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I need to write to several academics with a very similar request. Would it be disrespectful if I just copy-paste most of the body of the email, and change just the person-specific details?

On one hand, nobody likes mass-produced emails. It could be irritating for them and embarassing for me if one of them forwards the email to another, and the similarities become clear. On the other hand, what I need to say in each case is very similar, so once I write one "optimal" version of the message, it's hard to see how and why to produce another version.

For context: I have been working at a problem which is somewhat outside of expertise of me and of my supervisor (I'm a PhD student). I think I have a solution, but I am not sure how original it is and how interesting it is. It could well be that it's been known for decades, but I can't find it because of differences in terminology. Hence, I would like to write to some people who have more expertise in the field. The email explains roughly what the problem is, how I came to consider it in the first place, how the solution works, and what what specific pieces of the work of people I write to make me think they might be interested in problems like that (this is the person-specific part). If relevant, the field is pure mathematics

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    The main issue I could see is if they are not aware that you have asked several people and they independently take the time to provide the same information for you, in which case some of that time will have been wasted. – Tobias Kildetoft Nov 26 '16 at 9:02
  • @Tobias Kildetoft This is a valid concern. To deal with this, Jakub should make sure that the asked persons represent different perspectives (for example, they shouldn't be co-authors of multiple related papers), and he may start with a limited sample of persons (say, three authors of the most closely related papers) and extend the sample step-by-step, depending on the reaction. – lighthouse keeper Nov 26 '16 at 9:17
  • And then if they all come back with a similar answer, which contributes to the problem, they could all seek co-authorship on the paper... I think it's better to either send to a couple at first (as commented above) and/or notify them that you have already contacted these other people apart from you. – BioGeo Nov 26 '16 at 10:07
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It is not disrespectuful per se to send bulk e-mails. Academics get them all the time: conference announcements, field-specific mailing lists, automated e-mails from submission systems. If it is appropriate for what you have to do, there's nothing wrong with it.

However, I consider disrespectful the way you want to use them. If you just want to know if something is already well-known in the field, start by contacting one researcher. Writing to 100 of them means unnecessarily wasting their time.

Also, it seems like you want to put the introduction of your paper in an e-mail. Don't do that. Keep it short. Your paper should already contain an introduction with motivation and previous research (to the best of your knowledge).

Similarly, for the same reason of not wasting people's time, you want to make sure that your paper is readable to people working in that research area. Make sure that you know the basics of the field and use accepted notation. If your paper looks like it's written by a crank, most recipients will file it directly into the recycle bin.

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There are two situations. One of them is a brief, "announcement" email. Something like, my PhD defense will be on such and such a date, at such and such a place. That is fine for mass, "similar" emails.

That is not your case. Here, you are writing a fairly detailed email (about your problem) that requires a detailed response. As another poster wrote, in such a situation, you should be sending out such emails one or two at a time, not 100 at a time. Then it follows that your solicitation emails should also be more personalized/individualized.

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The person-specific part is crucial to how your e-mail will be perceived. I think there are two important thoughts here. First, put the person-specific part to the beginning of the e-mail, so the person will feel addressed personally. Second, make sure that your description of the person's work is specific enough to signal a non-superficial understanding of their work.

Since some people are scared by long e-mails, it might make sense to defer the discussion of details to a second e-mail, in case they reply to the first one with interest (or at least send them in an attached PDF file).

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