Table 4.2 in this reading shows the different words or "notations" that the Babylonians used before the development of the algebraic notations that we use today. In this table, we see the Babylonian quantities such as "ush" and their respective modern symbol, "x." I see this as the Babylonians translating words in their daily lives into algebraic applications.
These words were used to generalize the concepts of algebra and mathematics; showing the true essence of the Babylonian development of mathetics in relating math with the real world. This generalization is still used today to create tangible images in solving math problems. For example, in elementary school, your math problems likely sounded similar to "If Timmy had 3 apples and gave John 2, how many does he have left?" - showing how generalization can simplify mathematics.
Without algebra, I would argue that most math is quite difficult. Perhaps geometry and graph theory could be simplified without algebra as visual representation is a possibility. But when I think of calculus, I think of long equations with one or more variables and algebra is typically at the core of the solution. I believe using algebra is can be considered an abstract way of solving problems. Although generalized algebraic rules are used to get to the solution, it is an abstract method in that it doesn't have generalized applications outside of mathematics.
OK -- again, this is a pretty superficial treatment of the topic and it doesn't refer in very meaningful ways to the article. This needs revision to take the ideas more seriously and refer to the original reading in more ways.
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