The process of publishing a paper is an extremely long one, and it is not atypical to take several years from the first submission to the paper finally being accepted. The one part of the process that happens extremely quickly, however, is the moment when the journal sends you the galley proofs of the paper and then gives you 48 hours to make any final minor corrections. Despite the journal having taken up to several years to referee the
paper, these messages often come with breathless warnings that failure to respond within the time window puts your paper in danger of not being published at all. I remember in 2019 being given the (relatively generous) span of two weeks to look over the (96 page) galley proofs of my Duke paper with David Geraghty. Except that two week period happened to coincide with the holidays (the requested return date was December 24), and overlapped with a period where I was particularly busy. Moreover, I was also about to go on a trip to Australia (which I ultimately had to cancel because of the bushfires). I told them that I should be able to get around to going through the paper by February. The journal responded by telling me, and I quote, that “While we appreciate the fact that this is a long article and that it will take some time to review, a delay of two months to handle this seems excessive to us.” In response, I gently mentioned that the journal had taken 864 days to accept my paper followed by a further 147 days before they produced the galley proofs and that this seemed a little excessive to me, but that I would do what I could within my own time constraints. They followed up with a note that they looked forward to receiving my answers in February.
But at least the copy-editing done by Duke on this occasion made a few genuine improvements and did not detract from the paper. What is surprising is when a for-profit journal makes the paper categorically worse by adding errors and not even telling the author about it. And surprise surprise, it always seems to be the for-profit journals that do this. (My very best copy-editing experiences have been with MSP and with the AMS journals.) If you are anything like me, if you try to read over your own paper for typos, your brain is very good at seeing what it expects rather than what is actually there (the standard example is not picking up on “the the” in the middle of a sentence). In particular, the actual probability of finding any error in a 100+ page paper with a 48 hour window by looking at the galley proofs is vanishingly small. The two worst experiences I have had in this regard are at Springer journals. A bare minimum requirement for a galley proof where changes have been made to the original paper is that the journal should tell you what changes they actually made. What they should really do is send a diff file comparing your original .tex to their new version. What they should not do is make subtle changes that are impossible to pick up on a quick reading that change the mathematical meaning of the paper without telling the author. To take an example, I just found out that in my Inventiones paper with David Geraghty, every one of the 47 occurrences of “[[” and “]]” was replaced by single brackets “[” and “]”. The rings \(\mathbf{Z}_p[[X]]\) and \(\mathbf{Z}_p[X]\) are very very different — one is a complete local ring, the other is not. So now in the published paper we patch modules over the \(S_{\infty}\) which is now a polynomial ring; modular forms over a field \(K\) have \(q\)-expansions in \(K[q]\) and hence are polynomials, and so on. I think that every one of those 47 occurrences introduced an error of this magnitude. But at the same time, picking this up is close to impossible when looking at the paper because the mind naturally “corrects” to what it should be, especially if you know how the Taylor-Wiles method works already (which, if you are one of the authors of this paper, is certainly the case). What’s particularly annoying is the stupidity of this process — unilaterally making the change, not telling the author, and then giving them (in this case) 48 hours to look at the paper.
So what is to be done? The good news is that I am in the luxurious position that citations (or lack thereof) make no difference to me. (Hat tip to both the University of Chicago and the NSF for not being obsessed by such metrics.) So clearly the solution is that anyone who wants to cite my paper should cite the latest version on the ArXiV rather than the published version. If a journal complains that they want to cite the published version, simply point out that the published version is riddled with misprints and thus should not be cited. You have my blessing to do this!
Update Aug 2: I did decide to email the journal and ask if they could republish the online version. The mathematicians involved were perhaps not surprisingly very apologetic and upset as well, and have put pressure on Springer to fix the problem. We will see what actually happens.
More benign and somewhat amusing: In Khare-Wintenberger’s paper Serre’s Modularity Conjecture (II), there were a couple of references in the preprint version to “exp.8” in SGA2 that the copy editors (I assume it was them) at Inventiones changed to “Exercise 8.”
A favorite “correction” of mine is reference [5] of
Dunfield, Nathan M,
Examples of non-trivial roots of unity at ideal points of hyperbolic 3-manifolds, Topology 38 (1999), no. 2, 457–465.
Here the copyeditors expanded all the journal abbreviations used by Dunfield to the full title, but decided that “Invent. Math.” should be “Inventory Mathematics”.
In another Springer paper, they took the TeX file and deleted a bunch of return character. Now that doesn’t usually make a difference, but:
line one %
line two
line three
is very different than
line one % line two
line three
and in particular the statement of one main theorem is mangled with the second half of one sentence and the first half of the next unceremoniously deleted.
