23 - India's System of Mental Mathematics


ISSUE No. 23

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.


This issue’s article is taken from a longer article by Andrew Nicholas. The full article can be viewed at www.vmacademy.com


In the vedic system, the work is done mentally. This stems from the tradition being an oral one.

In practice, today, the initial problem or question is usually written down and the answer or solution also. The work being done mentally, a one-line answer results. This is the vedic ideal.


But what is this word ‘vedic’? It refers to an ancient period in India’s history. Tradition has it that the system of the vedas covered all branches of knowledge. Originally an oral tradition, it began to be written down around 1600 or 1700BC, according to western scholars. Over the next thousand years four vedas,  as they were called, were recorded - rig-veda, yajur-veda, sama-veda and atharva-veda.

An appendix to this last contained a section headed ‘Ganita Sutras’, i.e. mathematical formulae, or principles. In the nineteenth century scholars began to look at it, but could make no sense of what they found there: statements such as, ‘In the reign of King Kamsa, famine, pestilence, and insanitary conditions prevailed.’

Then a brilliant south Indian scholar, Shri Bharati Krishna Tirthaji (1884-1960), began a detailed investigation. He concluded that the above statement about King Kamsa was a cryptic form of the decimal fraction for 1/17, using letters to represent single-digit numbers, much as we might use the letter A to represent 1, and B to represent 2, etc.

Having obtained one clue, further investigation led him to conclude that the whole of mathematics is based on 16 sutras, and he finally wrote 16 volumes on the topic.

Then events intervened. He was virtually forced into becoming a Shankaracharya. Hindu India has four of these top religious leaders a bit like having four Popes.

The upshot was that he left his beloved vedic mathematics alone for many years. Returning to the subject in the 1950‘s, it emerged that the 16 volumes had been lost. On realising this, he decided to re-write them all, and began by writing a book intended to introduce the whole series. Ill health stopped him from getting any further, and he died in 1960. This introductory book is now all that we have by him. It was first published in 1965.


Western version           

When measuring weight, the bigger the number, the greater the weight. Similarly for temperature, length, electric current etc. We are used to the idea that larger numbers are weightier.

Vedic version              

In the vedic system, numbers are viewed differently. An analogy is telephone numbers, which we don’t associate with quantity. They are patterns of digits acting as addresses.

Similarly, when working to a base of ten (as we normally do), the vedic system deals with the single-digit numbers 1, 2, 3, 4, up to 9, together with the zero, arranged in different patterns. For example, we don’t divide by 52, we divide by 5, and take account of the 2 afterwards. This shift of focus eliminates the heaviness, or weight, associated with the common view of numbers. The vedic mathematician considers a number such as 52 as 5 and 2 in succession.



To answer the first question first, yes and no. It is used there to some extent. Here is a brief account of the developments.

Tirthaji died in 1960

Vedic Mathematics’ was published in 1965

Before going to India in 1981 I wrote to all Indian universities to find out what more was known about the subject. About 30% of them replied. No one could tell me anything more about it. Evidently the subject was being neglected. However, one or two letters pointed me to Tirthaji’s last residence and ashram in Nagpur. Visiting there, I was invited to return the following year to teach a fortnight’s course.

These days, the subject can be taught in schools, alongside the conventional system. Where this is done, I am told, the pupils have no problem with learning the two approaches side-by-side - the western and the vedic.

There is also a passionate debate raging about the status of Tirthaji’s system. Some argue that it is historically accurate, despite the lack of normal historical evidence. Others argue that, lacking evidence for its historical validity, it should be dismissed - despite the fact that, mathematically, it works.

My view (which I am not alone in holding) is that it is a reconstruction. At present we are unable to say for sure that it is historically accurate - nor to prove that it is not. This is because we are dealing with an oral tradition, and it is no surprise that written evidence may not be available.


