VEDIC MATHEMATICS

The Cosmic Software For

The Cosmic Computer
Dr. Narinder Puri
University of Roorkee
Uttar Pradesh, India

Dr. Michael Weinless

Maharishi International University
Fairfield, Iowa, USA

Presented at the National Council of Teachers of

Mathematics Annual Conference, Chicago, IL, 1988

Introduction

Vedic Mathematics offers a new holistic approach to mathematics and to mathe-

matics education. Its range extends from the most concrete values of numerical compu-
tation to the most abstract aspects of the dynamics of intelligence.

The computational methods of Vedic Mathematics have been found to be easier to

learn, faster, and more enjoyable than conventional methods. The intrinsic flexibility of
the Vedic system of calculation develops the students’ creativity and clarity of mind.

The system of Vedic Mathematics is derived from the Vedic tradition or knowl-
edge, recently revitalized and reinterpreted by Maharishi Mahesh Yogi in the form of a
modern systematic science, known as Maharishi’s Vedic Science. According to Mahar-
ishi, at its deepest level, Vedic Mathematics is the exploration and exposition of the self-
interacting structure of pure consciousness, which is the orderly basis of all phenomena
in nature. By connecting mathematics to its source in the field of pure consciousness,
Vedic Mathematics has the potential to bring fulfillment to all areas of mathematics and
to solve the current crisis in mathematics education.
 The Sutras of Vedic Mathematics

All the computational methods of Vedic Mathematics are based on sixteen sutras
(aphorisms) that are directly derived from the Atharv Ved, one of the primary texts of the
ancient Vedic literature of India. This mental computational system was brought to light
in recent times by the Shankaracharya of Puri, Swami Bharati Krishna Tirtha.

On one level, each sutra aphoristically describes the actual computational method
to be used for the various types of mathematical problems. On a deeper level, however,
each sutra may be seen as a refined formula for producing a high degree of coherence and
order in brain functioning, facilitating the rapid and precise solution to the mathematical
problem.

The coherently functioning brain, with its billions of neurons and interconnections
is, in Maharishi’s words, a “cosmic computer.” Through proper programming it can ac-
complish anything. The sutras of Vedic Mathematics are the “cosmic software” that create
the ability to compute most rapidly and precisely.

Applications to Mathematics Education

Vedic Mathematics offers a new approach to resolving the current crisis in math-
ematics education. It is not simply a collection of new computational techniques; rather
it provides an entirely different approach to mathematical computation, based on pattern
recognition.

The conventional methods of mathematical computation consist of rigid, some-

times monotonous procedures that are uniformly applied to all problems of a given type.
The result is often boredom, strain, and a lack of enjoyment for both student and teacher.

By contrast, the techniques of Vedic Mathematics allow for constant expression of

the student’s creativity. First, for any type of problem, there are always several different
approaches: at least one general technique, applicable to all cases, and also a number of
special techniques, applicable to cases having a particular pattern. The general technique
is always faster and easier than the conventional technique, while the techniques for spe-
cial cases extraordinarily fast, yielding solutions to complex problems, often at the speed
of just writing down the successive digits of the answer. Second, at each stage of a par-
ticular technique, there are usually options with regard to the next step. This flexibility
in the method keeps the mind lively and alert and cultures the ability to quickly discover
the path of least action on the way to the solution.
2
 In addition, the techniques of Vedic Mathematics have been found to be easier to
learn than conventional methods. Computational complexities are significantly reduced
by using digits and their complements. And finally, unique, independent cross-checking
methods make the system less prone to error.

In summary, then, the techniques of Vedic Mathematics not only provide a quick
and accurate solution to the problem at hand, but also develop clarity of mind and intu-
ition. In this way, Vedic Mathematics succeeds in fulfilling the two major goals of mathe-
matics education: to teach students procedures for solving specific mathematics problems
and to develop clear and logical thinking.

In teaching Vedic Mathematics, Dr. Puri has found that students derive great en-
joyment from it, even if they previously disliked mathematics. The problem of “math anx-
iety,” which confronts mathematics educators around the world, simply does not arise.
The Vedic mathematics research group in London has successfully applied Vedic Math-
ematics at both primary and secondary school levels. The Indian Ministry of Human
Resource Development recently held a workshop on Vedic Mathematics at Rajasthan Uni-
versity, which was attended by mathematicians, educators, and government representa-
tives. The workshop recommended that the government immediately introduce Vedic
Mathematics into the educational curriculum of the nation.

Glimpses of Vedic Mathematics

The following elementary examples provide a glimpse of the speed and simplicity
of the computations provided by Vedic Mathematics.

• 99976 × 99998 = 99974|00048

The answer is directly obtained in just one line using the nikhilam sutra.

• 374 − 253 + 254 − 433 + 327 = 374 + 253 + 254 + 433 + 327 = 269
The answer is directly obtained by treating the numbers to be subtracted as con-
sisting of negative digits, using the vinculum method.

• 252 × 254 = 14 × 256|008 = 64008

The answer is directly obtained using the anurupyena upasutra.

• 99932 = 9986|0049
The square is obtained directly by using the yavadunam sutra.

