I already had a pretty good (though vague) idea of what I wanted to do
when I got to California in May.  I wanted to, as I wrote in my thesis
proposal, ``write a thesis which combines mathematics and
creative writing, a thesis which makes math accessible to a general reader
and presents math as fun''.  I didn't know exactly how I wanted to
accomplish this, but I wanted to try to change the way math is perceived.

During the summer I considered some of the many myths of mathematics that I
have heard, among them that math is more difficult than other subjects,
math is dull, math is just about numbers, and that math's importance comes
from being applied to sciences.  At the same time I wondered why the idea
of a mathematics and creative writing thesis seems so strange to people.
I tried to find examples of mathematical fiction and recreational math
writing.  ``Why are there so few books in this category?'' I wondered.
Well, the answer is, in one sense, pretty obvious:  how large an 
audience is there for reading mathematics?  Why don't people just sit down
and read math?

So that's what I decided to do:  sit down and read math.  I read Edwin
Abbott's classic {\it Flatland} and Dionys Burger's sequel {\it 
Sphereland}.  I read almost the complete works of Lewis Carroll --- Lewis 
Carroll being a wonderful example of an author and a mathematician.  I read 
{\it A Mathematical Mystery Tour} by A.K. Dewdney, {\it The Number Devil},
a children's book by Hans Magnus Enzensberger, and two anthologies of
mathematical short stories edited by Clifton Fadiman.  I read books by 
Martin Gardner, Douglas Hofstadter, Theoni Pappas, Ivars Peterson, and Ian
Stewart; I read biographies of mathematicians and Lewis Carroll, books of
math puzzles, and old class notes.

Finally, I was ready to write something.  But what?  Some sort of an 
adventure like {\it Alice in Wonderland}, only with a curious girl who
learns math from a yellow pig.  I decided to write a five chapter short
story.  Each chapter would have creative writing episodes with some 
math.  Immediately following each chapter would be a more mathematical
explanation of the implications of Alice's travels.

In the first chapter I planned to primarily cover geometry while
introducing the characters of Alice and the Yellow Pig. The second
chapter, part of which is set in the Golden Garden, is a small subsection
of number theory, including a discussion of $\pi$, $e$, $\phi$, primes,
and the Chinese Remainder Theorem.  The third chapter is about
combinatorics, graph theory, and groups.  In the fourth chapter, Alice and
the Pig see a mathematical art gallery in which Alice learns more about
geometry and topology.  The fifth chapter finds Alice on the other side of 
a looking glass in Logicland, a world of probability, game theory, and symbolic
logic.  The story ends with Alice wondering about dreams and reality.  I
wrote a rough draft of this story in three months and have spent the last
month attempting to revise it.  The most current version can be found on the web at 
http://www.simons-rock.edu/\~{ }sara/thesis/.

That more or less sums up what I've been doing for the past six months.  I
feel that I have gotten a lot accomplished and am mostly happy with
it, though I really only like the middle three chapters.  I like the 
Yellow Pig as a character and am starting to like Alice.  I ended up changing my
model in some ways.  The main difference is that instead of adopting 
something like the dual chapters of {\it G\"{o}del, Escher, and Bach}, I have
incorporated almost all of the math directly into the story.  I think I
like this better, but I am not sure.

I have a lot left to do.  The story portion of my thesis is far from
complete.  It's awkward, choppy, and often inconsistent.  It's missing
diagrams (drawn as the Pig would draw them), some transitions, and the 
mathematical appendices to the chapters have yet to really be considered.  I 
need to decide how much math I want there to be compared to the amount of 
creative story.  I also have a lot to discuss in introduction and conclusion.  

One question that needs to be answered is:  Who is the audience for my
story?  I see the story as potentially useful for those with an interest in
math and the desire to learn something beyond classroom textbook
mathematics.  I also hope to make the text accessible enough that someone
with little background and interest in math can learn to appreciate it.


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