**Senior Thesis Proposal**

Presented by

Sara Smollett

**Approved:**

¯

Allen Altman, Thesis Advisor Date

**Thesis Committee Members:**

Jamie Hutchinson

J. David Reed

I'm proposing to write a thesis which combines mathematics and creative writing, a thesis which makes math accessible to a general reader and presents math as fun. Many people consider mathematics and creative writing to be extremely unrelated topics, but there is no reason that this must be the case.

One of my main inspirations for my thesis is Lewis Carroll. Lewis Carroll is a well-known author. In addition to writing children's stories, he was also a mathematician and logician. He is an example of someone who was a successful writer and amateur mathematician. I will attempt to adopt his tone and style for portions of my thesis.

My thesis will be an example of recreational mathematics. I want to create something which contains mathematical ideas, reads well (as a literary work, not a math text), and is entertaining and accessible to readers who possess little mathematical background. Ideally, someone might read my text and come away from it not only having been exposed to some new mathematics, but wanting to learn even more. I'd like to take a small step toward popularizing mathematics.

What do I mean by my tentative title? Who is Alice and what is Mathland? Alice is a heroine created by Lewis Carroll. My Alice is a small, fantastical, somewhat mathematically-confused girl. Mathland is an alternative wonderland, a strange place that Alice finds after falling down a hole. It is a world of beautiful mathematics.

The second part of my title is perhaps more confusing. What is a mathematical fantasy? What is mathematical fiction? These are questions that I have been struggling with, not because I don't know what mathematical fiction is, but because there are so few examples of such fiction. Perhaps there is so little mathematical fiction because math is not seen as a recreational topic. Math is generally considered to be something difficult, often something to be feared and avoided. That math is fun should not be such a radical idea. There is little mathematical literature because the audience for this genre is so small. At the same time, the audience cannot increase until there are more examples of texts. My thesis will contribute one such example.

Although there aren't many examples of mathematical fiction, I am
certainly not the first to write in this genre. One of the first to do so
was Edwin Abbott who wrote *Flatland: A Romance of Many Dimensions*.
*Flatland* is the story of a two-dimensional world inhabited by lines
and polygons. It is an instructive fantasy. Other mathematical
fictions include Dionys Burger's *Sphereland* (the sequel to *
Flatland*), A. K. Dewdeney's *A Mathematical Mystery Tour*, and Hans
Magnus Enzensberger's *Number Devil*.

In his introduction to *Flatland*, Isaac Asimov writes:
``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.''
This is one of my objectives in writing this thesis.

My ideas about both content and style have been shaped by the above
authors. One other major influence is Douglas Hofstadter, whose
*Gödel, Escher, Bach* contains dialogues of Lewis Carroll's
characters. Each chapter of his book begins with a short dialogue and is
followed by a lengthy discussion of topics covered in the dialogue. This
is the basis for the form of my thesis, though I would like to focus more
on the fictional pieces than the explanation. Ideally, the explanations
will fit naturally into the fiction. More in depth explanations, proofs,
and discussions will follow every few chapters. A less mathematical
reading can be achieved by treating these sections as appendices.

The story I am writing is one of Alice and the Yellow Pig. The Yellow Pig is her guide (like Carroll's White Rabbit and Dante's Virgil) who leads her through Mathland and teaches math to her and the reader. Alice follows the pig down a hole to find herself in a garden of mathematics. The pig gives her a mathematical tour of the garden and introduces her to some of his mathematician friends. The two proceed over some bridges to the pig's private art gallery which is filled with math. Alice finally leaves mathland after answering a series of Carrollian logic riddles. Along the way, mathematical topics are covered in the areas of geometry, number theory, algebra, topology, graph theory, combinatorics, probability, game theory, and logic.

The following tentative outline lists months in which the bulk of the creative writing part of the (rather short) chapters will be completed. The topics contained in single parenthesis are the mathematical topics to be explained within the chapters. The topics contained in double parenthesis are the more in-depth mathematical ideas which will be discussed in the explanatory sections. These will be completed and the chapters revised in the second month listed.

**Schedule:**

SEPTEMBER/JANUARY

* Down the Hole

Alice follows the pig down a hole.

(differential equations, the idea of change)

((fourth dimension))

* Into the Garden

Alice chases the pig.

(irrational numbers)

* What the Pig Said

Alice and the pig talk.

(rectangular lattice, slope, Cantor and infinities)

((Minkowski))

* A Pig and A Greek

The pig talks about geometry.

(distance, square roots, Pythagorean theorem)

((Fermat's Last theorem))

OCTOBER/FEBRUARY

* Most Irrational

The pig discusses some important irrational numbers.

(pi, e, phi, Fibonacci, Lucas)

((measuring irrationality))

* The Golden Garden

The pig leads Alice through a garden that is rich in mathematics.

(math in nature, phi, Fibonacci)

* The Pig's Friends

The pig introduces Alice to some of his mathematician friends.

(Gauss and sums, Pascal and probability, Fermat, Ramanujan and number
theory)

* Primes

The pig talks about prime numbers.

(infinitely many, Goldbach, twin primes, unique factorization, modular
arithmetic)

((Wilson's theorem, Fermat's little theorem))

NOVEMBER/MARCH

* Leaves on Kittens

The pig talks about combinatorics and pigeonholes.

(pigeonhole principle, Erdös, probability)

((more Erdös))

* Over the Bridge

Alice and the pig attempt to cross some bridges, color some
countries, and shake some hands.

(Euler and the Königsberg bridge problem, graph theory, coloring,
four color theorem, handshakes, Ramsey)

((more four color theorem and Ramsey))

* Through Another Door

Alice and the pig enter a room of tesselations and art

(art, tesselations, symmetry, groups, algebra, Chinese remainder
theorem)

((Galois))

* Stepping into a Picture

Alice steps into an Escher painting and discovers the Möebius
strip.

(Escher, topology, Möebius, Klein bottle)

((colorings on different surfaces, v-e+f))

DECEMBER/MARCH

* And Another Picture

Alice steps into Dali's tesserect

(fourth dimension, Flatland, slices, cycloids)

((hyperbolic geometry, proof of v-e+f ))

* Logicland

Alice and the pig continue on to logic land.

(strategies and the prisoners' dilemma, paradoxes, Hofstadter,
logic and Lewis Carroll)

((more puzzles from Lewis Carroll))

For more and up-to-date information about my thesis, refer to www.simons-rock.edu/~sara/thesis.

File translated from T

On 6 May 2000, 10:43.