or x(f) for a function, is certainly possible, but almost never a good idea. Good notation firstly allows the reader to forget that he is learning a new language, and secondly provides a framework in which the essentials of your proof are clearly understood. One technique to assist you in revealing the complex logical structure of your paper is a proper naming of results. The accepted format for research papers is much less rigidly defined for mathematics than for many other scientific fields. Example: "On a compact space every real-valued continuous function f is bounded." What does the symbol "f" contribute to the clarity of that statement? The next section will describe the difference between "formal" and "informal" parts of a paper, and give guidelines for each one. Once you have considered the structure and relevance of your research, you are ready to outline your paper. By the time you reach the final section, implications, you may be tired of your problem, but this section is critical to your readers. (By "theorem" I mean a mathematical truth, something that has been proved.

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There should be a clear definition of the problem at hand all the way through. Usually all that is needed to avoid it is to recast the sentence, but no universally good recasting exists; what is best depends on what is important in the case at hand. Does it provide a new proof for an old theorem? The purpose of this paper is to provide assistance for young mathematicians writing their first paper. "Where" is usually a sign of a lazy afterthought that should have been thought through before.