A diff file is a pain to use since you have to cross-reference everything to figure out what they did. The best system I have seen is the one used by MSP journals where they send you the page proofs with all their changes in red and with notes in the margins explaining all the changes. You can skim through and glance at each one. I recently had to do this to a 60 page G&T paper, and it took less than 30 minutes. Every journal should do this.
Of course there are better solutions, and MSP does a great job of this, but a diff is better than nothing…
Latexdiff is almost as good as what MSP does.
MSP is great about typesetting. Only publishing in MSP journals is the obvious solution to these issues. But I don’t think Springer could fix their typesetting by just adding this policy, because you can’t trust them to actually mark all the changes they made! The only thing that works is having in-house typesetters who are trained for the job of specifically copy-editing math papers.
That change of [[‘s into [‘s makes my neck hurt. Have you gotten any sort of apology from the journal?
I haven’t tried!
I seem to remember Annals simply had to reprint a paper of the Kuperbergs (mother and son) from the late 90s, due to so many misprints. And I saw an analytic number theory reprint from that era where Inventiones managed to delete all the horizontal lines in Legendre symbols, so they looked like binomial coefficients (I think the published version was OK though).
I think the journal should reprint your paper (the correct version of it). Another precedent is The Annals of Pure and Applied Logic, which reprinted a paper after noticing they had not printed “the correct pages”. See MR1130219 and MR1179016.
For those interested in the history of this, although the first printing of my joint paper with my mom looked replete with mistakes, actually there was only one overall problem. During typesetting, a TeX font mismatch slipped in and caused problems in many of the formulas. So it was really just one mistake that caught them off guard, it was not sloppy work in general. Moreover, the Annals editors were more upset than we were that this had happened.
For that matter, they were arguably a bit generous in accepting the paper in the Annals at all. It was a sequel to my mom’s more original first paper, which certainly did belong in the Annals. Our joint sequel was interesting too, but as far as I’m concerned, it could have been in some other good journal, not necessarily the Annals.
Did the copy editors also rearrange the bibliography to list references in order of first appearance?
Yes!
I share your frustration with publishers, but that doesn’t absolve authors from checking their papers. How could two authors miss the glitch with the brackets when it occurs 47 times in the paper? What is the point of publishing papers “riddled with misprints”? Whatever you say on your blog, people will cite your papers and try to read them. Is it that the University of Chicago and NSF aren’t quite so understanding about works published only on the arXiv?
How could two authors miss the glitch with the brackets when it occurs 47 times in the paper?
First, my co-author was no longer in mathematics so I think he can be absolved from any blame. Second, I think it is a well-established principle that it is very hard to catch typographical errors in your own work (https://www.latimes.com/socal/glendale-news-press/tn-blr-me-aword-20151218-story.html). The mind works very hard to make shortcuts while reading to speed up the process, and hence the more one knows the harder it is to catch such errors. It’s not a surprise to me that the person who caught this error appears to have been trying to learn about the Taylor-Wiles method. But just to make it clear (I thought it was clear in the original post but your answer makes me wonder) these are not our errors, but these are errors introduced by the copy editor into the paper without comment. My expectation of a copy editor in math is to make a few minor changes and then to indicate to the author what they have done (or possibly also to list a few questions for the author to answer). So when I am reading the proof, I have the disadvantage that 1. Never in a million years would I expect that the copy editors would arbitrarily change “[[” to “[” (or change any other symbols without indication), 2. When I see the ring \(S_{\infty}\) (say) defined in the text,my mind is already automatically imagining \(\mathbf{Z}_p[[X_1,\ldots,X_n]]\) and it is very hard to read otherwise. To pick up on this error would have required first imagining that errors could have been introduced for every single character of the entire paper and then reading the entire paper symbol by symbol. Since the paper is somewhat long (140 pages or so) that works out to about 1/3 of a million characters at a rough guess. With 48 hours to check the manuscript, that works out to about 2 characters a second. So certainly possible, I guess!
What is the point of publishing papers “riddled with misprints”?
Not much, but I think that is my point?
Not immediately related to the topic but in your survey on reciprocity on p.20 it is said “…but non-ordinary other…” probably a typo.
On p. 23 in the sentence “Moreover, this equality would not…” probably a word is omitted.
On p. 27 note 48 probably ends with “non-transverse.”
On p.20 does the inequality p>2n+1 have to be strict?
Interesting survey by the way! I like how you included bits from the many people involved.
Thanks! Corrections updated on my version (thought not the web page one yet…)