Mesopotamian Algebra

9. In what sense did the Mesopotamian authors “do algebra”? Did they have the concept of an equation or a classification of types of equations? The Mesopotamian authors didn’t “do algebra,” they solved problems by following a set of steps which allowed them to get a numerical answer. Today, if we tried to solve those problems, we would use algebra, but they did not (Cooke, 2005, p. 40). They had no concept of an equation, or of a set of rules that would allow them to solve a variety of problems, unlike the overriding rules of algebra (i.e. the rule that is taught to high school math students: solve equations by doing reverse order of operations). Because they didn’t have a concept of an equation, they didn’t have a concept of the classifications of types of equations. Although, they did have different sets of steps used to solve different types of problems. Therefore, they must have had some system of classification of types of problems, so that they would know which set of steps to follow. For example, the previous problem in this assignment asked us to find two numbers given their product and difference. The Mesopotamians knew the steps required to find the two numbers, although those steps would have not helped at all if the problem had been something like

First, most of our present day notation is an attempt to make equations shorter, with fewer numbers/symbols/etc… For example, if while working out a problem we came across the number 114/115, nobody wants to write out (115) ̅ (115) ̅ (115) ̅ (115) ̅ (115) ̅ (115) ̅…Our idea of using notation to shorten the length of math problems started with the idea of using symbols instead of words to begin with, as much of the ancient world did mathematics by writing it out in words. So things that we would today write as a short and simple equation like x+5=13, would have been written something like “thing and five more is the same as