Introduction

An amazingly sophisticated example of some of the oldest written mathematics known to humanity is the clay tablet Plimpton 322 (Figure 31.1), so called because it is item number 322 in a collection assembled by G. A. Plimpton in the 1930s and now housed at Columbia University in New York City. The tablet dates to the 19th century BCE, and can be traced to the Old Babylonian civilization that flourished in Mesopotamia, the fertile valley of the Tigris and Euphrates rivers (present-day Iraq). This exotic artifact is an ideal touchstone that can be used to spark interest in the study of representations of number and of arithmetical computational algorithms, say, by future computer scientists or prospective school teachers. It can also serve to deepen an understanding of the solution of quadratic equations by students of algebra at all levels.

Historical Background

Evidence of mathematical thinking is at least as old as the species homo sapiens. Older, in fact, provided we agree to classify certain animal behaviors, like the ability to differentiate quantities, to count, or even to employ geometric design in the building of shelters, as evidence of mathematical activity.

Once humans moved from hunting and foraging to farming and later to forming cities, new challenges of life required new forms of thought, including those that looked much more like what we would today identify as mathematics. Certainly, the first literate civilizations known to us also provided written evidence of their mathematics as well.