Vedic maths points to psychological processes that take place while solving mathematical problems, UK-based vedic maths expert JAMES GLOVER says to SONAL SRIVASTAVA
Vedic mathematics is not a bunch of mathematical tricks,” says James Glover, president of the UK-based Institute for the Advancement of Vedic Mathematics. He has been teaching vedic mathematics in the UK for 35 years and was in India recently to conduct workshops on the subject for young students and teachers. “Vedic mathematics helps make calculations and algebraic manipulations much faster, more efficiently — but one of the effects of that has been the commonly held view that vedic maths is a bunch of tricks, which is a pity!” exclaims Glover,who has written a number of articles, research papers, and more recently, text books on vedic mathematics. Titled The Curious Hats Of Magical Maths, the textbooks present vedic mathematics in an interesting and reader-friendly manner. Each vedic maths sutra is represented by a different hat that depicts the function of the sutra. He says that sutras of vedic maths are in Sanskrit and it is important to make them attractive for readers. Shankaracharya Bharati Krishna Tirtha of the Govardhan Math in Puri gave sutras or aphorisms of vedic maths in a book published in the 1960s. Glover feels that Shankaracharya’s book was an illustrative volume that didn’t spell out the whole system.The latest work on vedic maths has been to uncover what Shankaracharya was really trying to say. The second misnomer about vedic maths sutras according to Glover is that they are considered exclusive — something that is not true.The sutras are inclusive — all of them express thought processes that naturally take place when performing a mathematical process.They express processes that are universal.The vedic maths system reveals that mathematical problems can have different solutions.
It enhances strategy skills in problem-solving, which is a highly sought after characteristic in the modern world of commerce, engineering and computing. However,critics of vedic mathematics point out that there ‘is nothing vedic in vedic maths.’ Mathematician C K Raju wrote an article in The Hindu asking,“Where in the vedas is ‘vedic mathematics’to be found?”Glover wrote a rejoinder in the same newspaper,arguing,“Vedic maths is concerned with a universal structure of maths revealed through a personal approach to problem-solving” Talking about the ‘vedic’ in vedic maths, Glover says that the Shankaracharya had studied the vedas for several years and from stray references and from a parashishta, an appendix portion of Atharva Veda,he was able to construct the vedic system of mathematics. Nobody has been able to find that parashishta, so it’s possible that it was unpublished. The Shankaracharya had access to texts that the general public could not access. He also says that the term vedas can have two meanings — and that they are connected.The vedas are ancient texts and the word ‘veda’ also means knowledge that can be intuited and is applicable in spiritual, physical and mental realms. “You can’t claim vedas on any racial, geographical and religious grounds.Why I am quite happy with the word ‘vedic’here is that many of the sutras are not only highly practical, but also express spiritual themes and principles,” he points out. Glover gives the example of sunyam samyasamuccaye, a sutra which means that when the totals are the same, the result is zero.
“What it means is that when you have two aggregates, then there is no difference,and that expresses the idea of balance.The idea of balance runs through mathematics. An equation is about balance.That is also a theme within advaita philosophy where we are encouraged to find balance in our lives — both externally and internally,” He explains. He cites another sutra — sisyate sesasamjnah, which literally means the remainder is that which remains.“At first glance, that doesn’t seem to be saying very much, but it is speaking about the principle of invariants,”elaborates Glover. In mathematics, invariant is a function or property of a system which remains unchanged during transformation. For example, a number remains invariant when multiplied by one. “Invariance is another theme in advaitic philosophy where the innermost Self is invariant,” Glover rationalises. To firmly establish vedic mathematics and the advaita connection, he gives yet another example, yashti samashti, which means individual and universal or particular and general.“In mathematics, when you find the average of a group of numbers and divide it by a group of numbers, your average or mean is a single number representing the whole. This sutra also gives rise to the principle of selfsimilarity where an individual shape or entity reflects the whole.In advaitic philosophy, samshti the universal, is reflected within the individual. Self-similarity reflects in mathematics in such things as fractal geometry and in the chaos theory,” he elucidates.
Fear Of Numbers
Mathematics instils fears in some people, especially children. Could sutras help deal with this fear? Glover shares his own experience.“When I teach a class, I say there are only nine numbers and a zero.From those we make all others. Each number is a single entity,a unity. A son asked his dad — how many numbers are there.The dad said there are three answers, the first answer is infinite. The second answer is 9 and a zero and the third answer is one,because each one is a one.Difficulty in algebra is usually because some gap has occurred earlier on.The difficulties with algebra are to do with not understanding the syntax, such things as x2 means x times x which is different from 2x. So these foundations stones have to be put into place and teachers have to take great care so that the child can progress.The fear,‘I can’t do it, I don’t know how to do it, I’m stuck,’ is largely because of some gap.Something hasn’t been drawn out of the child,” says Glover,who was drawn to vedic maths because of its universality and expression of unity. Sometimes, while teaching vedic maths, Glover finds it difficult to draw people out of their comfort zones. He quotes the Shankaracharya who said in the book that one has to be open-minded, truth-seeking and humble. For Glover, mathematics may not be transcendental, but the meaning of the sutras reminds him of something that is transcendental.“They point to something that is much deeper,” he adds.■
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