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"Vedic Mathematics" - Preface


1. In the course of our discourses on manifold and multifarious subjects
(spiritual, metaphysical, philosophical, psychic, psychological, ethical,
educational, scientific, mathematical, historical, political, economic,
social etc., etc., from time to time and from place to place during the last
five decades and more, we have been repeatedly pointing out that the Vedas
(the most ancient Indian scriptures, nay, the oldest "Religious" scriptures
of the whole world) claim to deal with all branches of learning (spiritual
and temporal) and to give the earnest seeker after knowledge all the
requisite instructions and guidance in full detail and on scientifically-
nay, mathematically- accurate lines in them all and so on.

2. The very word "Veda" has this derivational meani ng, i.e. the
fountain-head and illimitable store-house of all knowledge. This derivation,
in effect, means, connotes and implies that the Vedas should contain within
themselves all the knowledge needed by mankind relating not only to the
so-called 'spiritual' (or other-worldly) matters but also to those usually
described as purely "secular", "temporal", or "worldly"; and also to the
means required by humanity as such for the achievement of all-round,
complete and perfect success in all conceivable directions and that there
can be no adjectival or restrictive epithet calculated (or tending) to limit
that knowledge down in any sphere, any direction or any respect whatsoever.

3. In other words, it connotes and implies that our ancient Indian Vedic
lore should be all-round complete and perfect and able to throw the fullest
necessary light on all matters which any aspiring seeker after knowledge can
possibly seek to be enlightened on.

4. It is thus in the fitness of things that the Vedas include (i) Ayurveda
(anatomy, physiology, hygiene, sanitary science, medical science, surgery
etc., etc.,) not for the purpose of achieving perfect health and strength in
the after-death future but in order to attain them here and now in our
present physical bodies; (ii) Dhanuveda (archery and other military
sciences) not for fighting with one another after our transportation to
heaven but in order to quell and subdue all invaders from abroad and all
insurgents from within; (iii) Gandharva Veda (the science and art of music)
and (iv) Sthapatya Veda (engineering, architecture etc., and all branches of
mathematics in general). All these subjects, be it noted, are inherent parts
of the Vedas i.e. are reckoned as "spiritual" studies and catered for as
such therein.

5. Similar is the case with regard to the Vedangas (i.e. grammar, prosody,
astronomy, lexicography etc., etc.,) wh ich, according to the Indian cultural
perceptions, are also inherent parts and subjects of Vedic (i.e. Religious)

6. As a direct and unshirkable consequence of this analytical and
grammatical study of the real connotation and full implications of the word
"Veda" and owing to various other historical causes of a personal character
(into details of which we need not now enter), we have been from our very
early childhood, most earnestly and actively striving to study the Vedas
critically from this stand-point and to realise and prove to ourselves (and
to others) the correctness (or otherwise) of the derivative meaning in

7. There were, too, certain personal historical reasons why in our quest for
the discovering of all learning in all its departments, branches,
sub-branches etc., in the Vedas, our gaze was riveted mainly on ethics,
psychology and metaphysics on the one hand and on the "positive" sciences
and especially mathematics on the other.

8. And the contemptuous or, at best patronising attitude adopted by some
so-called Orientalists, Indologists, antiquarians, research-scholars etc.,
who condemned, or light-heartedly, nay; irresponsibly, frivolously and
flippantly dismissed, several abstruse-looking and recondite parts of the
Vedas as "sheer-nonsense"- or as "infant-humanity's prattle", and so on,
merely added fuel to the fire (so to speak) and further confirmed and
strengthened our resolute determination to unravel the too-long hidden
mysteries of philosophy and science contained in India's Vedic lore, with
the consequence that, after eight years of concentrated contemplation in
forest-solitude, we were at long last able to recover the long lost keys
which alone could unlock the portals thereof.

