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I am preparing my math research monograph for publication.

In the current draft there is certain conjecture.

This conjecture was proved in my drafts (available on the Web) of the second volume for this monograph.

Should I:

  1. just remove the conjecture from the book because it is proved?
  2. leave the statement in the book titled as a conjecture because it's proof is not yet officially published (and also may be not enough checked for errors)?
  3. write in the book that I am going to publish the proof (either in a separate article or the second volume of the book)?
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    I think this has already been answered in response to another of your questions: "a subject is ready for treatment in the form of a book when it is relatively well explored and understood, so that you can write a coherent and definitive account. " You are facing this problem because you are ignoring the advice you've previously been given and trying to write a monograph on a subject that isn't fully understood yet.
    – ff524
    Commented Oct 26, 2015 at 21:06
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    Are you submitting this work to peer-reviewed journals? If not, why not?
    – user37208
    Commented Oct 26, 2015 at 21:25
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    @porton Simple: other researchers will be orders of magnitude more likely to take your work seriously if it makes it through peer-review. I assume your goal is to communicate your research to others, or you wouldn't be asking this question. Even if your work is good, you have to give people a reason to pay attention to it. There is quite a lot of amateur math research of dubious quality floating around the internet, so people are understandably skeptical.
    – user37208
    Commented Oct 26, 2015 at 21:40
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    @porton Why would anyone want to do that, though? I sure don't want to. I'm not going to randomly stumble onto your work, and I'm not going to randomly start doing your work for you for nothing. If you submit it to a journal and I was selected as a referee then if the paper passes first muster I might put some effort into it. But we have lives, you know? And what's more likely: a random ignorant schmuck who thinks he's Einstein edits your work, or Terrence Tao edits your work? There is a HUGE difference between "professional and expert" and "random internet guy". Commented Oct 26, 2015 at 21:49
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    There are too many things to be done to invest time+energy in less-obviously-productive courses. Without previously established "credibility" (whatever we make of this precisely...) there is scant motivation for relatively-expert people to spend time on a large document. In particular, experts have no obligation to look at every thing on the internet and correct or critique it. Many things simply languish. Thus, if you want useful feedback, you'll want to establish some credibility, which probably means playing the traditional game to some extent... not that I'm a fan of tradition. Commented Oct 26, 2015 at 22:19

1 Answer 1

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One of the most important principles of academic writing is that you shouldn't write anything misleading. If you present the result as a conjecture with no indication that you have already proved it, then you are giving readers a misleading impression (namely that you don't know how to prove it), so you shouldn't do that.

Should I just remove the conjecture from the book because it is proved?

That's an acceptable option.

Should I leave the statement in the book titled as a conjecture because it's proof is not yet officially published (and also may be not enough checked for errors)?

Don't just leave it there without comment. If you are worried that the proof might be wrong, you can address this by stating things a little more tentatively. As for whether it is officially published, most of your work seems not to be officially published, so why is that an issue for this conjecture?

Should I write in the book that I am going to publish the proof (either in a separate article or the second volume of the book)?

Sure, why not? It's probably preferable to deleting the conjecture: if it was worth mentioning as a conjecture, then presumably it's still worth mentioning as a theorem.

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