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I am asking this question to get further perspective on an issue that has come up with a student (undergraduate, mathematics) I am mentoring. At last summer's REU he wrote (in particular!) a solo paper. I was not directly involved with the research, but I gave him some feedback on the writing before he submitted it for publication a few months ago. He has now received a referee report, which is very positive and is of the sort that I would recognize as being 99% likely to lead to acceptance. The referee requests revisions, many of which I agree with.

However, one of the referee's suggestions is for the student to not explicitly state two well-known theorems that he is making use of. (In case it helps to know, these are Dirichlet's Theorem on primes in arithmetic progressions and Minkowski's Convex Body Theorem.) The referee follows up by saying that even if he does want to state them, he should not give citations to them, since they are so well known and google searches easily turn up references.

My questions:

(1) How would you respond to this referee request if you were the author?
(2) How would you advise a young student to respond to this request?

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    I have added a link to clarify the meaning of the REU acronym, which may be unfamiliar to readers. If I did not pick the intended meaning, feel free to revert the edit, but please insert a link to the intended explanation. – O. R. Mapper Feb 14 '16 at 19:11
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    If it were my paper, I'd leave the citations in the paper, explaining to the editor the reasons for doing so, but adding that, if (s)he really insists on deleting them, then I'm willing to comply. That should remove the danger of getting the paper rejected over this minor issue. (The relevant insistence would be the editor's, not just the referee's.) – Andreas Blass Feb 15 '16 at 1:40
  • Are the citations to the originals or to textbooks? – Noah Snyder Feb 15 '16 at 1:55
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    Three brief comments: 1) The fact that I know (roughly) what both those theorems say probably means that the intended readers of the paper really don't need their statements. 2) I find the referee's suggestion of giving an explicit statement without reference bizarre. More typical practice would be the opposite, in my experience. 3) I would advise the student to follow the referee's suggestion to leave out explicit statements (assuming my comment #1 is correct). It's just not important enough an issue to make a big deal out of. – Mark Meckes Feb 15 '16 at 15:38
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    One thing to keep in mind (although it need not apply here) is that it's sometimes necessary (and often helpful) to know the precise formulation of a well-known theorem that is used -- there can be subtle differences in assumptions and conclusions that would trip up a reader looking at the wrong formulation. For this reason, I tend to give references wherever I can, although I would only include the full statement (with citation!) if I a) expected that most readers would have to (or want to) look it up and b) wasn't already pushing the page limit... – Christian Clason Feb 15 '16 at 18:17
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I would recommend approaching a referees recommendation to drop a citation in the following manner:

  1. First, consider carefully whether there is good reason to keep a citation in the paper at all. The key factors to consider are reading audience and the customs of others in the field. For example, in cross-disciplinary work I have often cited extremely basic material because core dogma known by every undergraduate in one field are sometimes viewed as nearly unbelievable statements in another field. On the other hand, students in particular are sometimes prone to over-citation because they have been well-trained in citation and decide to err on the side of caution.

  2. If a citation is warranted, consider whether to use the primary source or a textbook source. Notation and interpretation change over the years, and for purposes of elucidating a well-known result, a readily accessible modern text is often a much better citation for the reader than a difficult to find or understand original. In certain cases, however, returning to the original is important: for example, the standard interpretation of the Turing test is different than what Turing originally proposed.

  3. Whether the decision is to keep the same citation, change the citation, or drop it all-together, in responding to the referee one should explain carefully why one made that decision. I would be startled if a paper could be imperiled by deciding to keep a citation when a referee recommended dropping it---it's just such a minor issue, all things considered. With a careful explanation of how the choice has been reconsidered and the final decision, most referees are likely to be sufficiently satisfied, even if they might have chosen differently.

Bottom line: no paper is going to be put in peril by a few extra citations as long as the author is reasonable in explaining their decisions. The citations might ultimately get dropped or not, but in every case we are talking about "minor revisions" territory and not the boundary between "major revision" and "reject."

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Here are my answers:

(1) Erring on the side of being slightly more careful / explicit / wordy has never hurt anyone. I agree that a large majority of the readers of this article will know the theorems of Dirichlet and Minkowski, but if some do not then omitting the statements signals that the paper is not for them whereas including them makes it much easier for them to continue reading. (Of course I agree that anyone can google and find the statements of these theorems and it is easy to do so...but it is even easier to put the paper down and go on to something else if your interest was borderline.) On the other hand, a reader who knows these statements well can just skip them: no problem. So provided that as an author I had made the expository choice to include these theorem statements, I would not be easily talked out of it by a reviewer. As to whether I would actually have done this: I have a paper where I state MCBT. I often say "by Dirichlet's Theorem" (more often: "by Cebotarev density"!) and assume readers know what I mean.

