Three interesting things in Joseph's The Crest of the Peacock

I enjoyed the figure on page 10 proposing an alternative map of the transmission of mathematical knowledge during the Middle Ages, particularly in how important the role individual cities played. Cities were often much more independent (culturally, politically, and intellectually) of the surrounding areas than they are today, so it makes sense they occupy such an important spot.

I had known that ancient and medieval India was partially responsible for our number system and that they made some incredible advances in mathematics, but I didn’t know the details, particularly that they helped spread trigonometry and indeterminate equations. India sitting somewhere in the middle of all these different regions and contributing to and drawing on knowledge throughout the world illustrates how much more connected peoples in the past were (at least at times) than moderns realize.

Civilizations growing comfortable with and accepting zero as a number is always fascinating to me. There was a similar resistance to irrational and imaginary numbers. I like to imagine Mayan and Indian mathematicians trying to convince a skeptical public that nothing is actual something.