## Vedic Mathematics

A few years ago I came across a book in a second-hand bookshop called ‘Vedic Mathematics’ by Jagadguru Swami Sri Bharati Krsna Tirthaji Maharaja. I started reading this book with fascination – it presented mathematics in a way that I had never seen before and never imagined existed. It presents various methods and techniques for carrying out mathematical computations with a minimum of working (often a single line) and these techniques are all derived from a small collection of ‘sutras’ (a kind of short statement) which the author spent many years meditating on and working out how the sutras were to be interpreted and applied to mathematics.

The first thing that I noticed when I started reading and working through this book was just how efficient the techniques were that were being presented. To start with only things like multiplication and division are covered but the author soon progresses on to simultaneous equations, partial fractions, repeated differentiation, amongst other topics. I was deeply impressed by what I was reading and was quite taken aback that these techniques had been available for hundreds of years and they had never seemed to catch on.

And there’s a good reason why they never caught on – it’s because, sadly, it’s an elaborate con.

The author spends much time denigrating what he calls ‘conventional methods’ – in other words, methods that would typically be encountered in classrooms around the world – and extolling the virtues of ‘Vedic methods’ which are derived from the Vedic sutras (or so he claims). These sutras are supposed to express a form of knowledge that is on a higher level and are revealed to people through extensive and deep meditation. The author makes us think that the sutras possess a special kind of logic that greatly differs from ‘conventional logic’ and that the sutras have a kind of absolute authority. Why, then, does the author have to use ‘conventional methods’ to prove that the ‘Vedic methods’ work in the way that he says that they do? Surely the sutras, if they are so authoritative, should be sufficient in and of themselves to convince us of their validity and superiority and shouldn’t require proof via inferior methods and techniques. Yet the author does this several times – and it started to really grate on me.

Not only that, and this is a big one – there is absolutely no evidence that the sutras are an ancient form of knowledge. Indeed, it seems that the author invented the sutras and they have no historical basis. In fact, it seems that the author took the techniques and came up with sutras to fit the techniques – rather than the other way round.

It is certainly the case that some of the techniques that the author presents are very efficient…  BUT… there is a huge problem. The techniques are often only applicable to very special cases. For example, there is a technique which shows how to solve equations such as $\dfrac{4}{x+2}+\dfrac{5}{x+3}=\dfrac{9}{x+7}$ where the numerators on the left-hand side and right-hand side are the same. This is great excepts this kind of situation practically never occurs. If the numerators do not add to the same number then a different technique will be required – so before I can apply one of these speedy Vedic techniques I have to identify the specific case that I’m dealing with. This is a problem because a) there is no extensive list of ALL different cases, b) there are a vast number of different cases that I have to sift through which takes time.

So the author trades a single ‘conventional technique’ which applies to all cases but may be a bit slower from time-to-time, for a range of different ‘Vedic’ techniques which apply, individually, to only very restricted classes. No matter how efficient these techniques are, things just don’t work like that for mathematicians. The Vedic techniques that the author presents are techniques that apply to special cases that anyone with a basic understanding of ‘conventional’ algebra would be able to figure out if they wanted to – though usually there is very little incentive to do so because it’s so pointless; these techniques which apply to such limited cases are nothing more than neat party-tricks.

The author claims that ‘The sutras (aphorisms) apply to and cover each and every part of each and every chapter of each and every branch of mathematics’ and ‘there is no part of mathematics, pure or applied, which is beyond their [the sutras] jurisdiction’. This claim is outrageous because it is simply not true – Vedic mathematics (if it exists at all) can only deal with simple computations which are mainly uninteresting to mathematicians and this is continually shown throughout the book. I might have been a bit more convinced if the author had actually managed to solve a long-standing problem in mathematics, such as Riemann Hypothesis, using ‘Vedic mathematics’. It is claimed that the author originally wrote sixteen volumes covering all aspects of mathematics using ‘Vedic’ methods but, would you believe it? he left them in the care of someone who ‘lost’ them and before his death he only managed to re-write a single volume (this book). Therefore, we can only speculate as to the contents, or even the actual existence, of the other books.

Sadly, therefore, I have to say that ‘Vedic mathematics’ is not something to be taken seriously. Unfortunately, it seems that many people do still get drawn in to ‘Vedic mathematics’ probably because of its ‘spiritual feel’ – but don’t be fooled, it is nothing more than a huge con and you would be much better off spending your time learning the ‘conventional methods’ that the author so dislikes!