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I asked a similar question previously, though this is more specific and directed. In the writing of mathematics research papers, when is information cited, such as definitions? I have read that if it is fairly recent, then cite it. But what is "fairly recent?" Also, should books from whence a definition came be cited? In other words, what deems something cite-worthy? I have read several articles on the matter and it all was very vague.

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"should books from whence a definition came be cited?" - why not? Better to err on the side of caution with respect to citations... –  Ｊ. Ｍ. Dec 15 '11 at 2:41
Part of "what deems something cite-worthy" is: the author. You might think the reader is well-served by being made aware of a particular paper, and cite it. –  Michael Hardy Dec 15 '11 at 4:38
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4 Answers

The standard for citation in mathematics papers is very different than in (say) humanities. The AMS Ethical Guidelines say

The correct attribution of mathematical results is essential, both because it encourages creativity, by benefiting the creator whose career may depend on the recognition of the work and because it informs the community of when, where, and sometimes how original ideas entered into the chain of mathematical thought.

As the quote implies, we are often interested in attribution to the original discoverer, rather than the most recent person to use the definition.

At the same time, there is a question of who the audience for your paper is. In general, a high-level research paper will be read (or skimmed) by other researchers and read by some of their graduate students. So the author has to ask herself what citations these readers would appreciate seeing.

If a definition is new enough that it does not appear in any graduate textbooks yet, I think it's good practice to include a citation to some paper, because otherwise people may mistakenly think you made up the definition. As a general rule of thumb, if you are going to say "This is a definition of Smith", you might as well include a reference to some paper by Smith, and this will prevent some poor graduate student from an afternoon of trying to locate the definition in the wrong paper.

For definitions that are in the standard textbook(s), it may be better to just cite one of the textbooks, if you think readers may not be familiar with the definition yet, or to just indicate that the definition is standard, if most readers will already know it, or say nothing, if the definition is completely standard.

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The first rule of academic honesty is: if in doubt, always cite. There is simply no downside, and it may help readers unfamiliar with the literature.

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Definitions that "every mathematician knows" need no citation. For example, if you define $\mathbb{N}$ as the set of positive integers (or, if you like, the set of non-negative integers), you do not need a citation.

"Fairly recent" means that there is currently no consensus, that is, other people have different definitions, terms, or notation for the same concept. I would say "fairly recent" covers the past few decades.

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An alternative interpretation of "fairly recent" might be "it hasn't been included in all the usual textbooks"... –  Ｊ. Ｍ. Dec 15 '11 at 3:08
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I've always been told to use the APA citation style.

APA citation style refers to the rules and conventions established by the American Psychological Association for documenting sources used in a research paper http://www.apastyle.org/

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Welcome to math.stackexchange. Note that your answer doesn't address the question (which is over two years old). If you want to contribute, it might be better to find newer questions that don't already have good answers. –  mrf Feb 9 at 14:29
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