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 Flatland and the stories in Clifton Fadiman's anthologies to be examples of mathematical fiction, and Douglas Hofstadter's Gödel, Escher, Bach to be an example of recreational mathematics. Hans Magnus Enzensberger's 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 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 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 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 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 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 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 Fantasia Mathematica and 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 Mathenauts. Like Fadiman's anthologies, 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 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 ``Gödel'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 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 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 Gödel, 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 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 - p, 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, 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 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.