I was impressed when reading how Babylonians could solve higher order equations by making them "look like" quadratics (for which they had a formula) using substitution. In some ways that feels one step away from our modern algebraic symbols. It does not quite fit the definition of syncopated algebra (though this term is new to me and I'm still not completely clear on the definition), but it feels like a sort of syncopation in the sense that they were seeing "x^2 hidden in x^4" for example so they could use their familiar tools.
I will say that following the descriptions of the Babylonian rhetorical algebra made my brain hurt. It was such a new way of thinking about these kinds of problems and really difficult to try follow their steps in earnest without resorting back to my modern algebraic tools, and in some cases I had to in order to understand what they were doing. Example 4.8 was one such case. I was really confused by the Babylonian step 1 and had to go through the algebra to grasp what they were doing so quickly. It's so interesting to think about how the ways in which we learned math shape our understanding in such a way that it becomes difficult to even think in another way, at least for me.
This reading gave me a re-appreciation for our modern algebraic tools!
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