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

 Carolyn Collette, English Giuliana Davidoff, Mathematics

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

Fermat's Last Theorem: Language and Mathematics

Meg Baker
March 24 1998

Andrew Wiles said that he first became interested in Fermat's last theorem when he was ten and reading a book about mathematics. What is intriguing about this story is that the problem that puzzled mathematicians for so long was simple enough in its language that a ten year old could understand it. Even granting that Andrew Wiles was far from the average ten year old (what ten year old do you know who reads a math book for fun?), it is impressive that a question so complex could be comprehended by one so young.

Another interesting observation regarding the use of language between mathematicians refers not to the question but to part of the answer. "What is a modular function?" asks the naive interviewer. The immediate answer is that it is impossible to define. And this is not a reply from simply one mathematician. It is rather the reply of all of the members of this community. "A modular function? You can't define a modular function!" "Well, it's sort of like a bridge…" "Like a dictionary…" Mathematicians in this case must rely on metaphor and figurative speech to translate this 'truth' into an understandable item. This use of metaphor and figurative language can be probably best related to the experience of one who has been asked, "What is God?" and told to give a short explanation. Like this person, mathematicians sputter and prowl around for a definition of something which in their society is apparently taken to be so intrinsically true, and so complicated that is rarely questioned, and never simply defined.

Mathematicians reaction to "What is a modular function?" indicates not simply another language which must be translated, but also the reflection of another culture entirely, founded on proof after proof, all stacked atop theories about the way that the world works. Perhaps it does these mathematicians some good to reanalyze this society, and to question all of its validity. So I ask, "What is a modular function?"