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Continuation of this post.

Basically, I emailed a publisher and two profs, asking for help on a paper I had written but not submitted. Turns out the method was not as novel as I thought, as an MSE post containing pretty much the same derivation was posted in 2016. Now, I'm trying to figure out how to break the news to them.

Off the top of my head, I considered saying "actually found it's been done before", but not sure how good that sounds. Probably this is as bad as I think it sounds, but any advice making it sound the best?

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    I've just been re-reading a biography of Alan Turing. One of his first results as an undergraduate was a proof of the Central Limit Theorem (which turned out to have been proved about 10 years earlier). So you're in good company ... – Ben Bolker Nov 27 '20 at 20:54
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    @BenBolker darnit. I was just about ready to submit my proof of the Central Limit Theorem. – emory Nov 27 '20 at 21:12
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    Did they reply to your initial email? – Noah Snyder Nov 27 '20 at 22:29
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    Ok, then Mark's answer is great. If they hadn't replied then I would have written an answer saying to just drop it. – Noah Snyder Nov 27 '20 at 22:31
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    Can you explain why "I actually found this has been done before" doesn't sound right to you? That's pretty much what I'd say in an email. – Simon L Rydin Myerson Nov 28 '20 at 11:31
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Don't worry, we do that all the time (figuring out something has been done/shown before). It actually shows that you do your work.

Maybe give a link to the other solution/work as well in case they are interested (though this is coming from a very different field).

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    How exactly do I phrase the email assuming that they are at the current stage of asking me the pdf? – Buraian Nov 27 '20 at 22:32
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    Yep! It happened to me too. I had a project that needed to compress a large range of numbers to fit in a small space, and I only needed logarithmic accuracy, not linear. I thought that IEEE 754 was too complicated for what I was doing, and I didn't have a floating-point processor anyway, so I invented my own. By the time I had solved all the problems though, I had simply re-invented IEEE 754! (at least I understand it now) – AaronD Nov 28 '20 at 20:32
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    @Buraian Cite the proof you found in your article. Render that as PDF. In your email: "Professor ____, I've attached the PDF as requested. Since we last communicated, I have discovered my approach has already been published. I've cited in my PDF appropriately, and you may find that existing publication at: [URL]. Notwithstanding, are there any improvements you feel could be made to my article? Thank you for your time! Sincerely, _____" – bishop Nov 30 '20 at 14:53
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This is actually excellent - it shows you're doing due diligence and that you're willing to be wrong. I would expect the professors to be legitimately impressed.

I would write something like 1) sorry for the hype the original email included, because 2) I found out it's already been done before and here's the link, and 3) thanks for your time. Who knows, they might say your derivation is publishable anyway.

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  • Well, OP is only so "wrong" considering they seem to have actually found the "right" answer, just a few years after someone else. – corsiKa Nov 29 '20 at 8:17
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This happened to me as well and is absolutely not uncommon in my field (maths). It did not prevent my paper to be published. So I would not worry at all. Actually, this is great because it is very unlikely that you both have exactly the same results so you may even be able to enrich your own results with new light on a similar problem.

You could add a discussion (which can potentially be just a couple of sentences) in the paper that goes along these lines:

" A similar approach was derived indepedently in [?]. However, blabla"

where blabla = some difference in the approach itself, in the observations about this approach, in the applications of this approach or provides a simpler/different proof, etc.

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    Problem is the actual paper which was prepublished on this was wayyy more extensive than anything I could do/ thought of while writing mine. – Buraian Nov 27 '20 at 22:33
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    It happened to Terrence Tao about a year ago. Compare the abstract of arxiv.org/abs/1908.03795v1 to the abstract of arxiv.org/abs/1908.03795v3 to see how he handled it. Quoting v3, the formula has "appeared in some form or another (albeit often in a lightly disguised form) in over two dozen references, and being independently rediscovered a half-dozen times." – Brian Nov 30 '20 at 21:57
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You have done due diligence and are honestly reporting that it has been done. Sad for you, but straightforward to explain.

Say that you unfortunately discovered that the method and proof is already known. You could express regret to have imposed on their time.

On the good side, you have shown that you are trustworthy, honest, thorough and that you have been able to prove something that is true. It's not as good as a paper, but it is definitely not working against you, just the opposite. You have shown yourself to be a professional.

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Answering somewhat generally. Having derived the method independently, you're now in the unique position of having all the necessary mental machinery to think deeply about the problem:

  • Does the preexisting work leave gaps?
  • Are there extensions to the approach?
  • Are there alternative routes that would provide the same result. Sometimes it's useful to prove the same thing in many, many ways?
  • Can you apply the technique to solve some applied problem?
  • If the problem is computational, can you achieve better performance by substituting some components?
  • If the problem is algorithmic did the previous authors release the source for their implementation? (If not, were they even doing science?) Venues like JOSS provide a place to get implementations reviewed, even if the method has already been published somewhere.
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Don't worry about it.

Results and methods are rediscovered many times over and in many different fields as well.

When you find it out, what you can do is to add some note "I was made aware of this person having previously done somthing similar" and then you cite them in your papers. Quite rarely the formulation is exactly the same so even if you rediscovered something similar or almost the same, maybe you had a different approach leading to the same conclusion.

In many things science the results are not the most important question, but how you get there.

Maybe you derived your method through an algebraic approach while someone else used a statistical techniques to reach the same result or develop the same method. It can be valuable to add both these approaches to the body of knowledge as often in science it is the concepts and approaches rather than results or methods which are very valuable in discovering new things.

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Leibnitz and Newton independently developed calculus, so you are in good company. Just inform others that you independently developed a solution. This happens all the time.

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  • This is not entirely clear. I believe to have read that Leibniz and Newton once met in their earlier years and may have discussed calculus-related ideas. If my memory is right, such a meeting sounds plausible, because it renders acrimony in their battle so much more understandable than if they had discovered it separately in that the contribution of the other side would have been expressly at stake here. – Captain Emacs Nov 28 '20 at 1:03
  • "Just inform others that you independently developed a solution." Then engage in a decades long feud with the person who previously published it. – Acccumulation Nov 30 '20 at 5:26

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