TITLE: How to balance writing professionally and being able to have a conversation with your reader?
QUESTION [27 upvotes]: Background.
I am someone at the very very beginning stages of my career as a mathematician, and am, for example, almost ready to (re)submit my first paper. I have already read a lot of essays on how to write well (i.e. http://terrytao.wordpress.com/advice-on-writing-papers/ is golden), but I still sometimes have doubts on what the best course of action is in certain situations. So that's the reason of this question. If it gets closed, because the only reasonable answer is 'it depends', I completely understand. But it would be great if you could bear with me for a moment.
Problem. To me, an article is (or at least feels like) a written monologue. But, on the other hand, the purpose of a paper is to explain new ideas to your reader, which generally is much more easy in a dialogue. Because in a dialogue you can interact with someone, ask questions to make sure he or she understands and re-explain things in a different way if he/she so desires. So if I am writing mathematics, I try to remind the reader where we are in the argument, why we are there, where we are going next, what the main ideas are behind all the calculations, etc. Let me give you an example: when I read something mathematical that Timothy Gowers wrote, it is immediately clear to me that his goal is to make me understand his ideas. If I remember correctly, his article on his proof of Szemeredi's Theorem by Fourier-analytic methods is over 100 pages long, but his writing style is very leisurely and he first goes through the case of arithmetic progressions of length 4, to make some important ideas clear, to show what else is needed to complete the proof, etc. To me, this is a delight. So I'd like to model my writing style after his. But, unfortunately, I'm not Timothy Gowers. So I'm not sure if I can get away with writing like he does, or if being that leisurely and involved with the reader actually makes me look unprofessional. And thus my question is:

When in doubt, should I acknowledge the fact that I am a human being, writing and explaining concepts to another human being? Or should I try not to break 'the fourth wall'?

REPLY [15 votes]: I can't help but reiterate here Serre's great maxim: "Precise yet informal". Striving for this goal in mathematical writing will avoid your looking unprofessional, but will make you look more human at the same time. It seems that mathematics that does this best is very professional (I can't help but think of Milnor's style, here).
Regarding writing that appears purely to guide the reader between theorems: as far as the guidance ALSO is precise yet informal, there should be no foul. It is when these comments are not really true...but close to true...that they should be omitted or left to the talk. Too many "sort-ofs" should be avoided in the body of a mathematical paper. Serre's maxim seems a good guidepost for this, too.

Comments to supplement original answer:
Also, as long as mathematical papers are valued for being interesting it seems that there will always be a bit of 'ought' along with the 'is'. Otherwise, one could just rattle along formally proving theorems without regard to how they will be received. This is evidence of the human part of mathematics that stands in opposition to the dispassionate precision of formal proof. Elegance is far from formal perfection, and is perhaps closer to human utility or aesthetic sense. Somehow, Serre's maxim expresses something important about mathematical life and work.