My Thoughts on Babylonian Algebra


It was fascinating to learn that the Babylonians used methods that resembled modern algebra to solve equations. In particular, they adopted what the author referred to as the "rhetorical algebra" using imaginative numerical tables (for multiplication, reciprocates, squares etc.) to expedite their problem-solving process. The logic and principles behind their techniques - solving math problems step by step using an established numbering system and framework - are still existent today.

Prior to modern algebraic notations, it was reasonable to use terms like "length" and "area" that have actual physical meanings in their daily lives to denote quantities. This makes understanding a mathematical problem much easier. From there, "hidden knowledge" that were obtained from previous problems and transcribed into records can be used as mechanisms to produce answers for each question.

As for facing a mathematical world without algebra, it is personally difficult to imagine how abstractions by themselves could allow us to reach the essence of mathematics. There is an unlimited set of problems in each area of study - geometry, number theory, calculus - that needs to be explored, and algebra is a tool we can use to define a set of rules to follow. Although it is still possible to find solutions without the use of algebra, it is much more efficient to rely on algebra, especially for understanding future problems and/or develop more advanced relationships between variables. However, in teaching mathematics, I agree that sometimes it is more effective to neglect algebra (in some cultures, that's how children are taught) and have students visualize abstract relationships to develop a basic knowledge of algebra and its underlying foundation.

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