Earlier today I finished revising and resubmitting a paper. It seems like the stages of revision after a referee report are very similar to the stages of grief: denial (no, referee, this proof is NOT incomplete), anger (this referee is such a jerk), bargaining (well, maybe I can fix this part but not this part), depression (I will never be able to publish this paper), and acceptance (well, maybe the referee is making some very good points and I should go ahead and fix everything he suggests). I am sure I went through all of these, and have come out with a renewed respect for referees and the jobs they do. I mean, there were a couple of important comments she/he made that I hadn’t even thought about before, and definitely fixing those things made my paper much much better. But until a few days ago, I felt so bitter about the whole thing. This is why I will put this referee into the “unsung hero” category. He/she did a great job, but it took me a while to recognize it.

In fact, all of my referee experiences have been similar, but I think I may have been very lucky in this respect. I mean, I was a bit more bitter when a referee report a while ago started with “This is a very good paper and very fun to read” and immediately followed by “but I can’t recommend it for publication because the results are just not that interesting”. What a perfect way to ruin someone’s day, right? However, a friend of mine pointed out that it wasn’t that much worse than the inverse: “This paper has very good results but I can’t recommend it for publication because the writing is abysmal” (which he got once). And I imagine, from the referee’s perspective, that bad writing can probably make your life very difficult. Some referees are aware that some of this comes from people for whom English is a second language (like my aforementioned friend). Another friend got the suggestion to get a native English speaker to help her with her manuscript, not knowing that she was one herself!

But I have certainly been very lucky, as I said before. I have heard some horror stories about really mean referee reports, and I’m glad that so far I haven’t gotten any. I mean, in every report that I’ve read it’s been clear (after going through the five stages of course) that the people on the other end were genuinely trying to help me.

I haven’t refereed any papers yet, but I have been editing for the American Mathematical Monthly for a while, and I get to pick referees for certain papers and if the paper is clearly wrong for the Monthly I get to reject it. So I can imagine how difficult it is to review a paper. You want to help other mathematicians (or at least, I do), but you do need to think about whether the paper is appropriate for your publication, and you have to judge with some detachment the results in the paper. In the case of the Monthly, the level of writing needs to be very good, too. I can’t understand being mean to someone, and I wonder if some of the stories I’ve heard maybe have come from people who haven’t yet gone through all the stages. I do know that there is a lot of competition in some areas, and that maybe rivalries can develop. How awful would it be if your rival got your paper to review? This is the true referee arch-nemesis situation. Still, a reasonable person would decline to review a paper if there were personal feelings involved, but movies have taught me that a true nemesis is not reasonable.

So, dear readers, I though I would open it to those of you with more experience in the matter. Does one referee in your past particularly stand out as an unsung hero? Do you have an arch-nemesis refereeing your papers? What is your worst or best story? Any advice for those of us who might get stuck in one of the stages of revision grief? Did you have a particularly difficult decision to make as a referee? Please share your referee stories in the comments below.

My favorite story was with the main paper of my thesis. The paper was too long for the journal and one of the referees recognized this, so s/he gave precise instructions of what to eliminate for the paper to be accepted. I’m super grateful for this.

As an author, I’ve had both good and bad referee experiences. My very first paper got such a careful, thorough, and thoughtful report. And I was completely panicked because I couldn’t figure out how to fix one big, gaping whole. It took me about 8 months, but when I did fix it the paper was way, way better. (I kind of wonder if it could have be accepted in a better journal at that point!

Then there was the circular refereeing: Paper submitted to journal X referee said “very good & well written, but not quite of the quality necessary for journal X… probably a good fit for journal Y.” Journal Y referee said “very good & well written, but not quite of the quality necessary for journal Y… probably a good fit for journal Z.” Journal Z editor (after three months) said, “We have a terrible backlog and I haven’t even sent this to a referee yet. I probably won’t for several more moths. But it seems like a very good paper. You should consider journal X.” Sigh.

As a referee, I work very hard. I know some people do not feel the referee needs to check every detail of every proof, but somehow I can’t get it out of my head that my job is supposed to be to verify the paper is correct. So I do, in fact, check every line. If results are cited from other places, I look up the results to make sure they’re being used correctly (though I don’t, admittedly, check every line of those proofs). I will say that I have found mathematical errors, often small and usually fixable, in several of the papers I have refereed. So I feel like this is an important part of the work.

Finally, “…but you do need to think about whether the paper is appropriate for your publication…” This is the thing I actually find the hardest, both as an author (deciding where to submit) and as a referee (deciding if the paper, if correct, is a good fit for the journal). I don’t think I’m very good at it yet.

My two experiences in this regard are not particularly good. In the first one, the editor rejected my paper for being too short. I expanded it in a way that was not related to the main content of my paper, and it was accepted.

In the second one, the referee took more than year to tell me that it was trivial to count the combinatorial objects I studied, but his/her calculations were completely wrong!

I’ll share this, if you’d like and be so kind to consider: more than 10 years ago, I submitted a paper to a journal of the AMS. Its content was perhaps 80% mathematics and the rest physics. The mathematical part was written in a manner close to 18th century style (although not in Latin!… and there was an excursus into rigid analytic geometry! ). It resumed to a theorem, its proof and its consequences, aiming at some applications in plasma physics.

The editor, at the time, was (still is!) quite a respectful top reference in the field of algebraic geometry. To my good fortune, or so I think: this circumstance, together with his remarkable openness of mind, granted that my paper was given a serious opportunity and was sent to two referees.

I had to wait about 5 months. Meanwhile, there was a change of editor, of which I was gently informed. I also remember the new editor as an extremely kind person.

The decision was for a rejection. Not because the proof was not rigorous (after all, it was just a bit of (very) sophisticated mathematics composed in a (very) very elementary way); in fact, its many imperfections, if any (surely some, I think), were not even mentioned on the rejection letter.

The problem, the editor told me, was that both referees agreed upon the fact that, in writing the paper, I had ventured and expressed myself in a way that, sometimes was accessible only to experts in algebraic geometry, and sometimes was accessible only to experts in tokamak and plasma physics… and everyone agreed that the intersection between both sets of experts was close to an empty one.

Needless to say, perhaps, I am a freelancer, so, I did not give any personal references, or academic titles (Mr. was enough). Probably, this is why I was then kindly advised (no deliberate irony at all, here, from the editor) to consider teaching the experts in one of these fields some of the ideas of the other field. And the rejection letter continued, addressing me as Professor, immensely kind and somehow anticipating that I could follow the advice, or challenge…

Which I could not, unfortunately… Still, no matter how strange this may look, the fact is that these words were quite a stimulus for me to continue my work… they still are…