Recently, I discovered a rather unexpected thing. We are writing an article in collaboration and we permanently have some discussions about how to write, in which order, how to organize material etc.
Today we have understood that we are reading articles in different maners.
I start from the abstract, then I'm reading the introduction where I expect all results stated clearly and the motivation is explained. If I don't understand the introduction, I don't read this acticle. Then, I am reading the text in the article which is kind of "water". Probably, at the end, I start to carefully check the details in theorems and proofs.
My friend usually proceeds in an opposite way. He skips the introduction, reads only definitions, propositions and theorems, and some stuff around which he could understand. Then, if he is really interested, he starts to read the usual text.
These two approaches result in writing: I care about the introduction, beginings and ends of each chapter, making proofs as short as possible and explaning motivation only in the introduction. I suppose that the reader reads from the beginning till the end. He only cares about all the important thing being stated in propositions and theorems, no matter in which part (in which order) of the paper. He also does not care a lot about the logical structure, but more about motivation explained and repeated.
So, what are possible ways to structure an article? Do you normally suppose that the reader reads from the beginning till the end or just skimming? Does it correlate with your writing style?
It is a big vague and personal, so I expect also rather personal opinions and strategies.
Best Answer
An Introduction, of course, should recall the history, and the state of the art of the problem treated, and give a motivation to it, a description of its difficulties, and maybe how people tried to overcome them. But especially for technical works, I'd like to have, after this general introduction, a special section named Main results, where the main theorem proved in the article is stated explicitly, and the main objects and ideas are introduced, even in slightly less general form than in the text, if this helps the comprehension. Then, a non-technical yet well detailed description of the structure of the proofs, that serves as a roadmap to the main result, with all links to the needed lemmas quoted in brackets. In other words, the explanation of your ideas that you would do talking with a colleague in your field.