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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.

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    $\begingroup$ Probably this question will get answers over at academia.stackexchange.com $\endgroup$ – Dirk Feb 19 '15 at 10:37
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    $\begingroup$ Apart from the content, making proofs as short as possible is something you have to stop doing right this moment. Replace short with simple. They are mountains apart. It is 2015 nobody cares if it is 2 pages longer on a PDF if it makes it simpler. $\endgroup$ – percusse Feb 19 '15 at 12:24
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    $\begingroup$ @Dirk As a user of both sites, I'd like it more to stay here. Papers in mathematics are different from those in most other disciplines, in their structure, contents and in the way people read and use them. This question really is something math-specific that does not generalize well to other fields. $\endgroup$ – Federico Poloni Feb 19 '15 at 12:41
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    $\begingroup$ As a reader, I read the abstract and if I find it interesting, try to get an overall idea of what the main concepts and results of the paper are. For the first and only so far article that I wrote and submitted, I sought some advice from a friend working in chemistry, and she was surprised that I didn't define things like field automorphisms and L-functions. She even said "No context is needed in math??". So definitely, this question is really not off-topuc for this site. $\endgroup$ – Sylvain JULIEN Feb 19 '15 at 13:18
  • $\begingroup$ If you and your co-author are writing a sequence of papers, why not take turns in taking responsibility for the structure of the papers? Also, within a single paper, you might agree on being responsible for different parts of the paper, once of course the overall structure is decided. $\endgroup$ – Igor Khavkine Feb 19 '15 at 13:33
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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.

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  • $\begingroup$ Are you reading articles following the same pattern? Do you always expect to understand the introduction or it does not bother you if you can not? $\endgroup$ – Nikita Kalinin Feb 19 '15 at 17:42
  • $\begingroup$ Say I'd mainly like to find the main result and main ideas clearly stated in some place that I can easily find; the introduction is a natural place. But I don't really bother where. $\endgroup$ – Pietro Majer Feb 19 '15 at 18:30
  • $\begingroup$ There are at least two reasons people would read a paper - for the result itself, and for the techniques used to achieve them. +1 for this answer because following this advice would help both types of readers as early as possible. $\endgroup$ – Rohit Chatterjee Feb 25 '15 at 0:48
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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.

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