I’m going to say something which, alas, will probably immediately alienate me from a large number of readers: I’ve always enjoyed math.
Times tables held no terrors for me, fractions I found fascinating, and algebra–ah, algebra! When I first started taking algebra, I enjoyed it so much I’d make up equations out of thin air and solve them just for fun.
No, I’m not from another planet: such people really do exist. In fact, many mathematicians look at math–and enjoy it–as if it were a game, especially those who develop new mathematics and solve previously unsolved or even supposedly unsolvable problems. As in other games, you have a goal, you have certain rules you have to follow, and you win the game if you solve the problem while playing by the rules.
Of course, we don’t usually think of math as a game. We tend to think of it as a tool as much as anything else, a tool that helps us solve problems in science, business and industry. That’s the way it began, after all: the Egyptians, whose mathematical texts are the oldest surviving (dating to about 1750 B.C.) used mathematics for the very practical purposes of determining how much grain to store and how best to distribute bread. They probably would have loved to have our computers and calculators, which have made math an even more powerful tool by enabling us to solve problems that were previously either extremely difficult or impossible.
On a more philosophical level, mathematics is a science: the science of logical reasoning, in which conclusions are arrived at based on a set of axioms, self-apparent (or previously proven) truths. We speak of someone having a “mathematical” mind, meaning clear-thinking and precise. (Think of Star Trek’s Vulcans. I’ll bet Spock enjoyed math class, too.) The most familiar (Earthly) example is Euclid, the ancient Greek whose system of geometry based on definitions, axioms, postulates, theorems and logic we’re all still learning in high school 2,200 years later.
But the precise patterns of Euclid’s geometry are more than just a construction of logic: they are also things of beauty–works of art. The patterns, relationships and symmetry in mathematics are like the patterns, relationships and symmetry in music, painting and literature. In fact, elements of these arts can sometimes be set out in mathematical terms–no one who has listened to Bach can doubt the mathematical underpinnings of music, and Leonardo da Vinci even wrote a mathematical treatise on the depiction of perspective in paintings.
The fact that he could do so demonstrates that mathematics is also a language, which, like other languages, uses agreed-upon symbols and grammar to describe objects and relationships. Using nouns (constants), pronouns (variables) and verbs (operations), you construct sentences (equations), which build upon each other to create whole paragraphs and even books.
Some of the basic books in the mathematical library (I love extended metaphors, don’t you?) are arithmetic, which deals with numbers and the fundamental operations of addition, subtraction, multiplication and division; algebra, which involves the operations of arithmetic but replaces unknown numbers with symbols called variables and gives you a way to calculate unknown quantities from known ones; geometry, which deals with sets of points in a plane or in space; analytic geometry, which is the study of geometry using algebraic principles; trigonometry, used to calculate distances (so you don’t have to measure them directly); analysis, which includes various sub-branches that all use the concept of a limit, especially calculus; and number theory, which deals with (what else?) numbers.
Mathematics is also often divided into “applied” and “pure” mathematics. Applied mathematie way to some new application in the real world.
Because of that, and because I’m a writer, of all the ways of looking at mathematics, I like the idea of it being a language most of all: the language of God, in which the book of the universe is written. The better we understand that language, the better we understand the world it describes.
