21 - Only a Matter of 16 Sutras


ISSUE No. 21

Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods.
The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics.
If you are working with Vedic Mathematics - teaching it or doing research - please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue or tell us about a course or talk you will be giving or have given.
If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.


The article below was published in the Indian newspaper "Education Times" on 7th January 2002. It is reproduced here, with minor corrections, with permission of the author, James Glover, Head of Mathematics at St James School, Twickenham, London.


All articles published in India are critical of Vedic mathematics, but it seems appropriate to give a response based on the work carried out within the United Kingdom. I have taught Vedic mathematics for almost twenty years at an independent school in London.

Our associate schools also teach Vedic mathematics. Both teachers and students have found Vedic mathematics of great benefit because it has so many positive qualities. The most obvious of these are found through experience of working with the sutras or formulae.

What is Vedic mathematics really about? What is it about the subject that an English school should use it so thoroughly? Is it really Vedic and what was the purpose of Sri Bharati Krishna Tirthaji's book on the subject? In this account I attempt to answer some of these questions.

Vedic mathematics is based on sixteen sutras together with a similar number of sub-sutras. Each sutra provides a principle of mental working applicable to many diverse areas of mathematics. The word Veda generally has two meanings. The first is the collection of ancient Indian texts relating to both spiritual and secular knowledge. The second way that Veda is used is to describe true knowledge in the present which resides within peoples hearts or minds. This is the meaning which we have accepted. It is quite possible that Sri Tirthaji intuited the sutras from his deep understanding of the subject, the Vedas and the nature of the human mind.

If only this first meaning is accepted then the question as to whether Tirthaji's system is or is not Vedic becomes an almost insurmountable task. In my experience it is better to approach Vedic mathematics from the second meaning relating to natural laws working within the human psyche. This is a practical approach and certainly most of the work in the UK has followed this line.

The introduction to Vedic Mathematics indicates that during the early part of the 20th century Sri Tirthaji rediscovered or reconstructed Vedic mathematics from stray references within the appendix portions of the Atharvaveda. He evidently spent a large proportion of his life teaching the system but it was only shortly before he passed away that he set down an illustrative volume on the subject. This was published posthumously in 1965 and is the main source of all the serious study on the subject.

His book offers a snapshot of the sutraic system. Some of the sutras are applied to relatively elementary topics in arithmetic and algebra, giving rise to fast and easy methods of calculation. The really surprising aspect is contained within one of his introductions where he describes these few sutras as having jurisdiction over the whole of mathematics.

Years ago when I was first involved with various groups studying Vedic mathematics we all thought this statement outrageous and absurd. How could sixteen sutras apply to the whole of mathematics? Our view was strengthened by the text due to the paucity of explanation of some of the rules. For example, there is a sutra, Vyashti Samashti, which is mentioned only once in the text and even then it is given in relation to a very particular type of biquadratic equation.

As it turns out this sutra is fundamental to mathematics particularly in statistics and mechanics. It has countless applications because it describes a common mental process. When we first came across Vedic mathematics in London we were impressed by the methods of calculation. We found the sutras really brought the subject alive and we still find that all students feel more alive by practising Tirthaji's methods.

Once our enthusiasm was kindled we studied and practiced the whole of his book. We worked through every sum and read and re-read every word to try and make sense of the system. Over a period of years this work continued and we gradually began to see more and more applications to fast methods of calculation, algebraic manipulations and geometrical theorems. The next step was to consider topics within mathematics and simply ask, what sutra is working here? For example, what is the sutra working when you bisect an angle or when simplifying an irrational number? The elementary topics are fairly straightforward but what about more sophisticated mathematics?

You are given two circles drawn inside a larger circle so that they all touch each other. The area between the circles is the Arbelos or shoe-maker's knife. The problem is to construct further circles within the Arbelos as shown in the diagram. We worked through some of the conventional solutions to this. There was one particularly elegant solution that seemed the quickest and easiest method. It required transformations of a series of circles. Whilst looking at this solution it dawned on us that the sutra involved was none other than Transpose and adjust, one of the most common sutras in this Vedic system. These anecdotal instances help describe the nature of what we see as Vedic mathematics.





