Mathematicians rarely have the opportunity to present their research directly to a broad scientific audience. One of the few venues to do so is publication in the Proceedings of the National Academy of Sciences (PNAS). Published weekly and online, this prestigious journal features papers covering a wide range of disciplines, from applied mathematics and computer science to molecular biology and the social sciences. PNAS also has a strong media relations effort, which encourages wide dissemination of research results to the general public. Unfortunately, even when mathematicians do take advantage of this opportunity, they often fail to communicate well and end
Read more →Posts Tagged Writing
One of the things that irritates me most when I’m reading, whether it’s a novel, a newspaper article, or a mathematics paper, is the misplaced “only.” If you write “Here we only calculate the position of two vertices” you probably mean “Here we calculate the position of only two vertices.” The word “only” is there to emphasize something, and it should be as close as possible to what you want to emphasize to be effective and to convey the desired meaning. As described in Mathematical Writing (MAA, 1989), newspaper copy editor Rosalie Stemer gives the following sequence of examples to
Read more →When you go to the trouble of writing an article for publication, it’s worth spending some time thinking about and composing an appropriate title. The title is your first chance to engage prospective readers—to get their attention immediately. A poorly chosen title can mean a significantly smaller audience than your work might deserve. In Writing Mathematics Well: A Manual for Authors (MAA, 1987), Leonard Gillman advised: “Keep your title short and include key words to make it informative.” Striking the right balance between brevity and informativeness (while still attracting attention), however, can be harder than it sounds. Consider, for example,
Read more →This assignment is from Andrew Snowden’s Undergraduate Seminar in Topology at MIT. The final paper is an approximately 10 page exposition on a topic in algebraic topology not covered in our seminar. The paper must be written in Latex (or some other flavor of Tex). You must select the topic for your paper by March 7th. I’d prefer that no two of you do the same topic, so if there’s something you’d really like to do you should tell me soon. When you know what you want to do, just send me an e-mail. Below is a list of possible
Read more →Revision is an important part of the writing process, but many undergraduates are not yet aware of its value. The following teaching strategies may help students to revise effectively: To help undergraduates to see the value of revision, consider describing your own writing process. By showing students an early draft and a later draft of your own writing, you can draw attention to those aspects of writing that you consider to be most important. See, for example, the description of Pedro Reis’ writing workshop. Include revision in the assignment schedule. Here is one example of how to grade a draft
Read more →The following writing can be used as a basis for discussion about good writing technique. The MAA Writing Awards These expository papers are often written at a level accessible to undergraduates. The I. Martin Isaacs Prize for Excellence in Mathematical Writing is awarded by the American Mathematical Society (AMS) "for excellence in writing of a research article published in a primary journal of the AMS" The Levi Conant Prize recognizes the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years. Books that win the Joseph L. DoobRead more →
As a mathematician, Paul R. Halmos (1916-2006) made fundamental contributions to probability theory, statistics, functional analysis, mathematical logic, and other areas of mathematics. He was also widely recognized as a masterly mathematical expositor. And he served as editor (1981-1985) of the American Mathematical Monthly. Halmos described his approach to writing in an essay published in the book How to Write Mathematics (American Mathematical Society, 1973). One paragraph presents the essence of the process: “The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do
Read more →The language of mathematics can throw up barriers to broad dissemination of information about mathematics. Mathematical statements are supposed to be precise, devoid of the ambiguities of ordinary speech. The language is unusually dense and relies heavily on a specialized vocabulary. The meaning and position of every word and symbol make a difference. Mathematician William Thurston once expressed the difference between reading mathematics and reading other subject matter in this way: “Mathematicians attach meaning to the exact phrasing of a sentence, much more than is conventional. The meanings of words are more precisely delimited. When I read articles or listen to speeches
Read more →Much of this site is primarily about “learning to write” math; this page is about “writing to learn” math. In other words, students may improve their understanding of math by writing about it. The following resources describe or illustrate how writing about math can help students to learn math. Please feel free to contribute to this page. Particularly helpful would be a literature review, a structured, annotated bibliography, or a comprehensive bibliography (even if not current). Many of the resources below were found by undergraduate researcher Artur Araujo. Editor’s-choice resources J. Meier and T. Rishel, Writing in the Teaching &
Read more →The characteristics of good math writing are too many to address in a single writing lecture or workshop; for a small sample of these characteristics, see the pages about general principles of communicating math. So the instructor should choose characteristics on which to focus. Examples of writing lectures and workshops A brief mini-lecture could present handouts about guiding readers through the content, writing an introduction, and using sources. Students could also be pointed to other resources for writing and for learning LaTeX. A longer (50-90 min) writing workshop could involve the students in some active learning. For example, Pedro Reis
Read more →