Hodgkin and Huxley's (5) revealing the origins of cellular excitability is one of the great triumphs of physiology. In an extraordinarily deft series of papers, they were able to measure the essential electrical characteristics of neurons and synthesize them into a quantitative model that accounts for the excitability of neurons and other cells. The Hodgkin-Huxley equations, a set of four differential equations, predict many of the electrical characteristics of neurons and muscle cells; however, these equations are somewhat beyond the ken of most undergraduate biology students. This article will show that if one wants to truly understand the origins of excitability, one cannot avoid its mathematical underpinnings. In this article, Alan Kay demonstrates how it is possible, resorting only to elementary mathematics, to show why the combination of certain ion channel makes cells excitable. The approach detailed here provides an introduction to systems biology thinking, where one has to synthesize all the essential elements into a model to account for a system's behavior.