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The story starts on April 2, when I found a critical mistake in a semi-famous recent applied math paper with 100 citations. I admire the paper and I find a very simple counterexample that high-schoolers may understand in 10 minutes. I contacted the original author, who is an editor of a top journal. He arranged a meeting with me on June 1.

On June 1, we finally met and I informally invited him to be a co-author to show my goodwill. He did not say yes or no. He was not 100% convinced. To be specific, he did not claim that my counterexample is wrong, but he also believe that his original 25-pages proof is flawless. He wants to know which step of his proof is wrong. He asked for more time.

On June 21, he said he is busy with work and will get back to me in two months.

My colleague says that he is kind of "bullying" me because I am a no name. However my initial feeling is that he is a kind person.

My concern is, since his paper is influential and many other researchers are working based on it, my correction to their paper will save our society tons of money and scarce resources.

What do I need to do?

Here is my plan: I will try to be as transparent as possible, stating my concern:

Dear Prof. X, I admire your abilities and your time invested. I understand that you have other commitments and I will happily wait for a two months.

My only concern is, since this paper is influential and many other researchers are working based on it, the correction will save our society tons of money and scarce resources. If this is reasonable, I am obliged to post the correction as a service to our profession as soon as possible.

So, my current plan is to fully respect your time frame without delaying the publishing of my paper. If, after two months, you find my manuscript is good with a minor revision and you are willing to endorse my points, then I'd formally invite you to coauthor the paper. If you find my manuscript not good enough, I'd still fully respect your words and accept the fact that I might have to work alone.

Is my letter professional and how do I improve my professionalism in difficult situations?

High GPA
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    I'm hard pressed to believe that a math paper directly leads to saving 'tons of money'. That letter is not particularly professional. Skip the first two paragraphs, tighten up the third. Do you really want them as a co-author? – Jon Custer Jun 27 '23 at 14:55
  • @JonCuster The community is not large. My best friend A is also my best colleague. A's previous advisor was also their previous advisor. I am trying to play the "cooperator" in any prisoner's dilemma game and don't want to harm anyone – High GPA Jun 27 '23 at 15:17
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    " I am obliged to post the correction as a service to our profession as soon as possible." what an unconventional way to express the utility of one's work. I hope you are honestly naive, and that you are not bordering the moral blackmail on purpose. Why do not put your work as a preprint? then you are morally fine, because the society at large in principle can be aware of the error. Or do you have some unexpressed second goals, like publishing with "big name"? You had already a meeting with them, whether something else comes out ... only time will tell. – EarlGrey Jun 27 '23 at 15:45
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    Surely science moves on time scales slower than two months... – Wolfgang Bangerth Jun 27 '23 at 16:29
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    Just to double check: are you sure your counterexample is that easy (as many people seem to invest (costly?) research on the paper? Is the error problematic for.the people citing the paper? – user111388 Jun 27 '23 at 16:44
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    So you also tried to publish a paper about 2 years ago claiming a flaw in another paper (and apparently having a lot of problems in doing so, given that you have two previuous questions dealing with those). This is highly unusual. – Tobias Kildetoft Jun 27 '23 at 17:14
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    This question is reminding me of https://academia.stackexchange.com/q/18491/43873 and https://academia.stackexchange.com/q/165526/43873 and https://academia.stackexchange.com/q/181336/43873 – shoover Jun 27 '23 at 17:51
  • @shoover Ok but I published in a top journal of my field so I don't consider myself to be a completely outsider. – High GPA Jun 28 '23 at 03:52
  • @EarlGrey The sole reason that I want to coauthor with him is I don't want to harm him because we are somehow connected. Except for that reason, I don't want to coauthor with big-name. A solo-authored paper carries much more weight. – High GPA Jun 28 '23 at 03:55
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    What exactly happened on June 1? I presume you showed your counterexample to the original author. Did you convince them that the counterexample is valid? Given that it can be understood in 10 minutes, it's unusual they want 2 months. What do they need to two months for? – Allure Jun 28 '23 at 04:17
  • @Allure They are about 50%-70% convinced. They said they have other commitments in summer. – High GPA Jun 28 '23 at 06:03
  • @TobiasKildetoft I'd say more than 10% of math paper have some minor or major sloppiness. Many of my colleagues met a few flawed papers, sometimes they correct them, sometimes they let it go. – High GPA Jun 28 '23 at 06:56
  • @JonCuster This is an applied math paper that leads to both theoretical work and expensive experimental verifications that involves hundreds of people. I'll follow your guides. – High GPA Jun 28 '23 at 06:57
  • @user111388 To prove that the counterexample work, I only need 10 lines of proof. The error is problematic for people citing the paper. – High GPA Jun 28 '23 at 07:00
  • @Allure I agree with you that since high schooler can understand the counterexample, it is unusual to take 2 month to rethink. He did not claim that my counterexample is wrong, but he also believe that his 25-pages proof is flawless. – High GPA Jun 28 '23 at 07:01
  • Does this answer your question? Who should the authors of a corrigendum be if I am correcting someone else's mistake? – EarlGrey Jun 28 '23 at 07:23
  • @HighCPA:So is the main result wrong in a problematic way? Or can it easily be repaired and is irrelevant for the applications? It seems hard to believe that people invest so much money and nobody checks it. – user111388 Jun 29 '23 at 16:08
  • @user111388 From my personal perspectives, non-theorists love to use funding on famous theoretical works, without the intention or ability to redo all the math by themselves. The main result is wrong and very hard to be fixed in my opinion. – High GPA Jul 02 '23 at 17:46

