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I have seen this enough times that I thought it was common practice, but I recently saw someone on a website about writing tips (can't find the link now) say that this was not good. I am hoping to get opinions from people who review or make publication decisions about whether this is viewed negatively.

Examples:

In [3], the authors prove that...

Our theorem generalizes the results in [ABH], showing that...

I kind of like it---it seems clear and succinct. On the other hand, I can see how someone could object to it.

Hope this is on topic for MO.

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    $\begingroup$ My advisor, who taught me about writing mathematics, said to use it sparingly, but said it's alright. He said it was acceptable if used properly. Sort of like the nomer "we;" don't use it too much but it's alright if dotted occasionally throughout. Although some people are incredibly strict about the use of "we" or "I" in academia... $\endgroup$ – user78249 Aug 17 '16 at 21:45
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    $\begingroup$ Tangential to the question, I do greatly prefer descriptive, explanatory references of the form [author~year], which seem to me completely fine as nouns, to the opaque [numeral] style which necessitates flipping back and forth... $\endgroup$ – paul garrett Aug 17 '16 at 21:58
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    $\begingroup$ Some journals have specific requirements. Algebra and Number theory requires the citations to use author names over just numbers; they usually don't even abbreviate the names. So "In [S] it was shown..." would not be acceptable, but "Siegel showed [Siegel, 1993]..." would be okay. However, they are willing to alter the citation styles and grammar as appropriate for you, and just have you review the changes for correctness. Personally, I find the [ABH] style better than [3], and in fact this style seems to be how people I know actually converse about the paper. "Didn't ABH show..." $\endgroup$ – zibadawa timmy Aug 17 '16 at 22:29
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    $\begingroup$ Discussed on Academia.SE. As of this writing, there's a +18 answer saying "No", a +22 answer saying "Yes", and a +28 answer saying "Ok if you use a citation style that includes names". $\endgroup$ – Nate Eldredge Aug 18 '16 at 15:16
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    $\begingroup$ This is the classical "\citet" versus "\citep" question (lookup natbib). In particular, it's ok to use "The proof is in [3]" but it is not ok to say: "It was shown by [3]" --- in the latter case, we'd say: "It was shown by Siegel [3]" or similar. If you use natbib, the latter is where you'd use \citet, and the former ("in [3]") is where you'd use \citep.... Whether it is [n], or [Sie27], or something else is more up to the journal's style requirements. $\endgroup$ – Suvrit Aug 18 '16 at 19:03
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First, I do it all the time and don't really see the objections. A phrase like "In [S] it was shown..." is a good alternative to "Siegel showed, [S], that ...".

Out of curiosity I did some cursory research and looked up the citation habits in Annals of Mathematics 1958. There one author (R.D. Anderson) does use "In [1] we considered..." and "an argument in [4]". On the other hand Dold sticks to phrases like "due to J.C. Moore [11]" or "defined by Eilenberg-MacLane [4]" as opposed to "defined by Eilenberg-MacLane in [4]".

So the habit is quite old. On the other hand, the list of references at the end of the paper has not been around forever. Again some research I did during some idle moments in Oberwolfach showed that a shift took place in the 1940s-50s. Before, references were handled either inline or via footnotes. Clearly these cannot be used in noun form. Instead,repeated references to the same paper were done using the rather clumsy phrase "loc. cit." or "the third paper by Siegel, cited above". Maybe the objections come from this time.

Edit: After reflecting on this issue a bit more I found that even though this style of citation is per se admissible it does have a pitfall which one should be aware of: It makes it all too easy to avoid naming an author explicitly. I consider it as very bad practice if somebody's name appears only in the references.

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  • $\begingroup$ Agreed, it flows much more naturally in comparison to the converse. Sort of like writing "u" instead of "you" in a text message. Technology and innovation has turned everything into shorthand. Nothing wrong with that. $\endgroup$ – user78249 Aug 17 '16 at 21:49
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    $\begingroup$ @james.nixon, it is not at all like writing "u" in place of "you" in a text message. Article references have an author name (or names), tite, journal name, year, pages, and so on. A format that allows this to be abbreviated is quite different from saving a half-second of your life by simplifying a three-letter word to a single letter due to an accident of pronunciation. $\endgroup$ – KConrad Aug 18 '16 at 4:39
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    $\begingroup$ "Technology and innovation has turned everything into shorthand. Nothing wrong with that" : I disagree with that opinion. I think that it is extremely important that math texts should be clear and easy to read (or even pleasant). Obviously it is much more pleasant to read "defined in Eilenberg-MacLane [4]" than "defined in [4]", and as a reader I don't want to keep turning pages all the time to check the references. $\endgroup$ – Matthieu Romagny Aug 18 '16 at 14:45
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I think it enhances readability to write: In Ref. [x] ...

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