Conclusion
Math Education
Despite dozens of examples, mathematical literature is not a very well-known
genre. Very few people are able to name any examples of such literature, and
many are uncertain as to what is even meant by mathematical literature. In
fact, the idea that someone would write or read such literature is a novel
(pun intended) idea to most people. This is because there is confusion
surrounding mathematics, including two common prejudices: that math is
non-literary and that math is non-fun. The ``problem'' - the source of the
confusion about mathematics - is that people don't know what mathematics is.
Mathematics is not just about computation; it is not simply a tool. Math is more than skills to be applied to science or to mundane tasks such as balancing a checkbook. Pure mathematics (in contrast to applied mathematics) is an end unto itself. Pure math is the exploration of math for the sake of math, just as art is often appreciated for art's sake. I envision my thesis as a tribute to pure math, a text that encourages math appreciation. Mathematics is an art in which clever insights lead to beautiful results, such as the proofs Alice learns from the Yellow Pig and the works of M.C. Escher.
Math is also a language or mode of communication; it is a way of expressing ideas clearly and rigorously from hypothesis to conclusion. Mathematics is a way of thinking, a kind of logic. It is a way of telling a story. The mathematical story is not just one of numbers, but of problems, of knowing how to interpret, approach, solve, and understand them. It is also a story of mathematicians, questions, methods, contemplation, and beauty.
Most people are not interested in reading math for fun, probably because they do not view mathematics as fun. The idea that math, its patterns, and results, are beautiful is a foreign one. This is largely a result of two intertwined problems: the poor math education received in schools and the societal view of mathematics. Primary and secondary schools have attempted a number of approaches to math education, ranging from stressing computation and exact solutions to de-emphasizing answers and focusing on problem solving approaches. Neither approach has been successful, and thus colleges are finding that students have an extremely weak mathematical background and instead of requiring them to take challenging math classes, are offering simplified classes at a much lower than college level.
A large part of the societal problem has been coined ``mathphobia'' - the fear of math. People are more afraid of math than of other subjects, in part because math is neither well-taught nor emphasized in schools, thus making it difficult for students to discover the intellectual pleasure that can be found in mathematics. Just as important and perhaps more disturbing than mathphobia itself, is the fact that mathphobia is caused by mathphobia; that is to say mathphobia is a self-fulfilling prophecy. And this fear of math leads directly to mathematical illiteracy.
Because mathphobia and math illiteracy seem to be socially acceptable, they become part of a vicious cycle. An intelligent or cultured person is perhaps considered to be one who is well read, familiar with the great works of literature, and knowledgeable about history and current events. The definition may vary, but it very rarely includes mathematical understanding. While most academicians would not want to admit to never having read William Shakespeare, there is no sense of embarrassment, or even discomfort, in not having studied calculus. Mathematical illiteracy (innumeracy) and mathphobia are not considered shameful. When parents and educators are lacking mathematical background and don't recognize the importance of mathematics, it is easy to see why math gets pushed aside. Even at the ``best'' schools, students are taught not only that math is difficult, but also that understanding math is not a necessary qualification for success. With this kind of example, it is no wonder that mathematical ignorance continues. And so math illiteracy becomes accepted, ignorance remains, and standards of excellence are lowered to those of mediocrity.
In summary, there are two problems to be addressed: that people don't know what math is and that people are afraid of it, believing it to be too difficult. One solution is to increase math awareness and make math fun. Mathematicians know that math can be fun, but most non-mathematicians do not because math is too often not made accessible to them. Math needs to be made accessible to everyone. One way to do this would be to have more works such as this thesis and the many examples of mathematical fiction mentioned in the introduction. These are all attempts to expose non-mathematicians to math and to encourage exploration in mathematics. Mathphobia must be addressed in schools and in the general society. The notion that math is difficult needs rethinking, and the expectations of math educators and the culture as a whole must be raised. Math books need to be enjoyable to read, and they need to be read. The goal of these books should not be merely to instruct, but to provide opportunities for the enjoyment of mathematics. Only by changing the negative perception of mathematics can we reasonably expect math education to be successful in creating a society that enjoys math and is math literate.
As a junior-high and high school student, I was fortunate enough to both want to learn math and to find, at both the national MathCounts competition and the Hampshire College Summer Studies in Mathematics, groups of individuals who were also interested in math. These people are represented in my thesis by the character of the Yellow Pig. They are a minority in our society. I wrote my thesis to demonstrate that creative mathematical writing exists and that math can be made accessible to non-mathematicians. I want to introduce people to mathematical concepts, share the beauty and pleasure I find in mathematics, and show that math can be enjoyable. I hope that my thesis has succeeded in convincing you that math can be fun.