17 - Vedic Sources of 'VEDIC MATHEMATICS'


ISSUE No. 17

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.
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:


The above is the title of an article by Dr N. M. Kansara, Director of the
Akshardham Centre for Applied Research in Social Harmony in Akshardham,
Gandhingar, India.

In this article Dr Kansara examines the arguments that have been circulating
in India about the authenticity and validity of Bharati Krsna Tirthaji's
reconstruction of Vedic Mathematics. In particular he discusses the lost
volumes and the validity of the term 'Vedic' for Bharati Krsna's system. It
is good to see the negative arguments that have been put forward in the past
refuted in such a scholarly way.

Bharati Krsna says he wrote sixteen volumes on Vedic Mathematics and
according to Dr Kansara ...at the age of his 34th or 35th year and for the
next few years he was busy working on these Sutras, and he seems to have
definitely written, in school notebooks, all of his sixteen volumes treating
each of his sixteen Sutras in one independent volume ...

These notebooks were left with a devotee for a long period, Says Dr Kansara,
so that the house in which they were stored passed on to the devotee's son
who sold them to a German scholar for 80,000 rupees. Professor Vijaya Sane
tried over a long period to locate the German scholar but without success.

Regarding the validity of the term 'Vedic' as applied to Bharati Krsna's
system Dr Kansara says: "The VM Sutras contain some very common mathematical
terminology, which has so far been hardly examined from this point of view.
Dr Satyakama Varma has concluded in his research paper that though the term
employed in these Sutras cannot be claimed to be of the Vedic origin, yet
they are later synonyms of the equivalent original Vedic terms, that the
Vedic texts include much of the scientific and mathematical statements, which
can make a strong basis for such like Sutras, and that when the Jagad Guru
claims that he has adopted nothing but Vedic Mathematics, he is right in his
own way." "Thus, in point of the language the VM Sutras too are similar and
cannot be segregated as non-Vedic; they are as much Vedic as are the Srauta
Sutras and the Sulba Sutras so far as the point of their language is
concerned. And this is perhaps, because of their likelihood of being of the
yet untraced Sulba-sutra of the Atharvaveda. And it is in view of these
sutras being a part of the yet untraced Sulbasutra, and therefore belonging
to the Sthapatyaveda an upaveda, of the Atharvaveda, that we may regard them
as 'Vedic', which is general term denoting not merely the texts connected
with some Vedic Sakha, but not necessarily the Samhita and Brahmana only".

The word 'Veda' refers to actual Vedic texts, but its literal meaning is
'knowledge' and this latter is the meaning stressed by Bharati Krsna himself.
Dr Kansara says: "But says Dr V. S. Agrawala, this criticism loses all its
force if we inform ourselves of the definition of Veda given by BKTM himself
as quoted abobe. It is the whole essence of his assessment of Vedic tradition
that it is not to be approached from a factual standpoint, viz., that the
Vedas as traditionally accepted in India are the repository of all knowledge,
and hence they should be, and not what they are, in human possession. That
approach entirely turns the tables on all the critics, for the authorship of
Vedic Mathematics then need not be laboriously searched in the texts as
preserved from antiquity."





A Vedic Mathematics course is starting on Tuesday 26th June at 7 pm sharp in
New South Wales, Australia. It is a 6 week course on alternate Tuesdays and
is given by Vera Stevens. The venue is the Shearwater Steiner School at
Mullumbimby and the cost is $8.00 per person. For inquiries ring Vera on
Australia 02-66801980.