9. And we were agreeably astonished and intensely gratified to find that
exceedingly tough mathematical problems (which the mathemat ically most
advanced present day Western scientific world had spent huge lots of time,
energy and money on and which even now it solves with the utmost difficulty
and after vast labour and involving large numbers of difficult, tedious and
cumbersome "steps" of working) can be easily and readily solved with the
help of these ultra-easy Vedic Sutras (or mathematical aphorisms) contained
in the Parishishta (the Appendix-portion) of the ATHARVAVEDA in a few simple
steps and by methods which can be conscientiously described as mere "mental

10. Ever since (i.e. since several decades ago), we have been carrying on an
incessant and strenuous campaign for the India-wide diffusion of all this
scientific knowledge, by means of lectures, blackboard-demonstrations,
regular classes and so on in schools, colleges, universities etc., all over
the country and have been astounding our audiences everywhere with the
wonder and marvels n ot to say, miracles of Indian Vedic Mathematics.

11. We were thus at last enabled to succeed in attracting the more than
passing attention of the authorities of several Indian universities to this
subject. And, in 1952, the Nagpur University not merely had a few lectures
and blackboard-demonstrations given but also arranged for our holding
regular classes in Vedic Mathematics (in the University's Convocation Hall)
for the benefit of all in general and especially of the University and
college professors of mathematics, physics etc.

12. And, consequently, the educationists and the cream of the English
educated section of the people including the highest officials (e.g. the
high-court judges, the ministers etc.,) and the general public as such were
all highly impressed; nay, thrilled, wonder-struck and flabbergasted! and
not only the newspapers but even the University's official reports described
the tremendous sensation caused the reby in superlatively eulogistic terms;
and the papers began to refer to us as " the Octogenarian Jagadguru
Shankaracharya who had taken Nagpur by storm with his Vedic Mathematics",
and so on!

13. It is manifestly impossible, in the course of a short note (in the
nature of a "trailer"), to give a full, detailed, thorough-going,
comprehensive and exhaustive description of the unique features and
startling characteristics of all the mathematical lore in question. This can
and will be done in the subsequent volumes of this series (dealing seriatim
and in extenso with all the various portions of all the various branches of

14. We may, however, at this point, draw the earnest attention of everyone
concerned to the following salient items thereof:-

(i) The Sutras (aphorisms) apply to and cover each and every part of each
and every chapter of each and every branch of mathematics (including
arithmetic, algebra, g eometry- plane and solid, trigonometry- plane and
spherical, conics- geometrical and analytical, astronomy, calculus-
differential and integral etc., etc. In fact, there is no part of
mathematics, pure or applied, which is beyond their jurisdiction;

(ii) The Sutras are easy to understand, easy to apply and easy to remember;
and the whole work can be truthfully summarised in one word "mental"!

(iii) Even as regards complex problems involving a good number of
mathematical operations (consecutively or even simultaneously to be
performed), the time taken by the Vedic method will be a third, a fourth, a
tenth or even a much smaller fraction of time required according to the
modern (i.e. current) Western methods;

(iv) And, in some very important and striking cases, sums requiring 30, 50,
100 or even more numerous and cumbrous "steps" of working (according to the
current Western methods) can be answered in a single and simple step of work
by the Vedic method! And little children (of only 10 or 12 years of age)
merely look at the sums written on the blackboard (on the platform) and
immediately shout out and dictate the answers from the body of the
convocation hall (or other venue of demonstration). And this is because, as
a matter of fact, each digit automatically yields its predecessor and its
successor! and the children have merely to go on tossing off (or reeling
off) the digits one after another (forwards or backwards) by mere mental
arithmetic (without needing pen or pencil, paper or slate etc)!

