Should authors omit statements / citations of well known results in response to referee requests? 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?
I would recommend approaching a referees recommendation to drop a citation in the following manner:


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.
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.
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."