It strikes me as a real structural problem of the mathematics community that math papers are on the whole simply not very well proof-read. Many papers, sometimes very important ones, are often full of errors, in large part because it is simply a very time-confusing and difficult task to check a math paper for errors. On a more general level, I think most math papers could use a good once over by a talented editor who also understands the mathematics. Too bad such people are in short supply, and generally have better things to do.

I’ll confess that proofreading is sometimes a bit of a problem for me, probably more so than for some more detail-oriented people. While there’s been quite a range in the number of errors found by the referee, I’ve gotten a couple of reports on papers I’ve submitted that found quite a few errors, and in fact, I received just such a report (for my paper with Geordie Williamson) just yesterday.

What’s most dispiriting about such a report is that it’s not as though I didn’t proofread the paper, more than once (as did Geordie, and at least one other mathematician). I just went right over a number of errors that become glaring when the referee pointed them out. And while it’s generally pretty easy to fix whatever the referee actually points out, one knows that there are yet more errors hiding in there (especially in this case, where the referee indicates that they lost patience, and didn’t carefully proofread the whole paper), and it seems hopeless to think you will catch all of them.

Does anyone have recommendations other than Ritalin? Of course, it would be best if one could dispatch a horde of flying monkeys blog readers to proofread one’s papers for one, but that doesn’t seem like a sustainable plan (not that I wouldn’t appreciate any comments readers have on the paper. It’s on my webpage here. Don’t look at the arXived version. That’s out of date).

13 thoughts on “Proofreading

  1. Do you print out your papers when searching for typos? Reading them on a computer screen is rarely good enough.

    Even better: print it out, cover it with a sheet of paper, slide that sheet down one line at a time, and read each line out loud.

    The main thing is to not let your eyes slide over the text while mentally going “yeah, yeah…”. You have to really look at each symbol and think “is this right?“.

    It’s work, but it’s worth it.

  2. One thing that will entice people to submit error reports to you is to add to the introduction of all your papers: “I would like to thank the following people who sent me corrections for this paper: Leonardo DiCaprio, Frankenstein, etc.”

  3. I’m in the process of editing my own 140 page document right now, and I find it difficult to focus on math errors AND choice of notation AND the grammar and local and global flow of the text all at the same time. At the moment, I’m trying to tackle one section at a time, and then first dealing with the narrative, notation, grammar and flow of each section, followed by a detailed check of arguments and symbols. I’m catching some math or symbol errors incidentally while looking at the language, and when that process is done, I find it easier to concentrate without distraction on any residual math errors.

    This editing process is turning out to be a much more time consuming job than I imagined.

    I agree with John that it’s much easier to be critical while working with printed documents, and I do that despite not liking to use all of that paper.

  4. Do you print out your papers when searching for typos? Reading them on a computer screen is rarely good enough.

    I’ve printed them out far more than the Sierra club would appreciate, I suspect (but paper in a landfill is a carbon sink!). I will have to give your technique with going line by line a try though.

  5. You could have a proofreading buddy, where you have some agreement to proofread each other’s papers.

    This disadvantage of this is that you would really have to read someone else’s paper (heaven forbid), and that would probably take more time than proofreading your own using some incredibly tedious but thorough method. But it might be worth a try, because proofreading one’s own paper is so soul-destroying. (Or maybe it’s just reading my papers that is…)

  6. I’ve heard that changing the font to make it look different is a standard trick for proofreading one’s own work. Haven’t gotten a chance to try it yet, but it sounds reasonable.

  7. This isn’t quite what you’re asking, but something I insist on in my own papers (and my students’) is that when you’re halfway through a sentence, there shouldn’t be an obvious but completely wrong guess as to what’s going to come in the second half. Frequently this can be fixed by switching the two halves. I try to reread my papers with the view of a malicious prankster who insists on misunderstanding everything possible.

    One thing I do recommend, though this is easier after the publish-or-perish stage, is to abandon your papers completely for a month or so before rereading them. Even a week can make a substantial difference.

  8. There is a very simple and extremely effective strategy that I learned from Jeff Siskind. Read the paper, out loud, to another person. You should read it dramatically, like you would read a short story or a poem. This catches an amazing number of error and awkward sentences.

  9. Thanks for all the good suggestions. Now the hard part is figuring out which I have time to implement.

    One suggestion I received over lunch today was to proof read the paper upside down (or just mirror reflected). It might be effective, but it also sounds like a good way to get a headache.

  10. I spent a summer during college only reading upside-down. I never got near to full speed, but upside-down is definitely not nearly as headache inducing as reading at weird angles.

  11. In terms of productivity, reading upside down beats playing video games 20 hours a day *cough*

    I’ve heard that reading backwards helps with things like misspellings (although I think we can delegate this job to computers). The “theory” is that you can concentrate on the shapes of the words instead of the context. Of course, I only tried this a few times. It might be worth your time to hire a local Princeton math major.

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