
Writing
and Reckoning: Sign Systems and Argument in Verbal and Mathematical
Communication
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 "nonmathematicians"
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 nonmathematicians.
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.
