Reviewer 2: “I did not read carefully past section 2. … I recommend that the article not be published in [redacted]”
This particular reviewer read to page 4 of our 18 page manuscript, when the main result was on page 10. This was what we received after almost a full year under review (11 months and 7 days to be exact, but I am not bitter!). Yet the first reviewer read the manuscript carefully and provided detailed feedback along with a recommendation to publish. We have contacted the journal’s editor to request a third referee report — a tie breaker if you will. What next? We wait. Hopefully less than a year…
This can be the reality of academic publishing. But let’s be honest: it is appalling that a reviewer would only read to page 4 of an article and be bold (arrogant?) enough to say that they did not read the article carefully after the fourth page. Yet my undying optimist, ever the academic, wants to find some lessons in this experience, or to at least reflect on what one can do prior to the submission of a manuscript that may help the overall outcome: getting an acceptance.
So here is a pre-submission check list you may find useful.
Giving a seminar talk
There are varying pieces of advice on this. Of course you should give talks about the results of the paper as often as possible. However, do make sure you have things written already and in draft form because people may ask to see the details and you want to be ready to present those when requested. Also, giving a seminar is a quick way of getting people to think about your work and possibly collaborate.
Have students read your work
As my dear mentor Rebecca Garcia, mentioned to me (as she gave me feedback on this post!): Getting your students to look at your work is a solid way to get some high quality feedback. Students are wonderful at finding inconsistent use of notation, lack of clarity in exposition, and have even spotted errors in definitions, examples, and results in papers they have read — just ask my students Alexandre Gueganic and Maryanne Masibo. Asking students to read preprints of manuscripts seems to be more common practice these days, since I’ve noticed various acknowledgements where authors thank their students for their feedback. Perhaps this could even be the start of a research project with the students!
Once you have given talks and polished the manuscript here is what I do next.
Let the work marinate
My dear friend and wise coauthor Erik Insko taught me the value of letting an article sit on the arXiv for some predetermined period — often 10 days. This short time gives people the chance to see the article and possibly send you comments on the work before you have submitted it to a journal. In fact, Erik sometimes sends an email to his math friends with a paper announcement saying something to the effect of “Hey, here is my new paper on X. Let me know what you think!” I recently found out that this is more common practice than I realized. In fact, I added my email to Bruce Sagan’s listserve where he sends a preview of his upcoming papers before they hit the arXiv. The point? If well-established mathematicians are sharing their work with their friends, so should you! This leads naturally to our next two items.
Request peer feedback
If you are a postdoc+ (+ denotes and beyond), it is likely that your peer (another postdoc+) will referee your work. Then you might as well give them the opportunity to ask you questions about the work out in the open rather than under the veil of anonymity the review process imposes. So go a head and email someone you cite in your references, who is at a similar career stage as you, and ask for their feedback. Sometimes they may even have suggestions on how to expand the work or what would be a natural direction for future research.
Send the manuscript to a more senior mathematician
This is scary (can you hear my teeth rattle?). Yet, to my complete surprise people do respond to a junior mathematician’s emails and they may even say your results are cool! Or tell you that they have some ideas on how to prove a thing you and your friends conjectured, from which a new collaboration may emerge (William T. Trotter this is a shout out to you sir!). Of course one can’t ask these things very often (not sure what very often is… once a year seems like a good guess) but this is one good way to solicit some advice from people who likely know the standards for journals in your area. One way to ask for help is to tell them about your work and ask if they may have a recommendation for a journal to which you could submit the manuscript. That way it is a precise question and if nothing else now these mathematicians know your name and the type of work you do.
Submit to a journal
After doing some/all of the above things, and implementing any feedback received (along with updating your acknowledgement section) you may find that you are ready to submit the manuscript. Don’t do it. Sleep on it. Then reread the manuscript out loud. I know it sounds silly but it is the only way I find typos. After all, you are trying to avoid falling prey to the best way to find typos — hitting the submit button!
Did you sleep on it? Ok then submit!
If you have any other advice to add to this checklist please use the comment section. I look forward to seeing your advice!
PS. I want to thank Alicia Prieto Langarica and Rebecca Garcia who I sent this blog post to for feedback, and I wanted to point out I did in fact sleep on it before submitting. Yet, its likly hat this post still contians typos 😉
PPS. Quick thanks to Rene Ardila for finding a typo that was unintentional.
Your advice is excellent but even following your own advice, which I’m sure you did, there will be rejections. Some fair and some unfair. Asking for a tiebreaker in this scenario makes sense to me. Here is a link to an AMS Notices about communicating with editors:
Sadly some journals will say all referees must be agreed to accept. You can check a journal’s policy before submitting a paper there. Some only need one editor to like a paper while others require three or even unanimous decisions by the editorial board. Here’s a link to an AMS Notices article on how some journals make their choices:
I rarely communicate with editors in my own behalf since as a full professor I have the time to spend another year sending a paper elsewhere. But I have helped postdocs I mentor communicate with them. In a scenario such as the Dr. Harris describes above, some editors will suggest submitting to another journal they are an editor for (often of lower rank). Some editors offer this without the request just because they want more quality papers in another journal. Of course you may wish to try for another higher prestige journal first especially if you have another few years before your next job hunt or promotion.
Two things not mentioned in the excellent checklist above before before publishing a (which may also help with getting an acceptance):
The introduction to a paper should be well written selling the importance of the results. This involves citing related work listing the authors of that work by name including less well known results as well as famous related conjectures or theorems. These people are often chosen as referees and only listing famous people will make it less likely the person has time to referee it. Theorems should be either stated or described with a reference to the statement within the paper. Examples justifying the hypotheses should be referred to in the introduction as well. End with an outline of the paper. The acknowledgements can thank people for inviting you to speak, or for discussions, or for looking over the manuscript. This is another source of possible referees so it is good to list supportive people here. After posting on the arxiv you can share with more people and you can add them to the acknowledgements in the version of the paper submitted to a journal.
Finally, it is easiest for a referee to review a manuscripts that is double spaced and in the fontsize required by the journals. Usually 11pt or 12pt. And all equations should be in their own line not hidden in paragraphs and should be numbered. Including really obvious calculations you don’t expect will be in the final published version is ok too. This makes the referees’ job easier. They may ask you not to number every line and to remove lengthy calculations in the final publication but it makes it much easier for them to write a report if they can say “there is trouble in (3.77)” or that “(4.58) needs further justification”.
There will of course still be difficulties publishing but these two points can help both with finding the rights referees and with pleasing them.
One issue that jumps out at me is that your main result is on page 10 of an 18 page manuscript! You can’t assume that a referee is going to read beyond the introduction when making their initial decision to accept or reject your paper (of course, if they decide that it should be accepted they will read the rest to make sure it is correct). So your new results (and a description of how they relate to the previous literature) need to be clearly stated in the introduction.
Moreover, the length of that introduction should be commensurate with the length of the paper (so if 10/18 of your paper is an introduction, you need to trim it down substantially). As an example, the last paper I had accepted was 19 pages long with a 4.5 page introduction (and the main theorem stated on page 2).
Another thing to add to the list — after having a very similar experience, I’ve made a point to be maximally clear, in both the abstract and the introduction (and even the title if possible!), what the new result is and why it’s a big deal. I know that mathematicians hate repeating ourselves but this is a place where it’s worth it.
I completely agree! This is the time to not be shy and brag about those new results.