Response to Joseph, "The Crest of the Peacock"

 As I mentioned in a previous post, while I had good math teachers, I struggle to remember even one time when a secondary math teachers made mention of the historical development of mathematics. So where did I get my ideas about math history? I ask this because what struck me as I read the introduction to The Crest of the Peacock is that I DID have ideas -- as it turns out, largely inaccurate ones! I guess you could say my views were very close to what Figure 1.1 of the text describes: "The 'classical' Eurocentric trajectory." I can only surmise that my sense of math history came from history courses I took or perhaps a course I once took in the history of religion and science. Or maybe I picked up concepts from reading short articles in popular science magazines over the years.

Whatever the case may be, the above explains why I found myself surprised on almost every page of this reading. I'll focus my thoughts on three such occasions:

1. While I was aware that the Egyptians and Mesopotamians had developed mathematics to some degree, I had no idea that, as Joseph says, "There is the full acknowledgement given by the ancient Greeks themselves of the intellectual debt they owed the Egyptians" (p. 5). I did not realize that Artistotle's teacher had studied in Egypt, or that Thales and Pythagoras reportedly travelled widely in Egypt and Mesopotamia and learnt math from these areas. In other words, I was unaware of the connections and transmission of math between different ancient cultures. Rather, I was under the assumption that the Greeks had developed their mathematics independently for some reason. How rich and interesting it is the learn otherwise!

2. Along similar lines, I was ignorant of the Arab contributions to the development of mathematics and indeed the sciences in general. The line that made me stop was this: "The course of European cultural history and the history of European thought are inseparably tied up with the activities of Arab scholars during the Middle Ages and their seminal contributions to mathematics, the natural sciences, medicine and philosophy" (pp. 6-7). I believe I thought Arabs had transmitted some information during the "Dark Ages," but I was unaware of anything like "seminal contributions." I didn't even know the word algebra was Arabic in origin! And the impressive list of Arab scholars in the footnote on page 7 also struck me. In fact, it made me upset: how could I have gone through high school and a 4-year liberal arts collegiate program and never encountered (so far as I can remember) anything about Arab scholarship during the Middle Ages? I thought the "Dark Ages" really were dark, not just in Europe, but everywhere...

It turns out the world of mathematical history is a much bigger and much more interesting place than I realized. I would have loved to learn some of this in my high school days.

3. It seems like a small thing, but I stopped at the line near the end in the section on the Maya where Joseph writes, "As regards zero, there are only two original instances of its modern use in a number system: by the Maya, and by the Indians around the beginning of the Christian era" (p. 22). Beside the interesting fact that that Maya were one of two groups who developed the concept of zero, I was puzzled by this statement. I would have thought zero was used in mathematics commonly in the ancient world and I found myself surprised to learn this was not the case. I don't understand how math works without zero, so I obviously have a lot to learn!

Which I guess I what I would say is the overall theme of my blog post: I have a lot to learn about math history! (This is motivation to make sure my students have a better framework than I was given in my high school days.)