10 week Teacher Training Course with Jain. Beginning Saturday 2nd Feb 2002, 10am to 4pm till 6th April, at 777 Left Bank Rd, Mullumbimby Creek, 2482. Phone : 0266 844409. Cost : $2,500 for adults, includes catered lunches and curriculum, notes + books and a certificate. $800 for children.


After an extra-ordinary successful workshop at Bhavan's College, Andheri in Mumbai we are organising 3 more VM workshops at G D Somani School, Cuffe Parade, Mumbai. The 2 / 3 days workshops will be conducted by Rajeshwari Mani Sharma. For more details contact Mr R. P. Jain at


The course started recently at Imperial College has made a good start with 49 enthusiastic participants. You can still join the course if you wish (see Calendar on the website, http://www.vedicmaths.org or http://www.vmacademy.com)


The article "Vedic Sources of 'Vedic Mathematics'", published in the Indian journal Sambodhi, Vol. XXIII, 2000 by Dr N. M. Kansaa can now be viewed on the website http://www.vmacademy.com This article was featured in Newsletter 17.


Apologies to anyone who had problems accessing the websites at www.vedicmaths.org and www.vedicmaths.com. This is now sorted out. If you sent an mail in the last week or so that did not receive a reply please can you resend it. If you know of anyone wanting to be put on the newsletter mailing list in this time can you ask them to resend if they did not get a reply. The structure of the .com site has been improved but the content is essentially unchanged.


A new Vedic Maths site has been launched by the Vedic Maths Society. Take a look at www.vedicmathematics.co.uk There is a lot of useful information and you can sign up for their newsletter.


If you buy books at www.vedicmaths.com you can now pay with a credit card.


Dr Abhijit Das in India has sent the following observation relating to 2-figure multiplications where the first figures or last figures of each number are the same. This holds good for 2 x 2 digit multiplication when either the tens or the units column have the same numeral. Take this example multiply 43 X 44 - what I do is this 3 x 4 is 12 , put down 2 and carry 1 add the nos. which are not common and multiply by the common no - in this case (4 + 3) x 4 = 48 , 48 + 1 = 49 , put down 9 , carry 4 4 x 4 is 16 + 4 =20 therefore the answer is 2092 I also do the same if the units are the same as in 67 x 27.


There was a very good response (about sixteen inquiries) to the offer to take this course in the last newsletter.



If you want to know about Vedic Mathematics Workshops or research in India send an email to Mr R. P. Jain at


Your comments about this Newsletter are invited.
If you would like to send us details about your work or submit an article for inclusion please let us know on

Articles in previous issues of this Newsletter can be copied from the web site - www.vedicmaths.org:
Issue 1: An Introduction
Issue 2: "So What's so Special about Vedic Mathematics?"
Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius
Issue 4: The Vedic Numerical Code
Issue 5: "Mathematics of the Millennium"- Seminar in Singapore
Issue 6: The Sutras of Vedic Mathematics
Issue 7: The Vedic Square
Issue 8: The Nine Point Circle
Issue 9: The Vedic Triangle
Issue 10: Proof of Goldbach's Conjecture
Issue 11: Is Knowledge Essentially Simple?
Issue 12: Left to Right or Right to Left?
Issue 13: The Vinculum and other Devices
Issue 14: 1,2,3,4: Pythagoras and the Cosmology of Number
Issue 15: A Descriptive Preparatory Note on the Astounding Wonders of Ancient Indian Vedic
Issue 16: Vedic Matrix Issue
Issue 17: Vedic Sources of Vedic Mathematics Mathematics
Issue 18: 9 by 9 Division Table
Issue 19: "Maths Mantra"
Issue 20: Numeracy

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Editor: Kenneth Williams

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29th January 2002


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