In terms of citation: I don't like the idea of a referee talking an author being talked out of citing work that they use in the paper. It feels like getting pushed in the wrong direction. I have to admit though that I would not myself cite either of these results, and I do have some sense that if you cite things which are too basic then people start to wonder about your background. ("No one cites Einstein..." And Einstein came after Minkowski and way after Dirichlet.)

(2) Not lightly do I advise anyone to do anything which could result in their paper not being accepted. But in this case I am tempted to advise the student to leave in the statements. He should respond to the referee: for instance if his response includes other papers published in the last decade by the same journal which include statements of one or both of these results, his case looks strong. That one should not rewrite papers so as to make them harder to read seems like an important lesson.

I am tempted to tell the student that I would not include these citations and the referee is really correct that they are not needed. If he does want to leave them in, then maybe he should go "whole hog" and include primary source material. I haven't seen many contemporary math papers with works by Dirichlet and Minkowski in their bibliographies...but I wouldn't mind at all if I did see them.

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    I've known a few mathematicians that, when they opt to cite something, insist on citing the oldest, most primary source material they can find. Even when more modern and accessible versions exists. I recently cited a result of Remak (early 1900's) in a (joint) paper. While the result is almost certainly either very well known to group theorists, or considered easy to prove on first sight, no modern reference for the result could be found. And the intended audience was more algebraists than group theorists. Thankfully the paper was actually freely available online. – zibadawa timmy Feb 14 '16 at 19:56
  • I cited Archimedes once, but it was out of playfulness --- I could not resist! I would advise making habit out of it though :-) – Boris Bukh Feb 15 '16 at 1:11
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    I do have some sense that if you cite things which are too basic then people start to wonder about your background. There's definitely a potential issue there. I've seen a paper, written by a student, which stated the Cauchy-Schwarz inequality as a lemma, which struck me as ridiculous. But it's not obvious to me whether Dirichlet and Minkowski are on the same side of the line as C-S (and, of course, where the line is depends on the paper's audience). – Mark Meckes Feb 15 '16 at 15:28
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Citations serve two purposes:

  • Acknowledging the original source of ideas
  • Giving readers easy access to a source to read more about a result that they may not understand.

In the case of standard theorems that are named after their discoverers and which are sufficiently famous to be in Wikipedia, I don't think citing a textbook accomplishes either of these goals. It's much faster and easier to google the theorem than to find the particular text mentioned.

I don't think there's any harm in this kind of citation, so I don't know why the referee cares. But I also don't see a good reason to include them.

If anything, I would cite Wikipedia with a hyperlink. That at least saves your reader some time.

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    ... and some referees will revolt at the notion that Wiki is a legitimate source for anything at all... (which I think is foolish, but nevermind). – paul garrett Apr 5 '16 at 15:15
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Well I'm sure you've already made your advice by now, but for future reference, here is my perspective.

First, my general philosophy is that one should try to make papers reasonably accessible to young people who have not spent months or years working on this specific problem. I generally feel that most math papers should do a better job of providing references than they do.

(1) I would hear the referee's suggestions and with those in mind, I would rethink about whether it is worthwhile to include references, taking into account both how well known those specific results are and the target audience (whether I would specifically refer to those theorems of Dirichlet and Minkowski depends on who I am writing to--for a "regular" research paper, I would probably do the same as you). As a somewhat experienced mathematician, I think I have a reasonable idea of what is worthwhile to provide a reference for and that I can make suitable decisions on my own. However, referee reports constantly remind me that things I think are obvious or well-known are not obvious or well-known to a lot of people. Consequently, what one thinks should be included as a reference varies a lot from person to person.

(2) When I was a student, I viewed comments like this from referees and my advisor as learning experiences about what to include and not to include. I would first of all tell the student (i) you don't have to make all changes the referee suggests but (ii) you should consider them seriously. However, as people may have different perspectives, and the student has limited experience, it would probably be useful for the student to hear other perspectives (e.g., yours and possibly another colleague's). After giving your advice/suggestions, let the student decide what exactly to do (as I'm sure you would).

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