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Are there known cases of plagiarism in mathematics? The writing practices in mathematics are clearly different from the writing practices in the humanities. In the latter area I roughly know how to characterize plagiarism because examples are known. But I do not know how plagiarism is possible in mathematics, except for blunt copies of text.

Do you know about examples how plagiarism in mathematics looks like?

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    One anecdote: someone cut and pasted bits of the PDF copy of one of my old papers (arXiv version) into the Word document that constituted their paper, which also cut and pasted bits of my abstract that referred to things which were not present in their plagiarized version. It was pretty inept, to be honest. The journal in question deleted the paper from their website but never made any official acknowledgement of plagiarism – Yemon Choi Jan 28 '17 at 14:43
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    I've had an experience similar to that of Yemon Choi; paragraphs of my book were pasted verbatim into a submitted paper. I think they were subsequently banned from submitting papers to that publisher. Of course, this is not public knowledge as there is no need for it to be. I imagine there are many such anecdotes. – David Ketcheson Jan 28 '17 at 17:02
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    Many examples can be found on retraction watch: retractionwatch.com/category/by-subject/… – CWsl2 Jan 28 '17 at 18:00
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    I was recently plagiarized for the first time, earlier this year I think. And I'm kind of a nobody in my field (Banach spaces). So if someone's going to plagiarize me, they'll plagiarize anyone. – Ben W Sep 17 '18 at 0:59
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    @BenW: The better known the plagiarized work the more likely the plagiarism is to be detected. A typical motivation for plagiarism is to add to publication counts, and the typical plagiarist has little interest in having the plagiarisms read, so the natural tendency would be to plagiarize little known but respectable (so republishable) work. – Dan Fox Dec 31 '18 at 9:26
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The American Maths Society has been caught:

A plagiarised book on maths history.

Another notorious case concerned an Eastern European academician in the bad old days. He began with a bit of self-plagiarism, re-publishing his own works in English language journals. But then he moved on to translating and publishing as his own papers from Russian journals. He was exposed when a Russian mathematician, on moving/escaping to Paris, discovered that his best theorems had been stolen. I think the AMS published an analysis of the whole sad affair.

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Plagiarism of profound and significant results in contemporary mathematics research seems to be close to nonexistent. It’s antithetical to the culture of the discipline and the likelihood of success is remote when the spotlight is bright. Around the more dimly lit edges, however, it can and does happen from time to time as attested to in the comments.

I’ve encountered it myself. In 2012, after publishing some results in matrix analysis, I contacted an academic who was doing research on similar topics who I thought might be interested in some of my results. I summarized my results and we had a brief exchange and our correspondence ended not long afterwards. A few years later, in 2015, I attached some appendices to my full-text version of the 2012 paper at researchgate.net to help assist readers of the paper with illustrative examples and related MATLAB code. Upon posting it, I noticed that someone at the same Spanish university as the academic’s co-author had almost immediately downloaded the updated full-text. Then, later, in 2017, I came across one of their publications that took the same novel perspective, had nontrivial mathematical overlap, and similar MATLAB code generation results as my 2012 paper with appendices. Notably, there was no citation for my 2012 paper listed among their references. Instead, they (Lebtahi and Thome) had trotted out their results as if they had come up with it all on their own, apparently assuming I wouldn’t notice this violation of academic integrity. I sent an email requesting an explanation, and after more than a year and a half of attempting to work something out with them (and mostly being ignored), I’ve largely accepted that no meaningful action will be taken on their part, and attached yet another appendix to the article full-text detailing the transgression as I see it [if interested, you can look over Appendix E by accessing the full-text link accessible from here]. As to what their motivation was, I can’t say for sure. Was it tied to career advancement? A struggle for tenure? The idea that they could lift results from a relatively obscure journal without offering credit and get away with it?

At any rate, unlike priority disputes (which still happen from time to time), accusations of plagiarism that relate to the central core of mathematical research seem to be largely a relic of the past. Perhaps the most famous mathematical plagiarism accusations were hurled during the acrimonious debate between Newton and Leibniz on the development of calculus. Although a number of historical accounts suggest that this development was independent on the part of both parties, there are several indications that Leibniz was less than forthcoming about his knowledge of the research results obtained by others. One fascinating discussion about this appears in the excoriating book review that Brian Blank gave in the May 2009 AMS Notices (Volume 56, Number 5) for the book “The Calculus Wars”. As one example, on page 609, Blank points to evidence that suggests Leibniz’s Tentamen de Motuum Coelestium Causis was based on his uncredited reading of Newton's Principia. This book review is superbly written, and provides interesting details about this historic mathematical event. For those interested in the calculus controversy, I highly recommend checking out the review.

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    Consider contacting Prof. José Alberto Conejero Casares who is the director of the dept of applied math at UPV Universitat Politècnica de València where Lebtahi and Thome are. – Just_to_Answer Dec 29 '18 at 2:17
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Yes, there have been. One case is publicly documented here: http://www.mathematik.uni-marburg.de/%7Egumm/Plagiarism/index.htm and another one documented at http://de.vroniplag.wikia.com/wiki/Ry that is a doctorate in chemistry containing much mathematics. The book has been withdrawn and the doctorate has been rescinded.

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Are there known cases of plagiarism in mathematics?

Yes. Retraction Watch has a searchable database.

Do you know about examples how plagiarism in mathematics looks like?

A search for (PHY) Mathematics with +Plagiarism of Article OR +Plagiarism of Data OR +Plagiarism of Image OR +Plagiarism of Text found 72 articles on 29 December 2018. Browsing these would provide example of plagiarism in mathematics.

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Some obvious examples could verbim that looks like:

https://www.reddit.com/r/btc/comments/8b5j7h/heres_the_paper_that_the_theorems_in_wrights/

Other non-obvious but famous case is the (suspected) plagiarising of Perelman's proof on Poincare Conj.

https://www.newyorker.com/magazine/2006/08/28/manifold-destiny

https://projecteuclid.org/download/pdf_1/euclid.ajm/1175789085

Two established mathematicians admited that they "forgot" to read about a famous "theorem widely understood by the experts in the field". I will leave the judgement to yourself.

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    How is the Perelman case related to plagiarism? – Tobias Kildetoft Dec 30 '18 at 9:33
  • @TobiasKildetoft There were two mathematicians who claimed that they proved Poincare but later withdrawed the claim. All their Lemmas used were taken from Perelman's work, and all the useful Lemmas were already proved by either Perelman or someone else. They proved one of the Lemmas indeed but it is not useful in the Conjecture. They cited none of the sources. – High GPA Dec 31 '18 at 8:25
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Plagiarism in mathematics is much similar to plagiarism in programming. People often try to manipulate the original equations to make them look like a new one.

Quite possible that people try to change variables or try to write the same piece of code in a different language. Same goes for core mathematics.

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