevier? Yes, Elsevier continues to “make an effort” with respect to Journal of Number Theory, including, apparently, even sponsoring a conference. But (to put it mildly) Elsevier is not a charity, and nobody should expect them to start behaving like one.

So I guess my question is: who is better off if the Journal of Number Theory becomes (or heads in the direction of becoming) a “top-tier journal” besides (possibly) Elsevier?

Do you have any thoughts about another new JNT policy described in that PDF you linked to, which is “The new JNT does not automatically referee such papers. For papers 20 pages or less JNT charges $200 a page or $2000 (whichever amount is smaller) to hire a referee, and for papers 20 pages or more JNT charges $100 per page. If no mistakes are found, the money will be refunded and the article published in JNT.”

Nevermind — it occurs to me that the charge is probably only for “crank papers”, not for reputable submissions.

One advantage to the JNT Prime strategy over starting from scratch is that from the very first issue everyone will agree that having a paper published in JNT Prime is at least as prestigious as having it published in JNT, which would not be the case for a new journal, no matter what its aims, editorial board, etc. In particular, young mathematicians can more safely publish in JNT Prime than a brand new journal, though admittedly said person would be better off still with publishing in Compositio or Duke if the paper is really at that level…

In any such situation, the author has to account for a certain amount of variance concerning what the eventual level of the journal will turn out to be. So why the anchoring with JNT might lower the variance, it also might lower the mean, which doesn’t seem like a good compromise.

I confess to not being able to track down this information on the JNT website, but I can envision at least one way of functioning in which this could be a useful thing: if papers submitted were automatically considered for both JNT Prime and JNT, then this could be an excellent service for early career mathematicians, who often have to balance the benefits of “aiming high” and getting published in a timely fashion. It could also eliminate some redundancy in the refereeing process; if I’m reviewing for a paper for Duke and I want to say “solid paper, not at the level of Duke, but just right for JNT,” then it sure would save everyone a lot of time if JNT didn’t need to go out and get another report!

Interesting theory. I have the sense that most papers which get rejected don’t have anything close to a referee report, so while your paper may come back rejected after 9 months at Duke, it’s not as if anyone has carefully gone through the paper to reach that conclusion (a systemic refereeing issue for another day). And in the rare cases in which a substantial report is produced and a paper is narrowly rejected, editors are usually happy to pass on the name of the referee to the next journal. If the model is instead “let’s highlight the best papers of the ones that are submitted” then you are also in danger of making the “non-prime” papers look worse.

I did have the sense at some point (maybe incorrectly) that Forum of math Pi/Sigma had a model something along these lines, namely that a paper which was submitted to Pi which was considered good but not good enough may be recommended for Sigma instead. I don’t know if this is true or not, or if it happens much. Or even when the opposite happens (something submitted to Sigma ends up in Pi). Does anyone know?

Occasionally for papers submitted for Forum of Math, Pi, the authors are asked if they would like the paper transferred to Sigma typically based on the initial opinions but sometimes after full reports. The other direction is possible and has been discussed but as far I know, this has not actually happened but if the reports were very strong, it is a possibility.

I agree that it is best if the authors decide where to submit rather than giving the journal the option.

Any faculty in the UC system might be worse off: https://www.theatlantic.com/science/archive/2019/03/uc-elsevier-publisher/583909/

At the risk of sounding inflammatory, I tend to be of the opinion that anything good for Elsevier is bad for mathematics.