Crest of the Peacock, Chapter 1

One question in particular struck me as I read this chapter: given that non-European cultures played such an important role in the development of early mathematics, why is almost all modern mathematics (by which I mean Newton and Leibniz's calculus and onwards) European in origin? Were there some cultural or geographical factors that prompted rapid mathematical discovery? Or maybe comparable work was being done by other cultures, but it was overrun by European mathematics as colonialism spread European cultural dominance. I would be very interested to learn more about this.

Another thing that struck me was early mathematicians' ability to formulate mathematical problems without notation and concepts that were developed later, and that we take for granted. For example, the author mentions the Babylonians' method of solving cubic equations by reducing them to the form x^3+x^2=c. The Babylonians would not have had the notion of a function, or even of algebra, and it's hard for me to imagine how I would even think about a problem like that without those tools. We are taught a very specific way of thinking about math, and we don't see ways of conceptualizing problems outside of that.

Finally, the achievements of the Maya mentioned near the end of the chapter were astonishing to me. To make predictions with such a high degree of accuracy, with almost no scientific tools available, would take incredible mathematical ingenuity, and, I presume, an advanced understanding of cosmology. It's especially impressive given that the Maya would not have had access to all the inter-cultural mathematical dialogue that the civilizations of Europe, the Middle East, and Asia had at the time. I suppose it's not too surprising that conspiracy theories sprung up around the Maya and their use of mathematics!