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The field is mathematics (functional analysis). As we get ready to post a paper on arxive, we realized that one of the results here disproves a conjecture proposed in another paper.

Assuming the author of that conjecture is still around, is it good practice to communicate with the author first before we post our paper?

Conversely, would it be impolite/rude to post our paper without notifying the conjecture's author?

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    The Golden rule is a good starting point for these sorts of question. If it were your conjecture, would you want the author to notify you? If you would, you probably should notify them. Sep 7, 2022 at 12:52
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    Is there any possibility that your disproof is wrong and the conjecture is actually true? If so, you could get some very useful feedback from the previous author.
    – David
    Sep 8, 2022 at 0:13
  • @David , Good point. That's a very real possibility.
    – Bilbo
    Sep 8, 2022 at 18:20

3 Answers 3

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Personally, I'd be more than happy to be notified and to see an early copy of your work. Among other things it might save me some work and would put my mind to rest in any case.

Assuming you cite the other author then it would be polite to notify them so that it isn't a surprise when your work appears.

You did cite them, I hope.


Note that sometimes such things happen when the new author doesn't know about the earlier work so it isn't always possible to notify the original author. But since you noticed, yes, let them know.

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    +1 I agree - although I don't think it's imperative to inform them before uploading the paper. Informing them right when the preprint becomes available on arXiv would also be fine, I'd say. Sep 5, 2022 at 22:35
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    I wish I had been notified, several times, for proofs and disproofs of conjectures I made/ Sep 6, 2022 at 2:20
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    @EthanBolker I hope these proofs and disproofs weren't all of the same conjecture, but if so, then I think we all wish to be notified :-) Sep 6, 2022 at 17:37
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    @Carl-FredrikNybergBrodda Several conjectures, some proved, some disproved. Sep 7, 2022 at 0:21
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    @EthanBolker Plot twist: Carl-Fredrik is an alias of Alan Turing :) Sep 7, 2022 at 14:02
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If you were claiming that someone had made a mistake in their paper (in mathematics), then in that situation you should notify them beforehand and give them a chance to rebut your claim. (Keep in mind one of the possibilities would be that the claims in your paper are correct but you didn't understand the claims in their paper.) However, a refuted conjecture isn't a mistake, because a conjecture isn't a claim at all, only an informed guess (or, in some cases, a provocative way to ask a question). Hence, you aren't under some obligation to inform them before making the paper public. You certainly can if you want, and they could have some further information, for example further context for the conjecture, that would help you produce a better paper.

However, if you're asking about notifying them roughly simultaneously with putting it on the ArXiv, I don't see why you're asking. Mathematicians have a hard enough time getting anyone to read their papers as it is; by some measures of what it means to 'read', the median paper is probably read by fewer than one person not including authors and referees. The person who proposed this conjecture is naturally someone who is likely to be interested in your paper, and of course it is to your advantage if they know about it. If this is a well-connected senior mathematician who organizes conferences and workshops and might help you publicize your work further, even better. Without being obnoxious about it (and letting someone know that you have resolved their conjecture is definitely not obnoxious), you want to publicize your work to interested parties as much as possible.

Also, this person is a likely referee for your paper, and it will speed the process along if they happen to have already read your preprint prior to being asked to referee!

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    It's not a mistake. The earlier paper said "X might be Y (or not), we don't know". OP has found that X is not Y. Proving or disproving conjectures is a typical (and quite high-profile) mathematical research. Sep 6, 2022 at 20:24
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    @OlegLobachev: This answer agrees with you. (See the bit starting from "However, a refuted conjecture isn't a mistake".)
    – ruakh
    Sep 7, 2022 at 4:12
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    I like the idea of "a provocative way to ask a question"!
    – davidbak
    Sep 8, 2022 at 1:16
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Yes, you should notify the author of the conjecture that you believe yourself to have rebutted.

In addition to the other reasons given, that other author, being human, will have some emotional investment in the conjecture, and thus will be motivated to give your rebuttal the highest level of scrutiny.

After all, it may be that you are the one in error and the other author's reasoning is in fact quite sound, and if this is indeed the case it is best for everybody involved to expose the error as soon as possible, wherever that error may be.

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