(v) On seeing this kind of work actually being performed by the little
children, the doctors, professors and other "big-guns" of mathematics are
wonder struck and exclaim:- "Is this mathematics or magic?" And we
invariably answer and say: "It is both. It is magic until you understand it;
and it is mathematics thereafter"; and then we proceed to substantiate and
prove the correctness of this reply of ours! And

(vi) as regards the time required by the students for mastering the whole
course of Vedic Mathematics as applied to all its branches, we need merely
state from our actual experience that 8 months (or 12 months) at an average
rate of 2 or 3 hours per day should suffice for completing the whole course
of mathematical studies on these Vedic lines instead of 15 or 20 years
required according to the existing systems of Indian and also of foreign

15. In this connection, it is a gratifying fact that unlike some so-called
Indologists (of the type hereinabove referred to) there have been some great
modern mathematicians and historians of mathematics (like Prof. G. P.
Halstead, Professor Ginsburg, Prof. De Morgan, Prof. Hutton etc.,) who have,
as truth-seekers and truth-lovers, evinced a truly scientific attitude and
frankly expressed their intense and whole-hearted appreciat ion of ancient
India's grand and glorious contributions to the progress of mathematical
knowledge (in the Western hemisphere and elsewhere).

16. The following few excerpts from the published writings of some
universally acknowledged authorities in the domain of the history of
mathematics, will speak eloquently for themselves:-

(i) On page 20 of his book "On the Foundation and Technique of Arithmetic",
we find Prof. G. P. Halstead saying "The importance of the creation of the
zero mark can never be exaggerated. This giving of airy nothing not merely a
local habitation and a name, a picture but helpful power is the
characteristic of the Hindu race whence it sprang. It is like coining the
Nirvana into dynamos. No single mathematical creation has been more potent
for the general on-go of intelligence and power".

(ii) In this connection, in his splendid treatise on "The present mode of
expressing numbers" (the Indian Historica l Quarterly Vol. 3, pages 530-540)
B. B. Dutta says "The Hindus adopted the decimal scale very early. The
numerical language of no other nation is so scientific and has attained as
high a state of perfection as that of the ancient Hindus. In symbolism they
succeeded with ten signs to express any number most elegantly and simply. It
is this beauty of the Hindu numerical notation which attracted the attention
of all the civilised peoples of the world and charmed them to adopt it".

(iii) In this very context, Prof. Ginsburg says:- "The Hindu notation was
carried to Arabia about 770 A.D. by a Hindu scholar named KANKA who was
invited from Ujjain to the famous court of Baghdad by the Abbaside Khalif
Al-MANSUR. Kanka taught Hindu astronomy and mathematics to the Arabian
scholars; and, with his help, they translated into Arabic the
Brahma-Sphuta-Siddhanta of Brahma Gupta. The recent discovery by the French
savant M. F. NAU proves that the Hindu numerals were well known and much
appreciated in Syria about the middle of the 7th Century A.D. (GINSBURG'S
"New light on our numerals", Bulletin of the American Mathematical Society,
Second Series, Vol. 25, pages 366-369).

(iv) On this point, we find B. B. Dutta further saying: "From Arabia, the
numerals slowly marched towards the West through Egypt and Northern Arabia;
and they finally entered Europe in the 11th Century. The Europeans called
them the Arabic notations, because they received them from the Arabs. But
the Arabs themselves, the Eastern as well as the Western, have unanimously
called them the Hindu figures. (Al-Arqan-Al-Hindu)."

17. The above-cited passages are, however, in connection with, and in
appreciation of India's invention of the "ZERO" mark and her contributions
of the 7th century A.D. and later to world mathematical knowledge.
In the light , however, of the hereinabove given detailed description of t he
unique merits and characteristic excellences of the still earlier Vedic
Sutras dealt with in the 16 volumes of this series, the conscientious
(truth-loving and truth-telling) historians of mathematics (of the lofty
eminence of Prof. De Morgan etc.) have not been guilty of even the least
exaggeration in their candid admission that "even the highest and farthest
reaches of modern Western mathematics have not yet brought the Western world
even to the threshold of Ancient Indian Vedic Mathematics".

18. It is our earnest aim and aspiration, in these 16 volumes, to explain
and expound the contents of the Vedic Mathematical Sutras and bring them
within the easy intellectual reach of every seeker after mathematical


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