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Suppose one is giving a talk about one's work (in pure mathematics), and another researcher(s) in one's field has published a paper claiming to be an improvement or generalisation of one's result, but one either believe this other paper is wrong, or that it is a trivial consequence of one's own result. Should one:

  1. state this other result in one's talk with no comment

  2. mention the other result with mild doubts (e.g. say 'so-and-so claims this, but I haven't had time to look at the paper properly')

  3. mention the other result and state clearly that one thinks it's wrong/trivial

  4. don't mention it at all / ignore it.

One doesn't know whether the author(s) of the other paper will be at this conference.

Edit: Assume a list of speakers is available but not of participants, so one knows the other researcher is not speaking, but doesn't know if they will be in the audience of one's talk.

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    Did you discuss this with the other researcher? Usually, the first thing to do on discovering an error or unclarity is contacting the author with a question (usually these things turn out to be misunderstandings, and the sooner they are corrected the better for everyone). – darij grinberg Mar 26 at 17:06
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    Being wrong and being a trivial consequence of your work are two very different things. Is there some reason you're asking both at once? – Pete L. Clark Mar 26 at 20:01
  • Comments are not for extended discussion; this conversation has been moved to chat. – eykanal Mar 31 at 1:57
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First, you should know that since your results appeared first (as you stated in a comment), you don’t actually have a strong self-interest to try to make the follow-up results of the other researcher look bad. In a typical scenario, their publishing something that improves or generalizes your result will actually make your own work look better, not worse, including possibly if their improvement is not trivial (actually a trivial improvement may be slightly more embarrassing to you, for example if they discover that a trivial modification to one of your proofs ends up proving a much stronger result. But even then you’ll get the credit of being the first person who published an innovative new proof technique that was used to prove that strong result). So all things considered, it’s pretty likely that your incentives are actually aligned with those of the other researcher, and being as kind and charitable to them as possible (without compromising your integrity, of course) will be beneficial not only to them but also to you. And remember you don’t have to discuss every private thought you have: you may think the improvement is trivial, but at the end of the day, who are you to say? That’s just an opinion anyway. Consider not mentioning it and letting people draw their own conclusions.

What I wrote above pertained to the scenario of a correct improvement. Coming to the other possibility you mentioned, if you believe the work of the other researcher is wrong, then it’s wrong and you shouldn’t pretend otherwise or feign ignorance but simply be matter-of-fact about it - if you discuss the result, state that you believe it’s wrong along with your level of certainty that that’s the case, without gloating or schadenfreude. Don’t say you haven’t had the time to look at it if that’s not true. But you may consider simply not mentioning the result at all if its relevance to what you are discussing is not high.

Incidentally, not mentioning the result may also end up offending the author if they are attending your talk... it’s a tricky business, academia! ;-) Anyway, good luck.

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    "Incidentally, not mentioning the result may also end up offending the author if they are attending your talk... " Yes, I am also worried about this. Thanks for the suggestions – Whatif Mar 27 at 7:38
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I either believe this other paper is wrong, or that it is a trivial consequence of my own result

Let me be blunt, if it's wrong and a trivial consequence of your own result, then your result is wrong too. Make up your mind: which is it? Wrong and trivial are not synonymous. The answer differs depending on which applies.

If you believe that the result is wrong.

  • If you want to publicly humiliate the other researcher, then you can say during your talk that the other researcher's result is wrong. You will not make any friends and will not impress anyone by doing this.
  • Otherwise, your first course of action is to talk about it with the other researcher in private. Have you even considered that you misunderstood something? Most people are reasonable, and if the result is truly wrong, then you will know how to act based on your discussion. Otherwise, this is a whole can of worms, and the answer depends on a ton of factors.
  • If for some reason you have not had time to talk with the other researcher, then I would not mention the result at all, and elude the question if asked about it during the talk. If you really don't want to elude it, say that you are aware of a possible contradiction between your paper and the other one and that you are looking into it. (See, that's called tact.) I would also take the opportunity of having the other researcher in the same room to talk about it after the talk, in private.

If you believe the result is a "trivial" consequence of your work.

  • If you want to insult the other researcher in public, then say that the other word is a "trivial consequence" of your own work during your talk. You will not make any friends and will not impress anyone by doing this.

  • Or you can simply not mention it at all. If asked, you can say that it's nice to see other people being interested in your own work and finding applications.

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    @YemonChoi is right, my paper predates the other one. Sorry if not clear in the question. – Whatif Mar 26 at 17:32
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    @user106021 I disagree with your interpretation, even if I think the OP would do best not to cause a fuss. Once again, it does seem like you are jumping to conclusions or projecting. How do you know the OP isn't more junior than the people who claim to have improved their results? This seems very possible to me in pure maths – Yemon Choi Mar 26 at 18:00
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    I disagree with this part: "say that you are aware of a possible contradiction between your paper and the other one and that you are looking into it. (See, that's called tact.)" In fact, either you are aware of a contradiction, which means you already verify that this is indeed the case, or you are not. In the latter case, you do not suggest that there may be a contradiction. Rather than tactful that is rude and potentially damaging to yourself if you end up being wrong. Better to simply say that you heard of the other result but have not had time to examine it. – Andrés E. Caicedo Mar 26 at 21:11
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    -1 This answer seems overly aggressive to me. "Make up your mind" is uncalled for; OP clearly gives these two possibilities as examples of where he is unhappy/not agreeing with something from another author ("either or"). The repetetive "If you want to insult" seems to be uncalled-for, nothing in the question from OP seems to indicate that he wants a confrontational course. OP knows that this is a delicate issue and is looking for good solutions. – AnoE Mar 27 at 12:11
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    Your answer implies that you know what tact is, but then you fail to use it... – msouth Mar 27 at 13:21
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I lean towards "ignore it".

In addition to the issues of academic politics, there is the much bigger issue of confusing the audience. They have limited ability to process information (and math is particularly hard, even for mathematicians). If you mix in a "he said, she said" into your topic along with new results, you end up overloading the presentation. They will have a hard enough time learning from and following the talk, let alone doing justice to an issue of controversy. You just don't have time enough for a good exposition of the rival's arguments and your replies. If someone brings it up in Q&A, deal with it then.

Of course in a paper, you can/should be more all encompassing. But the goals of a paper are different than the goals of a talk.

  • Yeah I seriously don't see where the harm is in not bringing it up. +1 – Mehrdad Mar 26 at 23:44
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    Well, I don't want to offend the author if they are there. But I think with these answers I'm also leaning to ignore it, thanks – Whatif Mar 27 at 7:39
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    @Whatif I'm not sure how you feel that saying a paper is crap (wrong, trivial, whatever), to an audience including its author, is less offensive than not mentioning it at all. – David Richerby Mar 27 at 10:25
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This happens a lot in other fields where experiments are fast, like Machine Learning, and there are often several iterations of the same research between the submission date and the actual conference.

If you have spare time at the end of your talk you can mention it briefly, stating that there has been new development in the field since you published the paper but you haven't had the time to focus on it yet, and very briefly talk about the implications of that work w.r.t your own research. It's important to do both, as just mentioning "X also published a paper on this" is not really useful enough to be worth mentioning.

Most likely you won't have the time to talk about it though, and it's fine to just not mention it during the talk itself, and only bring it up if someone strikes a conversation after your talk.

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