Kenneth Williams in his recent Vedic Mathematics Newsletter, Issue 67 (news@vedicmaths.org), wrote an article discussing the question of what Vedic mathematics is. It is a question I have been asked a number of times, and I have never been sure how to reply. This is a helpful approach. In general, he defines an approach to mathematics as specifically vedic if it is a basically one-line method. The article follows.
WHEN IS MATHEMATICS VEDIC MATHEMATICS?
The last 10 years have seen a huge increase in interest in Vedic Mathematics. The system reconstructed by Sri Bharati Krsna Tirthaji almost a century ago (and now known by the term “Vedic Mathematics”) is at last being recognised as having tremendous potential in all sorts of areas: educational, computational, scientific, psychological and so on. This new decade is sure to see this continue, and develop and expand further.
The influential and unbiased article by Dr N. M. Kansara1 in 2000 dealt with the criticisms aimed at Bharati Krsna’s use of the term Vedic Mathematics.
But though there is much positivity and much to look forward to there is one important area that needs to be clarified, and that is the answer to the question: “What is Vedic Mathematics: what is included within this term and what is not?”
Different people may have different ideas about the answer to this question. And it is not enough to simply refer to the book by Bharati Krsna as new material is being produced and termed Vedic Mathematics all the time.
How do we decide if a particular piece of mathematics is Vedic Mathematics or not? What is the defining characteristic, or characteristics, of Vedic Mathematics by which we can recognise something as part of the Vedic system?
Why is this question important? It is vital that this question is answered because there has to be some clear boundary to what is Vedic Mathematics and what is not. Otherwise people can declare all sorts of obscure mathematical results and claim them to be Vedic Mathematics.
Another reason why the question is important is that for many people Vedic Mathematics has become synonymous with tricks, short cuts and fast methods. This is unfortunate as it means it is not seen seriously by mathematicians and educationists, and it entirely misses the comprehensive and complete nature of the system of Vedic Mathematics.
Here are some possible answers to the question: what characteristic of a method, proof etc. makes it Vedic?
A method, proof etc. is Vedic if:
1) It comes under one or more of the Vedic Sutras
2) It follows a method given by Bharati Krsna
3) It is one-line
Answer 1 I must reject as I believe the Sutras describe natural ways in which the mind works 2, so any way of thinking or any method must use the Sutras. Even the current long multiplication method (that cannot be described as Vedic) uses these Sutras.
Answer 2 does not allow the possibility of methods being Vedic that are not given by Bharati Krsna and so is too restrictive.
For Answer 3, first look at the title of Bharati Krsna’s book:
“Vedic Mathematics
Or
Sixteen Simple Formulae from the Vedas
(For One-line Answers to all Mathematical problems)”
This is the full title: first Vedic Mathematics, then an alternative title, and then the words in brackets.
This title implies that the Sutras are the basis for Vedic Mathematics, and that they give one-line answers to all mathematical problems.
This is perhaps the criterion we are looking for: a method must be one-line. But this answer is no use to us unless we can say what ‘one-line’ means.
In the area of computation we can say ‘one-line’ means that the answer can be given digit by digit with an occasional carry digit (or digits), which can be held in the mind. The term also suggests that the flow of attention is one-line: that the attention is not fragmented.
A good illustration is perhaps the obtaining of the product of two numbers by the Vertically and Crosswise method and by the usual conventional method. In the Vedic method the attention moves through the numbers being combined, obtaining the digits of the answer one after the other (from right to left or from left to right) using a simple pattern.
The conventional method is fragmented, obtaining first one row of figures and then another until finally these rows are added up. In fact the same number of products are found in both methods, but the Vedic method flows, and flows in one direction: i.e. it is one-line.
Getting an answer digit by digit with an occasional carry digit also suggests that such a calculation can be carried out mentally, and in fact Bharati Krsna writes in his Explanatory Exposition:
“…by means of what we have been describing as straight, single-line, mental arithmetic”, suggesting that ‘one-line’ is equivalent to ‘mental’.
I therefore propose that the main criterion for a method to be Vedic is that it has this one-line feature. But a technique should not be rejected outright on the basis that it is not one-line. If it is better than the conventional method, it is worthy of consideration with a view to further development.
The above illustration of multiplication happens to be a convenient one. Mathematics is not just about computation though, but about proof, problem solving, structure and so on. So how does the one-line flow of attention criterion apply more generally?
It is hoped that this article will generate some response to these questions in those interested, and if so you are requested to email kenneth.williams@vedicmaths.org with your views. Without a clear idea of the boundaries of Vedic Maths the subject may gradually disappear, with only certain techniques which are popular remaining but not being known to be part of a complete system of Vedic Mathematics.
My thanks are due to Andrew Nicholas for his helpful comments during the formulation of this article.
1 “Vedic Sources of ‘Vedic Mathematics”, Sambodhi, Vol. XXIII, 2000.
http://www.vedicmaths.org/Free%20Resources/Articles/kansara/kansara.asp
2 Please see: “The Sutras of Vedic Mathematics”, by Kenneth Williams, in the Journal of the Oriental Institute, Vol. L, Nos 1-4, Sept 2000 – June 2001, pages 145 to 156. http://www.vedicmaths.org/Free%20Resources/Articles/SutrasVM/sutras_of_vedic_mathematics.asp
Kenneth Williams
Vedic Math 
I beg to differ with you on this.
Vedic refers to the vast body of literatures called the Vedas. It also refers to the culture which flourished thousands of years ago and was centered around the Vedas. “Vedic Mathematics” refers to that mathematics which was a part of that culture and which finds it’s roots in the ancient Vedic literatures.
It really has nothing to do with how long a sutra is nor with the more modern inventions of Swamiji Bharati, no matter how well intentioned. In the introduction to his book, the editor states clearly that these sutras are written by Swamiji. No doubt he was brilliant and a saint, but nevertheless he invented the sutras in his book and this has now been propagated all over and is accepted as “Vedic Mathematics” by the majority of those who don’t know better. The problem with this is that it creates confusion and those who wish to claim this as their heritage are criticized for falsifying this, which isn’t really an issue but nevertheless has become an issue.
There does exist quite a body of mathematics understood as actually Vedic. There are some videos available on the internet under the title: “Scientific Verification of Vedic Knowledge.” There you will find some evidence of Vedic mathematics.
I would just like this to be clarified, since the contributions to mathematics and science by the Vedic culture is so significant and great.
Hi, thank you for taking the time to respond to this article written by Kenneth Williams. I appreciate your thoughts, and I found the website you mentioned entitled “Scientific Verification of Vedic Knowledge.” The argument made here by Mr. Williams, as I understand it, is that Vedic mathematics can be defined to a considerable extent by the fact that it involves a one-line method: “I therefore propose that the main criterion for a method to be Vedic is that it has this one-line feature.” In defining it this way, Williams is concerned to point out that “Without a clear idea of the boundaries of Vedic Maths the subject may gradually disappear, with only certain techniques which are popular remaining but not being known to be part of a complete system of Vedic Mathematics.” How does this notion of a “complete system of Vedic Mathematics” conflict with your view that “the contributions to mathematics and science by the Vedic culture (are) so significant and great?”
The article starts from the premise that the Vedic Mathematics referred to is that of Bharati Krsna Tirthaji. The arguments for and against this use of the name need not be reiterated here (see for example the two quoted references) especially since the article is concerned with the distinction between mathematics and (Bharati Krsna’s) Vedic mathematics. But the fact is that Bharati Krsna’s Vedic mathematics is becoming very well-known and I think people can cope with a name that has more than one possible interpretation.