1

When we read books, we often see a few errors or gaps in proofs. Some typos are obvious and can be corrected easily. Sometimes there are more significant errors which forces us to "do an exercise" to fill in the gap caused by the error.

In the second case, since it is an "exercise", it's possible that we end up being unable to fill in the gap. If this is the case, then to ask a question here is an option. However, there are things which cannot be easily asked here - for example, if the gap appears in an expression, and the expression involves some notation which takes a few pages to define, and the notation is not "standard" (for example, some constructions doesn't have a name), then it becomes extremely difficult to ask for help.

What are some strategies to overcome this difficulty? How to prevent getting "stuck" on an error for a long time?

Ma Joad
  • 7,420
  • “How to prevent getting "stuck" on an error for a long time?” is (in my opinion) to abstract to be answered here. – If you are wondering whether (and in what form) to post a question on MSE about errors in papers then this should be asked on https://math.meta.stackexchange.com. – Martin R Apr 08 '21 at 09:11
  • 1
    Limit the time that you invest in trying to explain the situation (perhaps 30 to 90 minutes). Then, regardless of whether you are going to ask on MathSE or directly from a Math professor, invest another 30 to 90 minutes, organizing your thoughts, as if you were in a courtroom. Then present your case. – user2661923 Apr 08 '21 at 09:16

1 Answers1

2

My algorithm:

  1. Spend 15 minutes or less trying to fix it. Usually I'm the one who's wrong and that becomes clear in this step. This step includes checking for errata online maintained by the author.

  2. A. Work around the problematic passage by finding another source that gives a different proof of the same thing.

    or

    B. Skip it entirely and come back later if it ends up being important. If I still think it's wrong when I come back fresh, it's probably genuinely wrong.

    or

    C. Treat it as an exercise and devote some actual time trying to fix it myself. Be careful about time management.

  3. Talk to someone else about it. Potentially email the author(s) if I feel I've put in enough effort to bother them and my issue is sufficiently clear.

Getting to step (3) is rare. The last time I recall making it to that stage involved a conversation with some colleagues on a preprint. None of us knew what was going on at a certain step, we were convinced we had a counterexample, so we messaged the authors. It ended up simply being a little error in what they wrote. Our counterexample was right, but their underlying idea was correct too.

Joshua P. Swanson
  • 9,634