"Storytelling" in the introduction: Math papers 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.
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.