Question

I'm writing up a paper and I'm not sure how to cite a few things. It concerns a conjecture made by Quillen. Some work has been done showing it's true in some cases, false in others. These results I found in a book that had a chapter about the conjecture; of course, the book gave all the references. In the background of my paper, I want to briefly sum up these results. My question is, should I cite the articles, the book, or both? I wasn't sure what the etiquette/rules are in this situation.

Answer 1

The one sided answers neglect the complexity of the issue. First of all most of the papers in the science are nowdays difficult to judge, survey and check for an average reader, not to mention the users like science agencies and general public. The production is huge, there is lots of repetition and formalism differences make it difficult to bring knowledge and fruitfulness to the public and we need to fight this not by messy inclusion of everything but by making honest and informative choices to the reader. So, the main criterion is to write primarily for the reader and the author should have the stand weather the article she cites are likely to be useful to reader or not at all; if one does not take reader as the main criterion but some agenda of pushing the agenda for agencies, why would then the reader respect author's agenda of misleading the reader which reference is good and readable just to fulfill the political agenda ? In mathematics, the pointers from the text to the bibliography, together with the basic standard knowledge in the field should make obvious path how to achieve the results in the paper. This is already a difficult goal and making references only by history and not lead by self-analysis of the paper and its predecessors will make it too difficult to reconstruct the preliminaries used. Of course, one needs to account for balance in making clear what the original resources are either by making clear pointers to other surveys and also citing directly relevant and used work with some emphasis on the "primary" sources, where the latter term is not fully well defined, as each idea has some predecessors.

I disagree with much of the answer and comments of Deane Young, who is on one hand saying cite generously much, cite when in doubt etc. as if we live in an ideal world where the size of bibliography is allowed to be as large as you want, (Example: One of my papers was delayed for 2 years because it was 19 pages and the limit in the journal was 17. Roughly, two pages where bibliography.) and on the other hand saying that we live in a bad world where people depend on our citations, so cite even if you did not read/check and where we need to adapt to "funding agencies". Well, if we all adapt to present treand in funding agencies we agree with a wrong attitude that the citation is proportional to research credit what is not true: often the most cited are often surveys and books, popular digests, and also some original papers which are often only famous but nobody reads, or can read (so many times they are more readable than the public thinks, by inertion). It is better to push the agencies to take this into account and fund according to the full description of the discoveries of the author and description of their impact by listing consequences and new directions opened, and not of numerical quasi-impact. Conforming to numerical quasi-impact as a main principle may exactly push down honest people who cite only papers they trust, they check, they believe the authors and so on, we may also cite references which are written in bad way and not recommendable to the reader. To extend this remark to extreme which appears in practice, I know many people who cite famous people just to show that their own work is relevant for the trends pushed by those. This is the worst kind of citation.

There is also a pressure from referees and editors to include the references of their choice. In such cases one has to follow common sense, and decide if the request is reasonable, even with expense of possibly changing the journal. We should not regret the referees' and editor's time if they abuse their position to make people cite papers of their friends and their own; however we should appreciate it in good cases when their knowledge is channeled to point to the sources we did not use or appreciate and to learn what is the better or more original reference in many cases.

Answer 2

I feel compelled to repeat and stress my answer: Cite generously and often.

Some have expressed the principle of citing only references that they have read themselves. This seems attractive as some kind of ethical principle, but I believe it is misguided. It would make sense only if most people in the math community assume this when they see references in a paper. But, as far as I can tell, there is no such common view. References, like everything else in the paper, are there to communicate knowledge, as completely as possible, either by stating the knowledge direcctly or by citing references. When you cite a reference, you are telling the audience that you know about it and not that you have read it.

To me, what is far more important than such a principle is serving the good of the subject and community. Citing generously not only papers you have read yourself but papers you know about that are related to your own paper has the following positive benefits:

• As others have mentioned, it saves people the trouble of having to find things by looking up other secondary references first. Even if the primary source is now known to everybody, many of us want to know who and which paper. Even if the theorem no longer has a name attached to it, say whose theorem it is and where the primary reference is. Why make us chase it down?

• It helps promote and demonstrate the vitality of the topic of the paper. As Andy Putnam mentioned, too many mathematicians are stingy with their citations, making our citation numbers much lower than other fields. This has hampered our ability to compete for positions and funding relative to other fields, because funding agencies and deans have doubts about how many people know or care about our work. So if you know about a paper and believe it to be good work (perhaps based on either other papers you have read or recommendations by other mathematicians you trust), you should cite and help promote it, even if you have not read it yourself.

• Citing contemporaries who have done good work on the same topic helps their reputation and careers. You want them to do the same for your work, so you need to do it, too. Imagine if you were the first to prove a theorem but everybody started citing only the paper that had a much simpler proof.

Let me also give a concrete example: Nash's original paper on isometric embedding is extremely difficult to understand, and, as far as I can tell, almost no one has ever read it. Luckily, people such as Moser and Sergeraert figured out much simpler proofs of the $C^\infty$ theorem, and that's what most of us read and learn. More recently, Gunther found a way to reproduce the full strength of Nash's original theorem using an extremely simple argument. So I have never read Nash's original proof. I think, however, it would be absurd for me not to cite Nash's original paper just because I haven't read it.

Answer 3

A citation should make reader's job easier! A textbook with the best exposition, or a survey with all the relevant references (if it exists) is a preferred choice, especially where the original sources are obscure, hard to locate, and/or read. So I would write, "by a theorem of Perelman (see e.g. [Morgan-Tian, Theorem 1.2.3])".

Speaking about promotion, by the time the stuff that made it into textbooks, this is (usually) no longer an issue, and in many cases the person responsible for the original result may have achieved a god-like status. Then it is common to even omit the author's name, let alone give a reference to the original source, e.g. people say "by the s-cobordism theorem".

Answer 4

When in doubt, cite. Cite the paper, cite the book, and explain what is it where. You've already done the hard part, so let the reader benefit from your work. It does you no harm, and is helpful for your readers.