Different styles of writing/reading articles

Question

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.

Answer 1

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.

Answer 2

I do not think you are asking the right question. I think the question you should be asking is "How should I structure my article, given the possible ways my audience will read it?". The answer is to make it clear, simple and easy to understand. Naturally, this is easier said than done.

I think it impossible to understand how each person reads a paper - how are you going to put a measure on that? Take someone like me - I have no fixed structure when reading papers.

How I read papers depends on the type of paper, the journal that it is in, the author and most importantly what I am trying to achieve from reading it. Sometimes, I dive straight into the paper and get a high level understanding of what is going on. Then I attempt to replicate the results, only to get confused with something - so I look back and start learning the definitions. Then I start thinking what the point of the paper is - so I look at the abstract. And so on.

Other times I make a concise effort to read the abstract, understand the structure and the author's intentions. I can think of three texts that would be impossible (in my opinion) to read if this approach were not taken:

Brownian Motion and Stochastic Calculus by S. Shreve.

Stochastic Equations in Infinite Dimensions by G. da Prato.

Measure Theory Volume I and Volume II by V. Bogachev.

It is worth reading those books just to see how the authors structure their content - they know the reader is in for a long road (of torture) and take their time to ease them in - they provide intuition, give examples and make you excited about the subject.