Early in every school year I took a class period to ask my math students what they thought were the origins of the subject they were about to explore. The answers would range from empty stares to hazy references to tablets and Mt. Sinai. Some of the more adventurous would throw out some vaguely familiar names like Pythagoras, Archimedes, and Einstein.

Much to my chagrin, Pi was often included in this discussion. In an attempt to restore order I would quickly take back control of the conversation with the comment that like most games or activities, math began with a set of simple rules and regulations. The most remarkable characteristic of the fundamental principles of math, from elementary arithmetic to the most complex calculus, is their simplicity.

There are only eight basic principles that serve as the underpinnings of one of the most complicated subjects they will undertake in their entire academic careers. The removal of any one of the rules listed below would severely cripple math as we now know it. (Please note: there is not total agreement on the precise names of all of these principles. I have used the labels with which I am most familiar.)