September 12, 1995 Section 1: Introduction: Why bother? Good mathematical writing, like good mathematics thinking, is a skill research paper customer value must be practiced and developed for optimal performance.
The purpose of this paper is to provide assistance for young mathematicians writing their first paper. The aim is not only to aid in the development of a well written paper, but also to help students begin to think about mathematical writing. I am greatly indebted to a wonderful booklet, “How to Write Mathematics,” which provided much of the substance of this essay. I will reference many direct quotations, especially from the section written by Paul Halmos, but I suspect that nearly everything idea in this paper has it origin in my reading of the booklet. Mathematical communication, both written and spoken, is the filter through which your mathematical work is viewed.
If the creative aspect of mathematics is compared to the act of composing a piece of music, then the art of writing may be viewed as conducting a performance of that same piece. As a mathematician, you have the privilege of conducting a performance of your own composition! This essay will begin with general ideas about mathematical writing. The purpose is to help the student develop an outline for the paper. The next section will describe the difference between “formal” and “informal” parts of a paper, and give guidelines for each one. Section four will discuss the writing of an individual proof.