Last week I wrote about ancient Indian math, which George Gheverghese Joseph covers in the eight and ninth chapters of The Crest of the Peacock. In the tenth chapter Joseph turns his attention to Kerala, on the southwestern tip of the Indian subcontinent.
Modern Kerala first came on my radar when I was living in Qatar, which also home to some 650,000 Indians. Whenever I asked where they were from, they seemed to always say Kerala. Qatar Airways, for its part, operates eight nonstop flights per day between Kerala and Doha, Qatar. But I digress.
This chapter covers a range of subjects, from important mathematicians like Madhava and Paramesvara, to countering the notion that all non-European math was purely utilitarian. Pure mathematics, as it is known today, is the field of math that does not intend to serve practical application (even if practical applications are eventually found). Joseph writes:
“I have a vision of a group of pure mathematicians in Kerala between the fourteenth and sixteenth centuries indulging in their passion and probably proud of the fact that the mathematics that they did was of no use to anyone!”
What really struck me about this chapter, though, is wherein Joseph considers the “case for transmission” of Kerala mathematics. Or, in other words, the argument that certain mathematical ideas were transmitted from Kerala to the West rather than discovered independently.
On the surface, it seems like an easy thing to do. After all, we can trace the spread of goods, so why not mathematics? Then again, how does one trace an idea?
Joseph doesn’t use this example, but to me it’s like trying to trace the spread of a rumor. Where did it begin? Who shared it with whom? You might have physical evidence to go on, but what if you didn’t? Where would you begin?
Joseph suggests a couple points that give strong evidence for the transmission of a mathematical idea (like the quadratic formula, say):
- Translations of the idea from one language to another.
- Errors in calculation or formula that are unlikely to have been come upon by chance.
The second one makes me think of cheating on a test. What are the chances that multiple students all found the product of 9 and 9 to be 83? It’s possible that they were all making the same mistakes, of course, but probably more likely that they were sharing answers. As Tolstoy wrote, “Happy families are all alike; every unhappy family is unhappy in its own way.” Or at least they should be.
Without translations or errors to go off of, Joseph volunteers a second class of evidence that follows the legal ideas of motivation and opportunity. The motivation the West had to import the mathematical ideas of Kerala were the trifecta of astronomy, date keeping, and navigation. And the opportunity for transmission was provided by trade and Jesuit missionaries.
Establishing motivation and opportunity would still make for a weak legal case, as Joseph admits (though he does go into much greater detail than I’m able to here). That said, I find it an interesting way to think about the question, and a reasonable to way to think through other questions like it.