The Workshop on Vedic Mathematics at the
Society For Integrated Development Of Himalayas,
Hazelwood, Landaur Cantt., Mussoorie, 248179
tel./Fax : 91-135-631304 / 632904
will be held on Jun 28 to 30..2001 for teachers.
The contact person is : Dr. L. N. Mittal (Consultant, SIDH)
email Id : ,


A study has just been completed comparing some Vedic and traditional
multiplication methods. Michelle Thompson at Edge Hill College, Lancashire,
England is training to become a teacher of mathematics at secondary level.
She taught two similar year 8 classes at Bedford High School, Leigh: one was
taught Vedic methods and the other the equivalent traditional methods. The
classes did a test followed by a week of teaching and then another test. A
third test was given a month later to find out what had been retained.
Michelle writes in her report:
"I would say that the evidence of pupils in class V [the class taught Vedic
methods} maintaining the same or similar performance overall and in the
mental test (tables 3-4) one month later would support the theory that Vedic
methods can help to increase the performance of pupil's multiplication
abilities. However the mental tests made it difficult for me to fully assess
how many pupils were using the Vedic methods mentally. Some pupils in class V
did return to other written methods in the third test but with greater
success. This may imply that the teaching of Vedic methods helped the pupils
to understand other methods such as traditional multiplication and partial

The teaching of the vertically and crosswise multiplication method was well
received by class V:
"In class, Group V was taught the general multiplication method of
"vertically and crosswise". They were encouraged to use "nikhilam"
multiplication to recall any products they did not know. This was well
received by the group with many completing thirty 2 by 2 arrays in less than
30 minutes with a maximum of two errors. The primary striking feature was
that it was difficult to get the pupils to stop once they had started. It
took more than 5 minutes to get everyone to stop together so we could mark
and check progress on account of several of the pupils wanting to do "just
one more, Miss". The class teacher commented that she had never seen a class
so eager to continue with multiplication."


Following the article on the Vedic Matrix by Dr Blidi Stemn in the last
newsletter we have heard from Luigi Di-Martino who was amazed when a friend
showed him the article as he had arrived at something similar through
studying the musical scales! We hope to show something of his work in a later


Dr T. Venugopal has organized an MSN Web Community called Vedic Mathematics.
Here is the Web address of the community's home page:
Why not join the community, read the discussions and add your own.


There was a Vedic Mathematics stand at the Natural Health and Ecology Show on
2nd, 3rd June at Ryton Organic Gardens near Birmingham, England. Two talks
were given to fascinated groups who were, as usual, amazed at the beautiful,
simple Vedic methods. Many useful contacts were made.


Is anyone aware of any comparison done between the Trachtenberg and Vedic


We included a note about Jain in Australia who has had some useful responses.
He writes:
"So thanks for the liason, your incredible work pays off considerably in
helping young artists and intellectuals like myself who need exposure...
want to thank you again for being a catalyst in getting my Life'sWork out. I am
teaching Vedic Mathematics every New Moon and Full Moon, lately, and am
starting to attract the attention of some of the local Maths Teacher's.


From a trainee maths teacher:
"What surprises me is how little interest and ability maths teachers show in
mental arithmetic for themselves. I am interested, but I haven't made a
serious study, yet I am aware that other maths teachers at school and other
PGCE students at college are impressed by quite basic steps in mental calculation.

For example, there was a talk at school given just to maths teachers by the
Borough of Ealing's Numeracy Coordinator. The speaker asked how we would
calculate 13 x 15. I was already being discouraged from putting my hand up
because I always had an answer. She went round everyone else and then
suggested using 6 1/2 x 30 (ie doubling and halving). Finally she came to me,
and I said: "I happen to know that 14 squared is 196, so by the difference of
squares it must be 195." I knew by the two seconds delay and then the whoops
and cheers that my fellow teachers thought that impressive. I don't mean to
boast, nor belittle my colleagues, but I just know there is a long way to go
with the kids when the staff are impressed by that."


Just a quick note to say that your book, Discover Vedic Mathematics,
is absolutely wonderful! Your examples and explanations are comprehensive in
their scope; upon reading the text, working out the sample problems, and
completing the corresponding exercises, I feel that I am well on my VM
I am using your text in conjunction with Jagadguru Swami Sri Bharati
Krsna Tirthaji Maharaja's Vedic Mathematics. Working sutra by sutra, I am
enlightened by the fascinating knowledge that resides within both texts'
I am currently informing my college math instructor about the
intrinsic value of VM. Also, I am sharing my VM interests with everyone I
know who loves and appreciates mathematics. I have received very positive
feedback! :)


Mr Mohammad Fazal, the governor of Panaji, inaugurated a two-day workshop on
Vedic Mathematics at the International Centre, Donna Paula, Panaji on March
21. The workshop has been jointly organised by the Goa International Centre
and Motilal Banarsidass Publishers, New Delhi.


