Crest of the Peacock
I really found it interesting to see the stages of mathematical development throughout the years; way before I was born. In fact, Joseph (1991) mentions "a concise and meaningful definition of mathematics is virtually impossible" (p.3). It made me realize what does Mathematics really mean in the current sense and would that definition be different from the earlier days? In my personal views, I would view mathematics in the financial sense because everything we do involves the usage of money. Some examples include purchasing goods from a store, investing in stocks and purchasing a house. The most notable work is from the late nineteenth and early twentieth century. In fact, most work from centuries ago are not really learned in school and I am also guilty of that.
I also found it interesting that Mathematics is mostly credited to the Europeans and work outside of Europe was barely acknowledged. Most notably, the neglect of early Indian mathematics and neglect of Arabian mathematics. It made me realize how all contributions to Mathematics are very important and all parties should be credited for their discovery. I did not know at all the Arabs were responsible for "bringing the technique of measurement" (Joseph, 1991, p.7) alongside with the Indians being responsible for the instrument of computation. There were references to China in some parts, but the bigger question I was wondering about is if there are any important mathematical developments from other countries like South America or South Asia. The field of Mathematics is very broad and obscured. I wonder if there are many more discoveries to be made.
Finally, I am very impressed with the Mayans' discovery of telling time without the aid of technology advancements we have today. With only basic tools at their disposal, how is it possible to measure the passage of time and make their own version of their calendar. Luckily, I am very glad to know that their prediction of the world ending a decade was found to be untrue. It made me realize that with hard work and determination, nothing seems out of reach.
Joseph, G.G. (1991). The History of Mathematics: Alternative Perspectives. The Crest of the Peacock: The Non-European Roots of Mathematics (Third Edition, pp. 1-22). Princeton University Press.
Juyoung, I like that you are thinking philosophically about what mathematics actually means or is, along with this reading. Financial exchange was a huge reason for mathematical development. As civilizations grew food for many people and created items to exchange, they needed to create a system of keeping track of inventory and recording the value of goods. I hope that your understanding of mathematics histories beyond European narratives is something that you can one day bring into your math teaching.
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