Reading: Babylonian word problems

The article discusses the notions of "practicality," "generality," and "abstraction" in the context of historical mathematics. It suggests that Babylonian mathematics, while often dealing with practical problems, was limited in its discourse, and remained "applied in form." This implies that even when addressing abstract mathematical concepts, Babylonian mathematics was firmly rooted in real-world applications. In contrast, Greek mathematics aimed for "purity of form" as well as substance, striving to solve problems by extending mathematics and devising new methods.

Diophantus's mathematics highlights a transition from "rhetorical algebra" to "syncopated algebra," a bridge to modern symbolic algebra. This shift represents a move from word-based mathematical expressions to more abstract symbol-based notation. Together, these perspectives underscore the evolution of mathematical thought and notation over time, emphasizing the role of symbolic algebra in achieving greater generality and abstraction in mathematics. These historical developments ultimately contributed to the development of modern mathematics, marked by its highly abstract and generalized nature.


Comments

  1. stephalafOctober 2, 2023 at 12:28 PM

    Hi Sheng, nice development of the text. I wonder if you might extend on how this impacts your understanding and beliefs around practicality, generality, and abstraction in classroom math problems.

    ReplyDelete

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