Tirthaji points out that it normally takes about 16 years to go from first steps in mathematics to a Degree in the subject. (e.g. from age 5 to age 21).  But he states that with the vedic system the course in its entirety could be done in about two years! Of course, at present we don’t have all the material that’s needed available.

Needless to say, however, this would benefit everybody - not least those who are not interested in mathematics and would prefer to spend less time on it!

I think, myself, that once vedic mathematics begins to win general acceptance it will lead people to question other academic disciplines. Are rapid methods available in other subjects? If so, are they being used, and if not can they be developed?




New course in london

Following the successful recent course at Imperial College another introductory course is to take place at the Regency Hotel, Queen’s Gate, London, SW7 5AG, on five Mondays from 29th April 2002. Time: 7.00 to 8.30 pm. Course fee: 30 pounds (20 pounds, students and concessions). Enquiries: tel. 020 8688 2642. Topics covered: Squares and Cubes, pi and the Vedic numeral code, Easy Calculus, Fibonacci within Nature, Mathematics and Mind.


“Business India” has published an interesting article by Chetan Dalal entitled “Practical application of Vedic mathematics – Vedic mathematics has certain visual solutions which could be applied in problem solving”. This is on the application of Anurupye Shunyam Anayat (zero value of one of the variables in Simultaneous equations where the other variables are in perfect proportion to constants) illustrated in an Insurance claim. The article ends:

“This illustration . . . emphasizes on the simplicity of the tenets of the sutras of vedic mathematics. Perhaps research and intensive study of vedic scriptures might reveal even more advanced applications. What is illustrated above is a very elementary application of the sutra. The depth and richness of the vedic knowledge is beyond description. Greater research and more teamwork in sharing of ideas and interpretation may provide revolutionary results.”

It would be good to see more such applications of the Vedic Sutras.


A lot of interest was taken in the article in the last newsletter. Mr. Carlos Javier Maya from Mexico has given an idea for doing multiplications of 2 digit by 2 digit on the hands when the multiplier is 19. Mrs Sharma is developing the methods further and is currently conducting a series of courses on Vedic Mathematics.

Dr Abhijit Das in Mumbai, India, has also been researching this area, but without using fingers. We hope to have an article by him for the next newsletter.


As stated in the last newsletter this Vedic Maths course, that covers the National Curriculum for England and Wales, can now be obtained. In India you can purchase whatever you need from Motilal Banarsidass shops and presumably from other bookshops.

The ISBN’s are as follows:

Full set: 81-208-1871-7

Book 1: 81-208-1862-8

Book 2: 81-208-1863-6

Book 3: 81-208-1864-4

Teachers Guide: 81-208-1865-2

Answer Book 1: 81-208-1866-0

To purchase the course in the UK contact:

Motilal Books, PO Box 324, Borehamwood, WD6 1NB

Tel: 0208 905 1244


Price 39.75 pounds

For the USA contact:

THE SACRED SCIENCE INSTITUTE who have the books on order.

Address: PO Box 3617, Idyllwild, CA 92549-3617



Tel: +1 (909) 659-8181

Fax: +1 (909) 659-8383



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




First of all I am thankful to those who are behind this effort of rejuvenating vedic science or mathematics.

I have learned very few mathema-tactics when I was giving some scholarship exams in 4 th standard. These were taught to me by my Nanny at that time. I could score 99/100 in that exam. and much of it due to use of vedic maths. But afterwards I never pursued it. I have done engineering and after so much of years have passed now I have decided to study vedic maths from scratch. I have done tutorials from your site and they are simply best to add my interest. So please subscribe me as student and pls. guide me what next I should do.


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

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 Mathematics
Issue 16: Vedic Matrix
Issue 17: Vedic Sources of Vedic Mathematics
Issue 18: 9 by 9 Division Table
Issue 19: “Maths Mantra”
Issue 20: Numeracy
Issue 21: Only a Matter of 16 Sutras
Issue 22: Multiplication on the Fingertips

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Editor: Kenneth Williams

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15th April 2002


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