Alex's Adventures in Numberland - Alex Bellos [56]
The symbol that emerged in ancient India for zero perfectly encapsulated the Shankaracharya’s overriding message that mathematics cannot be separated from spirituality. The circle, 0, was chosen because it portrays the cyclical movements of the face of heaven. Zero means nothing, and it means eternity.
Pride in the invention of zero has helped make mathematical excellence an aspect of Indian national identity. Schoolchildren must learn their times tables up to 20, which is twice as high as I was taught growing up in the UK. In previous decades Indians were required to learn their tables up to 30. One of India’s top non-Vedic mathematicians, S.G. Dani, attested to this: ‘As a child I did have this impression of mathematics being extremely important,’ he told me. It was always common for elder people to set children mathematical challenges, and it was greatly appreciated if they got the answers right. ‘Irrespective of whether it is useful or not, maths is something that is valued in India by one’s peer group and friends.’
Dani is senior professor of mathematics at the Tata Institute of Fundamental Research in Bombay. He has an academic’s comb-over frizz, rimmed tortoiseshell glasses and a moustache that frames the length of his upper lip. And he is no fan of Vedic Mics; he neither believes that Tirthaji’s arithmetical methods can be found in the Vedas nor does he believe it is particularly helpful to say that they do. ‘There are many better ways to bringing interest into mathematics than resorting to inputting them into ancient texts,’ he said. ‘I don’t believe that they are making mathematics interesting. The selling point is that these algorithms make you fast, not that it makes it interesting, not that it makes you internalize what is going on. The interest is in the end, not the process.’ He is doubtful they do make calculation quicker, since real life does not throw up such perfectly formed problems as finding the decimal breakdown of 1/19. At the end of the day, he added, the conventional method is more convenient.
So, I was surprised that Dani spoke empathetically of Tirthaji’s mission with Vedic Maths. Dani related to Tirthaji on an emotional level. ‘The dominant feeling that I had for him is that he had this inferiority complex that he was trying to conquer. As a child I also had this kind of attitude. In India in those days [shortly after Independence] there was a strong feeling that we needed to get back [from the British] what we lost by hook or by crook. It was mostly in terms of artefacts, stuff that the British might have taken away. Because we lost such a lot, I thought we should have the equivalent back of what we lost.
‘Vedic Mathematics is a misguided attempt to claim arithmetic back for India.’
Some of the tricks of Vedic Mathematics are so simple that I wondered if I might come across them anywhere else in arithmetical literature. I thought that Fibonacci’s Liber Abaci would be a good place to start. When I got back to London I found a copy at the library, opened the chapter on multiplication and Fibonacci’s first suggested method is none other than…Vertically and Cross-wise. I did some more research and discovered that multiplication using All from 9 and the last from 10 was a favoured technique in several books from sixteenth-century Europe. (In fact, it has been suggested that both methods might have influenced the adoption of×as the multiplication sign. When×made its first appearance as a notation for multiplication in 1631, books had already been published illustrating the two multiplication methods with large ×s drawn as cross-lines.)
Tirthaji’s Vedic Mathematics is, it would seem, at least in part, a rediscovery of some very common Renaissance arithmetical tricks. They may or may not have come from India originally, but whatever their provenance, the charm of Vedic Mathematics for me is the way it encourages a childlike joy in numbers and the patterns and symmetries they