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{\huge \bf Introduction \\ \bigskip Mathematical Literature \par}
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In September I proposed to write a thesis which combined mathematics
and creative writing, a thesis which would make math accessible to the
general reader and present math as fun. I began by considering both
what math I wanted to include and how I wanted to present that
material. As part of this process, I looked at examples of popular
mathematical literature, a somewhat unknown genre.
Popular mathematical literature, in contrast to math textbooks, is
designed to appeal to a general audience. I have subdivided this genre
into mathematical fiction and recreational mathematics, two categories of
literature whose boundaries are sometimes blurred. Mathematical
fiction is based on a fictional story model, whereas recreational
mathematics is similar to an instructive essay. In other words,
mathematical fiction concentrates on the story, using a mathematical premise,
while recreational mathematics presents mathematics in an entertaining and
accessible way. Normally, the narrator of mathematical fiction is
omniscient or a character within the story, whereas in recreational
mathematics the narrator is likely the author.
I consider Edwin Abbott's {\it Flatland} and the stories in Clifton Fadiman's
anthologies to be examples of mathematical fiction, and Douglas Hofstadter's
{\it G\"{o}del, Escher, Bach} to be an example of recreational mathematics.
Hans Magnus Enzensberger's {\it The Number Devil} seems to be a bit of both,
though I would place it on the side of recreational mathematics because it is
instructive (in tone). I feel that my thesis, like {\it The
Number Devil}, predominantly falls into the category of recreational
mathematics. Both are fictional stories, but they use the story primarily
as a vehicle for mathematical instruction.
As part of my thesis, I have read many examples of popular
mathematical literature. I will now briefly summarize some of
these books and stories. Edwin Abbott's {\it Flatland} is the classic example
of mathematical fiction, written 120 years ago. It is a somewhat satirical
story of a flat land inhabited by two-dimensional shapes. In 1960, Dionys
Burger wrote {\it Sphereland}, a sequel in which Flatland is visited by a
three-dimensional being. By way of analogy, he leads the reader to consider
the meaning of the fourth dimension.
Enzensberger's {\it The Number Devil} is a children's story about a boy who
dislikes mathematics until a magical number devil visits him in his dreams.
It is written on a pretty basic level, and there are a lot of gaps and
imprecise terminology, but it is an enjoyable and informative story.
Just as I was finishing
my thesis I stumbled upon another batch of books. These included Erik
Rosenthal's {\it The Calculus of Murder}, an entertaining detective story in
which a part-time private investigator, who also happens to be a
mathematician, investigates the murder of a well-known San Francisco
businessman, and Marta Sved's {\it Journey into Geometries}, a story
intended for readers with little mathematical background that explores
hyperbolic geometry as it is taught to a girl named Alice.
I also found dozens of mathematical short stories.
Clifton Fadiman edited {\it Fantasia Mathematica} and {\it The Mathematical
Magpie}, two anthologies of math fiction. The stories in
these anthologies are examples of science fiction that are largely based on
the mathematical. Aldous Huxley's ``Young Archimedes'' is a
tragic story of a young Italian mathematical and musical prodigy. ``The
Devil and Simon Flagg'' by Arthur Porges is an amusing tale of the devil and
a mathematician working together to solve Fermat's Last Theorem. Robert A.
Heinlein's ``And He Built a Crooked House'' explores the possibilities of
four-dimensional geometry in real estate. In Martin Gardner's ``No-Sided
Professor,'' some members of the Moebius Society become nonlateral surfaces.
In ``The
Island of Five Colors,'' also by Gardner, a mathematician attempts to paint an island off the
coast of Liberia with four colors, only to discover that five colors are
needed. Edward Page Mitchell's ``The Tachypomp'' is about a struggling math
student who loves the professor's daughter and must discover infinite speed
to win her hand in marriage. ``The Feeling of Power'' by Isaac Asimov is
about a futuristic society in which computers are relied on for computation
to such an extent that no one knows how to perform arithmetic. Mark
Clifton's ``Star, Bright'' is the story of an exceptionally gifted young
girl who uses the fourth dimension to travel.
