One thing that surprised me after reading this article is that the history of mathematics can be very different depending on the purpose and perspective of the historian. Mathematics itself is based on proof, so usually there is a clear answer about whether it is correct or not. However, history is different. A historical explanation may not be false, but it can still be partial because people choose to focus on different evidence and different questions. The author’s criticism of the traditional Eurocentric history made me think that when we study math history, we should not treat one version as the complete truth. We need to keep an open mind.
The second thing that surprised me is how much attention can be given to the question of who invented a mathematical idea first. I do not deny that this question can have cultural or even political value. It is also meaningful to correct the underestimation of Chinese, Indian, or other mathematical traditions. However, personally I am not very interested in proving that one civilization was “first.” For example, ancient China had highly developed astronomy, calendars, architecture, and engineering. It is hard to imagine that these achievements could exist without substantial mathematical knowledge. To me, a more interesting question is how those mathematical ideas developed, what problems they were trying to solve, and why people needed them in the first place.
The third thing that surprised me was the network model of mathematical development. I think this model is more convincing than a simple line from Greece to Europe. At the same time, communication in the ancient world was difficult and expensive because of language and transportation barriers. Compared to the high cost of transmitting mathematical ideas across long distances, I believe developing some mathematical ideas independently could sometimes be more economical for each culture. Besides, it can also explain the development timeline of each culture better. However, I'm more interested in studying how math developed within each culture and what historical demands led to that development.
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