3 Answers3

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They already gave you a hearing and were not convinced. So just write a letter saying that you plan to submit your paper within the next month unless you hear from them.

Beware that these statements make you look like a crank:

My only concern is, since this paper is influential and many other researchers are working based on it, my correction will save our society tons of money and scarce resources. If this is reasonable, I am obliged to post the correction for our society as soon as possible.

and

I admire the paper and I find a very simple counterexample that high-schoolers may understand in 10 min.

If I were to receive an email with those statements, I would probably ignore it. That does not mean that you are wrong. But the only way to know is to submit it for publication and see if the reviewers agree with you.

Cheery
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    +1 you are right. The second statement is a bit emotional and not professional. I'll try not to make this expression anymore. What wording shall I choose? – High GPA Jun 27 '23 at 15:10
  • FYI I haven't include the two quotes in any emails (yet). – High GPA Jun 27 '23 at 15:11
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Here is another option. You can send a note to the editor of the journal in which the paper was published. Once the editor of the journal is convinced, they would require either update of the paper or attach your updates with the paper. Push coming from the journal editor will carry much more weight and can expedite the process.

Anuj
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    By *note to the editor, would that also imply commentary* on a published article: should the journal allows for commentary. – semmyk-research Jun 28 '23 at 04:31
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    You can just start with an email. They will be happy to provide you guidance for the next steps. It may vary by journal – Anuj Jun 28 '23 at 04:42
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You've already met and discussed the topic, you've already given the offer to co-author, all there's left to do is give them a heads up about the new timeframe

Dear Prof. X,

I'm XYZ, we met early June to discuss my input on Your paper xyz, specifically, my suggested correction for such-n-such.

Currently, my planned timeframe is to publish it between date-n-date, let me know by then if you have any input on the manuscript or anything else on the matter.

Thank you for Your time and it was a great pleasure meeting You (can add more niceties here if you're inclined to do so)

That's the quick and succinct communication I would be happy to have between two academics. Obviously, I don't know the specific culture you're navigating and if this gives you a gut reaction of being much too informal and straight to the point - absolutely follow your gut. I'm just here to provide a different sample for your consideration to help you find something you're comfortable with.

vspmis
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    I think this is the only reasonable course. You're not blackmailing them into being a co-author, you're not trying to convince them that you're correct, you simply publish, and let the two papers stand on their merits. The research community can figure out which side they find most correct. All part of the process of research. – lupe Jun 28 '23 at 08:21
  • Now I sincerely agree with all of you that my wording does sound like blackmailing. FYI they might be too busy to know there are many experimentists working with their results, and those experiments cost money and manpower. Is it possible to pass this information to them without being sounding like blackmailing? (possibly I need to ask a new question) – High GPA Jun 28 '23 at 11:45
  • @HighGPA Is there a specific reason you want to make sure they're aware of the costs of the mistake? – vspmis Jun 28 '23 at 11:57
  • @SpaceGiraffe To signify the importance of our results. Now they decide to work on something else and assign my paper low priority. I'd like to have them understand that our results are important. – High GPA Jun 28 '23 at 12:41
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    @HighGPA Well, the good news is they don't need to understand or admit the importance of your results for you to be able to publish your results. It would be nice, yes, I agree completely, but do you really need it? The described effect of your correction will do much better job signifying the importance than their awareness of it, wouldn't you agree? – vspmis Jun 28 '23 at 18:04
  • @SpaceGiraffe Yes I do agree. So it seems like everyone agrees that my statement of "saving the community a lot of money" sounds like a nasty manipulation. – High GPA Jun 28 '23 at 19:11
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    @HighGPA I'd say more "insinuation", but, yes, that's the one. Main point is that that statement doesn't improve your proof, but that statement can certainly be used against you to question your intentions and character. Therefore I don't think it's worth adding. Matter of fact is even if your proof would save exactly 1 cent, it's still important and worth addressing in timely manner. That's just scientific integrity. You gave them all the chances, now just give them the timeframe and publish your proof. – vspmis Jun 29 '23 at 06:57