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The Crest of the Peacock - Chapter 1 response


        For someone taught a primarily Europe-centric math history, such as myself, there was a wealth of new and enlightening information to be gleaned from this chapter. One of the first things to catch me by surprise was the foundational beginning of math originating not in Greece, but in Egypt. The vision I was often presented with was one of famous Greek thinkers coming up with new ideas, as if out of thin air. The intelligence and creativity of the classic Greek thinkers is beyond doubt, but their reliance and debt to even earlier Egyptian mathematicians is essential to understand when trying understand a complete history of mathematical development. What makes this common omission so egregious is that the Greek thinkers themselves attributed the foundation of many of their ideas to Egyptian mathematics. 

        In the chapter, this neglect of anything mathematical originating prior to ancient Greece was exemplified in the quote from twentieth century by Kline (1953). Seemingly by the time this was written, there was significant research and evidence surrounding the ancient development of mathematics in Egypt, Mesopotamia, China and other areas, but it was entirely ignored. This simplistic view, portrayed in Figure 1.1 (Joseph, p. 4), provides an easy narrative to follow but looses out on the nuance and dynamism of the real history.

        A small, and perhaps easy to miss section, mentioned the origin of our modern word 'algorithm'. With the prevalence of algorithms in determining almost everything we do (and certainly everything we see online) today, it was of great interest to me to learn that it originates from a mis-understanding or corruption of the name al-Khwarizmi. He was an Arabic mathematician who wrote a book documenting and explaining the Indian number system. 

        Translation of the book into European languages is what lead to our common mis-attribution of the western number system as an Arabic creation, as well as giving us the word 'algorithm' as an adulteration of al-Khwarizmi. While it's important to recognize the many contribution of Arabic mathematicians to the field, to me this story shows how we, in the west, often readily accept accept inaccurate translations and simplified histories. 

        One last thing that completely blew me away was the short section near the end of the chapter of the mathematic of the Mayan people. Not only did they independently discover the use of zero and create a place-value number systems, but they were able to invent incredibly accurate and precise astronomical calendars with very rudimentary tools. While I have heard discussion of the ancient Mayan calendar system (most notable in 2012), this is my first time learning about their mathematics and their number system. I would be very curious to learn more about their base 20 number system; time to do more research!


Reference

Joseph, G. G. (1991). The crest of the peacock: Non-European roots of mathematics. Princeton University Press. 

Comments

  1. Amanda FritzlanSeptember 21, 2022 at 12:15 PM

    Tim, I appreciate your articulation of the mythology of "out of thin" air mathematical discoveries, particularly ancient Greek. There are a number of mathematicians, like Euclid for example, who gathered and recorded the work of a great many mathematical thinkers who came before them. The often serendipitous fact that their work was not destroyed attributes to a patchwork narrative of "great mathematicians". I agree with you about he significance of the word "algorithm" in our worlds today. There is a wonderful and terrifying book by Cathy O'Neil, Weapons of Math Destruction" about the absence of ethics in algorithms that shape contemporary life. Great post!

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