It's AMS/SMT proposal season (somehow!). When serving on program committees, I noticed a lot of common problems with proposals that prevented good work from getting accepted to conferences. Some strategies for proposal-writing: a thread.

Don't copy and paste sentences/paragraphs from your paper. You really do have to write something new from scratch! The exercise of sitting in front of a blank screen and re-articulating the paper's argument results in a clearer and more compelling proposal.

Many abstracts begin: "Scholars have long argued X, but have never discussed Y. This paper aims to fill that gap." (1) The 1st claim isn't interesting. (2) The 2nd claim is rarely true. (3) Your work is interesting on its own; its value is not merely that no one has done it yet.

An alternate strategy to try: convince me that something is interesting (e.g. "Isn't it strange that Brahms never used the note F#?"), and then explain why no one has written about it already (e.g. "The field of F# studies has largely devoted its attention to the music of Bach").

Use your clearest, most accessible writing. Use short sentences. Start sentences w/ concrete nouns & vivid verbs. Avoid nominalizations, passive voice should not be written in, reimagine imprecise verbiage; embedded clauses frustrate. The reader should be UNABLE to miss the point

Your first paragraph should include a sentence that begins "this paper argues" or "this paper demonstrates."

Don't merely describe what you will do in your longer paper; give us the results! Your conclusion should be in your proposal. Replace "I will discuss how food blogging impacts topic theory" with "I will show that food blogging impacts topic theory by ..."

Give the reader enough information to evaluate your claims. If you say something that might be controversial, accompany it with a citation, a figure, or both.

Show, don't tell! I can't stress this enough. Rather than merely asserting that Byrd increases chromatic density towards cadences, provide an example or chart that illustrates this phenomenon.

Take full advantage of the format. Make sure you use all 500 words (or close to it). Fill your extra pages with heavily annotated examples and figures. Provide captions that tell us how to interpret these figures and refer to them in the text. Use color!

Last, but not least: revise, revise, revise. Send your proposal to friends and ask for feedback. Try structuring your proposal in different ways. Don't try to crank out a proposal in an hour. The proposal can be both the trickiest & the most rewarding part of the writing process.