By Susan Ruff Johann’s presentation on partitions was carefully crafted. The math was completely correct, the board work was neat and legible, the delivery was professional, and the timing was perfect. But the talk was so dry and formal that the other students quickly reverted to the blank look that suggests they have more interesting things to think about. In contrast, Karen’s presentation on generating functions gained and held the attention of many of the students. She successfully conveyed the beauty and power of generating functions . . . to the front half of the class. The rest couldn’t hear
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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 →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 →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
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