How to get a research paper all together The "research portion" of my paper is mostly done, but I'm having trouble putting together my research. (Keep in mind this is at the undergraduate level). It's not so much that I don't know how to organize my thoughts; in fact, I've written a very detailed outline. I seem to have a two questions I'm wrestling with (I apologize if this is a tad long-winded)


The monotonous proof-theorem-proof-theorem style that essentially consists of a list of facts with no exposition seems to be most accepted. But will this really make my paper stand out? When I think about texts with proof-theorem-proof-theorem, I think of the color gray. If I try to be clever and witty, it could certainly backfire on me, but such papers are the most memorable papers I've ever read! 


  So what should the tone/style of my paper be? 

I'm struggling very much with how detailed my paper should be. By no means am I writing a textbook, but I need to show the audience (namely admission committees) that I know what I'm talking about.  On the other hand, I have a deadline! There's always this looming thought in the back of my head that says "But you can't leave that out!" when I debate if I should skip something just to speed up the process -- it's as if I have a hoarder living in my head. I have this same issue with considering how much background/prerequisite math I should include for the reader -- it is confusing, to say the least,  writing to an audience that is more knowledgeable than the author. This is certainly very difficult for me to figure out. 


  So how detailed should my paper be? 



I'd really like to hear feedback from professors and/or admission committees members. But, of course, feedback from anyone with research experience is appreciated!
Apologies for stealing scaaahu's comment into this answer, but I wanted to stress that it is really the only possible answer to this question: ask your advisor! 

Getting a hang for the appropriate level of detail is a very tricky thing, and only comes with experience. Also with being clever and witty; if you can pull it off, great, but if you can't, then it distracts from the content of your article. There are no general rules for this, you need advice from a more experienced mentor.

If I were you, I would write up a quick draft without stressing too much over these issues, and go over it carefully with your advisor; they would be able to tell you whether your humour is working, or where you need more or less detail.

That said, a few general tips:


Look at the papers you cite; if they all treat some theory as standard or well-known ("By class field theory....") then you probably can too. Same goes for tone.
Often you can save space and omit details by rephrasing your results in a way that suggests how the proof should go. For example, let's say I have a lemma about a linear operator that gets proven by choosing a basis and then something straightforward; I might then state the lemma in terms of the matrix, so it would be more obvious to the reader how to complete the proof. 
(and the most important, imo) Engaging papers are not engaging because of witty one-liners, they are typically engaging because a great deal of effort went into organizing them well. The key is to ensure the reader always knows where they are, where they are going, and how they're getting there. This is not at all easy to do, but if you practice writing with this in mind early on, it will serve dividends later.