Reflections on the Crest of the Peacock
I generally consider myself decently knowledgable about the history of mathematics, for someone with no previous formal training or coursework in the area. Nevertheless, I was surprised to find the lengths that Western (meant to denote Europe, Canada, the US, New Zealand and Australia; Joseph prefers the term European) historians and writers went to in order to devalue the mathematical contributions of non-Western societies. Reading Joseph, this makes sense, since one of the implicit goals in writing these histories is to “[Ignore and devalue] the contributions of the colonized people … as part of the rationale for subjugation and dominance” (Joseph 2011, p. 5).
Nevertheless, it was surprising to me that it was known, at least by some, that there was “full acknowledgement given by the ancient Greeks themselves of the intellectual debt they owed the Egyptians” (Joseph 2011, p.5). I don’t know the exact timeline in which these acknowledgements were discovered, but it strikes me as very plausible that, at least until the weight of the evidence could not be ignored, writers and historians brushed these acknowledgements under the rug to preserve the popular view that mathematics was born, developed, and perfected in Europe and Europe alone.
Along less nefarious lines, I was very interested to see the extensive flow and interchange of mathematical knowledge across Eurasia, from Greece to the Arab world to India to China. As Joseph notes, “cultural barriers [are relatively ineffective] in inhibiting the transmission of mathematical knowledge” (Joseph 2011, p. 13); though I had not thought much about it before, this makes sense to me, at least on its face. Philosophy and literature, for example, are extremely specific to the culture in which they are created, and often require an extensive knowledge of, or even a lived experience of, that culture to understand fully. On the other hand, while mathematics develops in a specific context, to actually understand a piece of mathematics does not require the same level of familiarity and understanding of the culture from whence it originated.
A final thing I found surprising in the reading was the isolated mathematical achievements of the Mayan civilization. I will use the example Joseph gives of the “principle of place value” (Joseph 2011 p. 22), which we encounter in modern mathematics today in the form of the decimal system. Joseph is quick to point out that a place value system was discovered independently four times in the history of math. What makes the Mayan discovery of a place value system unique, to me, is that they were really and truly isolated from the other mathematics-producing civilizations. I am no historian, and am not in a position to adjudicate whether or not the three discoveries of place value systems in Eurasia were truly independent; but as a non-historian, knowing that the Mayans also discovered such a system helps to illustrate how universal mathematics is. As an aside, it also probably supports the notion that math is discovered rather than invented, though of course this question is beyond the scope of my current blog post (but is a fascinating question to think about!).
Ben, I appreciate your critical insights into the implicit goals of those in power recording history. You raise an interesting point about Joseph's notion of Western mathematics being focused only on Europe. In many of the regions colonized by Europe, like Canada, we are only beginning to recognize and incorporate Indigenous mathematics into our education. Also, I agree with your that the reoccurring isolated 'discovery' of concepts like place value is fascinating. Great blog post!
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