On the third day of the unit, Giuliana Davidoff came to class to discuss the reading for that day, a set of readings including f a Scientific American article on the same topic as the video ("Fermat's Last Stand," Nov. , 1997, 68-73), written by some of the mathematicians who appeared in the previous class video, a New York Times Book Review of the book The Number Sense: How the Mind Creates Mathematics, by Stanislaus Dehaene (Oxford, 199 ? ), and a February 10, 1998 "Science Times" article, "Useful Invention or Absolute Truth: What is Math?" (NY Times). The class began with students were asked to respond to their experience of reading the Scientific American article. When they said that they had gotten "lost" in the explanation in both the movie and the article, Giuliana Davidoff proceeded to explain the mathematics of the article in a manner that was so clear and direct that the class immediately recognized the dependence of higher mathematics on verbal symbols and, quite interestingly, the use of substitutions in the process of proving that elliptical curves are modular forms. That pattern of substitutions was the subtextual foundation of the thinking in both the video and the article; making it explicit allowed students both to understand the large issues involved in solving Fermat's last theorem, and to recognize in mathematics a form of a principle we had been working with all semester: the fundamental usefulness of analogy in communication in all kinds of writing. The unit ended but it didn't conclude. In the first place, it ended differently from where I thought it would, in that it was much more complex and that it opened many new ways about thinking about the "languages" of math and English than I had imagined when we first formulated the idea of metaphor as a property of verbal signs and not of the mathematical sign system. Clearly the role of analogy and substitution in both systems is a complicated and intriguing area. We were able to raise student awareness of this fact. We were also able to interest students in reading on current thinking about whether or how the human brain is hard-wired for math as it seems to be for language; this leads to thinking about all the kinds of mathematics that humans can create, and the question of whether there can be as many kinds of mathematical systems as there are languages. This topic lead to consideration of current interest in defining mathematics not so much as reflecting eternal Platonic verities and cosmic harmonies, as a construction of cultures that, in many ways, explains and derives from natural patterns in the external world, as well as physiological patterns in the human brain. Because the class was an advanced writing course elected by students many of whom are already strong writers and thinkers, the discussions we had were wide-ranging, open and allusive. The discussion of mathematics was in part shaped by student interest and experience (only two or three of the 18 students in the class were currently taking math). The discussion was also shaped in part because of the orientation of the course whose primary goal was to help students c communicate effectively in language and forms that sounded natural and felt comfortable. The course paid a good deal of attention to structure of writing and the importance of reader's imagination. In this respect some basic principles of semiotics underlay all our discussions; as a result a great deal of attention was directed to analogy and metaphor as crucial ways of engaging the reader's mind. In that way students were oriented to think about mathematics as one kind of language, and to think about how it communicates a way of describing the world. Carolyn Collette, Department of English |

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