If you are please let us know as someone is looking for a teacher.



EMAIL: Have you ever heard of Jain method of mathematics? Jainism is a
practiced by approx 2-3% Indians. Or probably less. Many Monks/Sadhus/Saints
of this religion practices maths for reasons best known to them ( I have not
asked them, that is :-) ) Mathematics and Logic forms a vital part of Jain
Philosophy and probably they practice it for increased concentration and
control over mind. They can perform calculations at phenomenal speed and can
remember/recite very large numbers spoken in any order etc. When I meet a
Jain monk next time, I will ask them about it and will try to compare their
methods with VM.

EMAIL: I loved the vedic square/matrix article [newsletter 16]- amazing,
someone using it in a teaching place - brilliant. I found it very interesting
to read - I hope others do to.

EMAIL: Did you know that the multiply method with the abacus is the same as
the cross multiply in vedic?

EMAIL: I am currently in my junior year at United World College of South East
Asia in Singapore. I am interested in writing a research paper - which is
necessary for me to obtain my International Baccalaureate diploma (extended
essay) in the field of Vedic Mathematics.

EMAIL: I am doing my Masters in CS and have been closely studying Vedic Math
the past 8 to 10 years (with breaks in between to get back to studies). I
came to US and saw that people (even Indians) hadnt even heard of it and
since then I have just been explaining to them some basic sutras, the reason
behind why they might have come up with such a thing and stuff. I am more
than interested in doing research in Vedic Maths. I am trying to write
programs which use similar logic to make things easier and faster. I havent
studied in much detail as to how much faster they would be. But its fun.
Keep me posted on whats new in Vedic math.

EMAIL: I have just completed a Bachelor's Degree in Commerce from the Bombay
University. I am interested in undertaking 1/2 yrs of formal studies in Vedic
Maths. Could you tell me about any such courses, preferably in India?

EMAIL: Dear Sir, Could you please tell me in detail what exactly is vedic
maths &what is it's importance.

REPLY: Sri Bharati Krsna Tirthaji studied the Indian, Vedic texts between
1911 and 1918 and according to him reconstructed a system of mathematics that
was contained in them. He wrote a book called Vedic Mathematics in which he
outlined the system. This describes a very coherent and elegant system which
rather puts conventional mathematics teaching to shame. Since this book was
published in 1965 some people have developed and extended to work. Others who
have not looked closely have rejected it. The importance of VM is that it
contains all the features that you would want to have in a system of
mathematics: it is easy to do, most methods being done mentally as they go
direct to the answer using a simple pattern or technique. The system is very
integrated so that methods complement each other. Furthermore children love
it because it is so easy and so much fun. One other unique feature is the
sutras or word-formulae which are used. These help the child to know how to
use their mind in answering a question.

EMAIL: In the recent Teaching Children Mathematics the article on Vedic Math
gave an example to multiply double digits that works fine but please explain
how 22 x 45 works. Thank you for you response.

REPLY: In the Vedic system there are special methods that can be used when a
sum falls within its range, and there are general methods.

The method referred to in that article is for multiplying numbers near a base
(like 10, 100, 2000 etc).

For 22 x 45 you could use the general method which comes under the vertically
and crosswise formula (answer in one line) or you could use the
proportionately formula which means change the sum to 22 x 45 = 11 x 90 =

Or thirdly you could actually use the method described in the article by
finding 44 x 45, using a base of 40 (or 50) and halving the answer.

One of the many remarkable features of the Vedic system is that there is a
variety of methods to choose from, which leads to creativity and
experimentation, or you can just stick to the general method if you prefer.


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

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Editor: Kenneth Williams

Visit the Vedic Mathematics web site at


21st June 2001


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