• 1952 = 19 × 20|25 = 38025

The square is obtained using the ekadhiken purvena sutra.
3
 • 988 × 996 × 995 = 979|128|240 = 979127760
The product is obtained in one line using the nikhilam sutra.

• 1/39 = 0.0̇25641
The answer is obtained in just six seconds using the ekadhika sutra.

• 4 yd. 1 ft. × 8 yd. 2 ft. = 32|16|2 = 37 sq. yds. 56 sq. ft.

The answer is obtained using the urdhava sutra.

2
• 202892 = 20311 = 4|0|1 2|4|5|6|5|2|1 = 412456521 = 411643521
The result can be directly obtained by working from either left to right or right to
left in four alternative ways using dwandwa yoga.

These examples provide just a glimpse of the most elementary applications of

Vedic Mathematics. More sophisticated application include computational aspects of lin-
ear algebra, curve fitting, evaluation of transcendental functions, solution of cubic and
higher order algebraic equations, and the solution of certain types of nonlinear problems
in analysis.

The Foundations of Vedic Mathematics

Computational techniques are just one aspect of the complete approach of Vedic
Mathematics. Maharishi’s Vedic Science locates the deepest value of Vedic Mathematics
in the mathematical structure of consciousness itself. The founders of the Vedic tradition
discovered the capability of the human mind to settle into a state of deep silence while
remaining awake, and therein to experience a completely unified, simple, and unbounded
state of awareness, called pure consciousness. In this experience, Maharishi explains, the
conscious mind becomes identified with an infinite, all-pervading unified field, an eternal
continuum underlying all existence.

By gaining familiarity with the silence of pure consciousness, one develops the
ability to cognize within that silence an eternal and unmanifest “fabric” or “blueprint” of
all the laws of nature; this fine fabric of activity is the Ved. The Vedic seers gave expression
to the self-sufficient, infinitely dynamic, self-interacting qualities of this unified state of
awareness; and they articulated the dynamics by which it sequentially gives rise, through
its own self-interacting dynamics, to the field of space-time geometry, and subsequently
to all the diverse forms and phenomena that constitute the universe. These expressions
and articulations constitute the Vedic Literature.

At its most profound level, Vedic Mathematics is the mathematics of the Ved, the
structure of pure knowledge; it reveals the precise mechanics by which the infinite, ab-
solute reality of pure intelligence knows itself and thereby creates, from within itself, all
4
quantified values and relationships. On this basis, Vedic Mathematics is able to portray
the quantification of all levels of intelligence (pure mathematics) and also to describe the
dynamics of intelligence found in all levels of nature’s functioning (applied mathematics).

Maharishi describes the Ved, within the field of pure consciousness, as existing on
the level of undivided unity. Within this unity two values, existence and intelligence, can
be located. It is the intelligence value that knows itself and thereby conceptually creates
three values within itself—the knower, the process of knowing, and the known. Thus,
one becomes two, and two becomes three. Through the further interaction of these three
values, the infinite diversity of the universe is created from the sequential quantification
of unity. This unfoldment is portrayed with perfect precision by Vedic Mathematics.

According to Vedic Science, all values of relationship and transformation, both ab-
stract and concrete, are simply expressions of the self-interacting structure and dynamics
of an underlying, totally unified field of pure intelligence. The unlimited variety of re-
lationships and transformations, ranging from the most abstract areas of modern mathe-
matics to the most concrete phenomena of nature, can thereby be described in terms of the
inner relationships of pure consciousness. Vedic Mathematics provides this description.

This general principle is familiar to modern mathematicians. The unified founda-

tion of modern mathematics is provided by set theory, the mathematics of the infinite. At
the foundations of set theory are mathematical principles that directly describe the nature
of an abstract, infinitely dynamic field of intelligence. All of mathematics is described as
sequentially unfolding from the internal dynamics of this field of pure intelligence. For
example, all sets are sequentially created from the unmanifest point value of the null set.
This self-referral nature of the field of intelligence at the basis of set theory is expressed at
a deeper level by the reflection principle, which underlies the mathematical description
of the different quantified values of infinity provided by the theory of large cardinals.

In Vedic Mathematics, all the fundamental principles are derived from direct ex-
perience of the unmanifest source of orderliness within the unified field or pure con-
sciousness. Vedic Mathematics is, therefore, the mathematics of the most fundamental
structures of natural law. This is its unique stature and contribution to the field of knowl-
edge.

Invitation to All Mathematicians

The computational applications of Vedic Mathematics are only the first step in an
ongoing research program. All areas of modern mathematics, both pure and applied,
fall within the scope of Vedic Mathematics. We are just beginning to tap the enormous
potential, of this more fundamental and complete approach to knowledge,
5
 By connecting mathematics to its source in the field of pure consciousness, Vedic
Mathematics has the potential to bring fulfillment to all areas of mathematics. All math-
ematicians and mathematics educators are invited to join this research program, to apply
the sutras of Vedic Mathematics to all areas of mathematics, and to enjoy the full creative
expression of mathematics for the benefit of mankind.

For more information write to: Institute of Vedic Mathematics, Maharishi International
University, Fairfield, Iowa 52556.