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This question is about best practices of writing manuscripts in mathematics.

Q. How much "storytelling" in the introduction section of a math paper is "appropriate"?

To clarify what I mean by "storytelling" let me give an example but of course one can find numerous of such cases: In the introduction of a math paper(which I'd rather to keep the names anonymous) almost half of the first page is dedicated to saying what happened in friends gathering and that the author bet on bottle of wines that certain problem has solutions and what not. It was really annoying to me. I wondered why readers need to know all that and how are these stories are even relevant?

Side note: It seems to me sometimes journal editors demonstrate double standards and approve/disapprove this "story telling" matter depending who you are and where you stand in the field.

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    It also depends on the venue. Often this kind of things is accepted in special and "Festschrift" issues (i.e., "for the 65th birthday of prof. Bigname"), but not in regular papers. – Federico Poloni Nov 14 '16 at 21:15
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    I am starting to feel that the word "ethics" is being drastically overused on this site. Is determining the maximal amount of allowable fluff in the introduction of a math paper really an ethical issue? At the moment I'm not seeing how. (As a picky side note, the phrase "scientific manuscripts in mathematics" is maybe a little strange. What is an "unscientific manuscript in mathematics"?) – Pete L. Clark Nov 14 '16 at 21:19
  • @PeteL.Clark good points. Icorrected the second one. Regarding "ethics" being over used, in case of my post it is merely because of the fact that I could not find a better word. I definitely welcome suggestions slash edits. – BigM Nov 14 '16 at 21:25
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    I made an edit with some language / tag changes. Feel free to roll back if you don't approve. – Nate Eldredge Nov 14 '16 at 21:39
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    I like the stories I've read in papers (and elsewhere). – Antonio Vargas Nov 14 '16 at 22:01
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I propose the following guideline as a basis for answering your question: what is "appropriate" is for the author(s) of the article to try to write the best paper they can write, and for the journal editor and reviewer to make helpful suggestions about small changes the authors can make to improve the paper even more. In my humble opinion, the editor should generally not require changes to the paper unless they feel that they are seriously necessary to keep the quality of the paper at the standards of the journal. Thus, there should be a bit of room for authors to impose their creative vision on the work, which also includes the freedom to make wrong judgment calls that annoy some readers.

If you accept the premise above, it follows that if the authors of the paper thought the story with the wine bottles makes the paper better, the editor should let them include it, even if he/she personally disagrees with the decision.

TL;DR: within reasonable limits (and half a page sounds reasonable to me), it is the authors who should decide what is appropriate. Some readers may be displeased, but that is true about almost anything that one writes.

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Seconding @DanRomik's answer, I think that it is generally harmless to inject anecdotes, even if silly or frivolous, but vaguely connected to the issues at hand, if only to avoid the other (extreme) tradition of "austere formality". At its worst, the latter implicitly includes a pretense that we are trans-material entities without human failings, etc., which might in itself be off-putting.

The point is that people who don't want to read (small) frivolous bits can skip over them, while people who might be soothed by small frivolous bits may not be easily able to imagine them in the context of a cold, austere discussion. I certainly do not wish to pretend to mandate chattiness for those disinclined, but (if it does not compromise the precision of the mathematics) in small doses it's surely harmless.

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