Writing and Reckoning: Sign Systems and Argument in Verbal and Mathematical Communication

  Carolyn Collette,


Giuliana Davidoff,


Index | Syllabus  |  Language of Mathematics  |  Fermat's Last Theorem

Reflection Paper: Language of Mathematics

Jennifer Kwak
March 24, 1998

        The Nova film, featuring Andrew Wiles and his proof of Fermat's last theorem, brought the mathematical complexities of the proof into a light that appealed to mathematicians and "non-mathematicians" alike. The film accomplished the great task of explaining mathematics in a not so mathematical way- so called "humanizing" of an area that most people associate with logic, reason and all ideas outside the realm of human emotions. By bringing out mathematics as a special type of language and the proof of the theorem as a composition of language, the film made mathematics and Fermat's last theorem accessible to non-mathematicians. The film presented three aspects of mathematics and the proof which brought to light the language of mathematics.
        The first aspect of a mathematical proof brought to light was the construction of the proof. The construction of a proof resembled the construction of an essay. The film showed the flow chart of the proof on the black board which showed how Andrew Wiles attacked the proof. He first visualized the whole picture then literally broke in down into parts which were then brought together by links. In writing an essay, a writer comes up with a big idea of what he/she wants to write about then breaks it down into components like paragraphs then uses transitions to link the ideas together. In the process of construction, another similar aspect arose between a mathematical proof and an essay creativity. To understand mathematics, one has to visualize mathematics in his/her head, and to be able to do so takes a significant source of creativity. Often, people speak of the creative writer or artist, but do they know about the creative mathematician? In addition to creativity and construction, the proof is rigorously edited like an essay, line by line by the author and his/her peers. This brings into light another important aspect of language the community. A language is a characteristic of a certain community. People in that community "speak" the language. It was hard to visualize mathematics as a spoken language, but the film showed that mathematics is truly a discourse between people. The several frames which captured a number of mathematicians being able to finish each other's sentences captured the sense of community. People's sentences could be segmented and pieced together coherently showing that mathematics truly is a language that is shared among mathematicians.
        The film brought to light the aspects of mathematics that make it a language not just a group of numbers and symbols. It was shown as a source of creativity, community, and construction that made it a language. By understanding mathematics as a language, one gains a sense of new found respect for it- although it may seem strange and difficult making it easy to dismiss, by thinking of it as a language, one respects the differences and difficulties because one understands that languages are a different means of expression and that the special feature of a language is its difference from other languages.



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