Andy H. Davis
davisa@smccd.edu

Why study math ...

Because mathematics is intriguing. As Bertrand Russell put it, "mathematics is the subject in which we know neither what we are talking about nor whether what we say is true." So, perhaps, first and foremost, we should study it to find out what it is. We owe it to ourselves to at least know what mathematics is before we claim that it isn’t really important in our daily lives or before we close off career opportunities which depend on it.

Mathematics is about relationships, or put more "mathematically" , it is about structure. Even at its most basic level, relationships are the name of the game. First you learn to count, and the important relationship is "order". Then you learn to add and multiply; you start to pair off numbers to produce new numbers, according to what seem to be arbitrary and mysterious "laws". But you soon learn, much to your dismay, that although they might be mysterious, these laws are not arbitrary. If you don’t get them exactly right, the teacher puts a big red check next to your answer. And later, if you don’t get them right, you’re late and miss your friends or you don’t have enough money because you didn’t figure in the sales tax.

And soon, these relationships aren’t between numbers anymore; they’re between letters that merely represent numbers or letters that represent points in a plane. And you must learn to combine the letters according to the laws which govern the relationships among whatever the letters represent. And this is just the beginning. Next you learn "algorithms", relationships between relationships. For example, if you want to know your average electric bill, first you need to add, then to count, and finally to divide.

Eventually, if you survive all of this, which too few do, you may get to the point that those arbitrary and unforgiving numbers disappear and what’s left is just the relationships. That’s what Russell meant what he said that mathematics was the subject in which we "do not know what we were talking about", because in the end we aren’t talking about what the numbers represent anymore or even about the numbers themselves; we are talking only about relationships and structure. At this point, mathematics is more like philosophy or art than it is like physics or economics. Mathematics is the study of form and structure. It is pure logic; it is a mind game, as challenging a mind game as any you will find.