Rudy Rucker also edited an anthology of math fiction, entitled {\it
Mathenauts}. Like Fadiman's anthologies, {\it Mathenauts} is a collection
of science fiction short stories. Greg Bear's
``Tangents'' is about a small boy who has a gift for understanding the
fourth dimension. Rucker's own ``A New Golden Age'' is about the
consequences of popularizing pure mathematics. His ``Message Found in a
Copy of {\it Flatland}'' locates Abbott's Flatland in the basement of a
Pakistani restaurant. ``The Maxwell Equations'' by Anatoly Dnieprov is the
story of a mathematician and a Nazi war criminal who is forcing mathematicians to be computers by
manipulating their brain frequencies. George Zebrowski's ``G\"{o}del's
Dream'' is about a computer program that must run forever. ``Cubeworld'' by
Henry H. Gross discusses the implications of turning the Earth into a cube.
As my thesis is a longer work, these short stories did not have any
significant direct influence on {\it Alice in Mathland}, but I found many
of them delightful to read and was encouraged by the number of authors who
have written mathematical pieces.
The site {\it http://math.cofc.edu/faculty/kasman/MATHFICT/default.html}
led me to a number of books; many more examples of mathematical
literature are listed there.
Using some of these as examples, I experimented a lot with the style of my thesis. I began
envisioning something with clear divisions between the creative stories and
the mathematical instruction. I anticipated having something like the
dialectic vignettes (Platonic dialogues) of {\it G\"{o}del, Escher, Bach}
that would be both entertaining and serve as jumping off points for delving
into further mathematical exploration.
But over time these more creative sections grew in proportion to the
solely instructive sections, and they encompassed the math that I had
anticipated having in those meta-sections. In order to demonstrate that
mathematical creative writing can be done, I wanted to merge the two
distinct styles. Fortunately, my writing was doing this on its own, and
in a way
that improved the story. As a result of having the math and the story
intertwined, I think my thesis flows better and is able to emphasize more
strongly my idea that mathematics and creative writing are not mutually
exclusive. I believe I have succeeded in creating something which is both
mathematically instructive and entertaining.
In addition to drawing heavily on examples of mathematical literature, my
thesis is
derived from non-mathematical literary models, including the dialogue and
the journey. Much as in {\it The Divine Comedy}, I have a Virgil
and a Dante. My Virgil is the Yellow Pig, a fantastical and entertaining math
teacher. My Dante is Lewis Carroll's Alice, a curious and
inquisitive young girl with whom I hope the reader can identify. My story
is a physical journey through a mathematical wonderland as well as a
mental journey in which Alice is exposed to mathematics and learns to enjoy
it. I have chosen Alice as my character because I see Lewis Carroll, an
author and a mathematician (logician), as one of my inspirations.
My story consists of five chapters, each etching the surface of a branch of
mathematics with topics that I hope are interesting.
The first chapter introduces geometry, including
the Pythagorean theorem; the second explores numbers --- $\pi$, $e$, the
golden ratio, and primes; the third discusses combinatorics, the Pigeonhole
principle, graphs, and
groups; the fourth considers more geometry and topology, the study of surfaces; the
fifth describes probability, game theory, and symbolic logic. Each
chapter contains several sections of dialog between Alice and the Yellow Pig.
At the end of my thesis are a handful of appendices in which I consider these
mathematical topics in more depth. This is my way
of experimenting with different forms and providing more historical
and mathematical information. I encourage readers not to neglect these
appendices.
Although it contains a lot of mathematics, {\it Alice in Mathland} is not a
textbook. It is meant to be both informative and entertaining. My story is
meant not for mathematicians, but to educate the general public.
As such, even though the topics considered are advanced, very little
mathematical background is assumed. My goal is to make mathematics
accessible. In his introduction to {\it Flatland}, Isaac Asimov comforts
the reader: ``Fear not, however. It contains no difficult mathematics and it
won't sprain your understanding. [It is] a pleasant fantasy. You will have
no sensation of `learning' whatsoever, but you will learn just the same.''
I hope you, like Alice, find your journey into my mathematical world a
pleasant and rewarding one.