Post Made Community Wiki by S. Carnahan
1

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.