Singing mathematics

Yesterday we had a fascinating colloquium talk about the Kerala school of mathematics, given by Aditya Kolachana from IIT Madras (where, by a remarkable coincidence, I am giving a remote talk next week).

I knew a bit about this subject, since when I visited Kerala in 2010, I was given a book about the Kerala school and its founder Madhava (14th century CE). Two of his achievements were to find the power series for the inverse tangent and hence the alternating series for pi usually attributed to Leibniz, and then (since this series converges very slowly) to discover some remarkably ingenious tricks to get faster convergence, so that he was able to compute pi to 11 places of decimals.

One remarkable feature of the talk was that the speaker showed us several times the Sanskrit verse in which the mathematical results were expressed, and proceeded to sing or chant them. He explained that it is much easier to remember a song than a piece of text, and so this was done for the benefit of students. I do not know whether he was taught mathematics this way, or whether he studied the chanting of mathematical verses when he became a historian of mathematics. But it seemed remarkably effective.

One downside of the Indian method of writing mathematics, which has led outsiders to think that Indians were not interested in proofs, is that the proofs were not included in the primary texts but only in commentaries on them, and while some primary texts have been unearthed and translated, this has happened much less for the commentaries.

But we should not feel superior about this. Today, in several application areas including statistics, some journals take the view that mathematical proofs should not be included in the paper but relegated to the supplementary material.