Vedic Mathematics-India’s Opulent Benefaction

Contributed by:
Harshdeep Singh
This PDF contains :
i) Pertinency of vedic mathematics:
ii) Exemplification of Vedic mathematics:
iii) Leg –up:
iv) The field of vision:
v) Anonymity between vedic mathematics and
integration simplification:
1. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017
Vedic Mathematics-India’s Opulent Benefaction
Shikha Singh#1, Akshmeet Kaur#2, Anandita Gautam#3
Research Associate, WISDOM, Banasthali Vidyapith, Rajasthan, India
Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India
Student, AIM & ACT, Banasthali Vidyapith, Rajasthan, India
Abstract – Mathematics referred to as the queen of Romans etc. The Vedic system invented the zero,
sciences reflects the “the active will and the reason for Aryabhata was followed by Brahmagupta who
aesthetic perfection”. Logic and mathematics are developed the use of zero, followed by Pythagoras’
commutual. As per the reports, India is facing a huge theorem which was discovered in India and gravity was
Maths Crisis in which 26.1 per cent of children in Class explained in the Rig Veda, 2,400 years before Newton’s
V know division and only 44.1 per cent in Class VIII apple injury. Vedic Mathematics was not known to the
could solve a three digit by one digit division problem. world but with an increase of interest in ancient Sanskrit
In other words, abstract and logical reasoning is their text, the ancient Vedic Mathematics was rediscovered
hurdle. To overcome this, scholars have revived interest by Swami Bharati Krisna Tirthaji (the former
in Vedic Mathematics which was born in the Vedic Age, Shankaracharya of Puri, India) in 1911, he was a great
deciphered towards the beginning of the 20th century, scholar of Sanskrit, Mathematics, History and
by Swami Bharati Krishna Tirthaji. The Sanskrit word Philosophy. His deep study and careful research had
Veda is derived from the root Vid indicating deep deciphered the great mathematical formulas known as
acquaintance. The Sutras apply to almost every branch Sutras that were completely ignored as no one could
of Mathematics making calculations of large numbers relate these to mathematics. Vedic Mathematics (1965)
easier that was nearly impossible in systems like those that is a pioneer work of Bharati Krishna Tirthaji has
of the Greeks, Romans etc. In the vedic system complex techniques of Vedic mathematics. It is considered as a
problem or difficult sum or lengthy equations can often first work towards Vedic Mathematics. In late 1960s a
be solved immediately. It has striking and beautiful copy of his book reached London and from there Vedic
methods which beautifies and systematise mathematics. Mathematics was reborn. The verses are guides to turn
The Vedic system invented the zero, Aryabhata was difficult sums into quick mental math using simple
followed by Brahmagupta who developed the use of rules. The Nikhilam Navatashcaramam Dashatah - 'all
zero, followed by Pythagoras’ theorem which was from nine, last from ten’ – for example, speeds the
discovered in India and gravity was explained in the Rig multiplication of large numbers by breaking them down
Veda, 2,400 years before Newton’s apple injury. The to their common bases: To multiply 48 by 52, the
debate has raised an uncomfortable question for Hindu numbers are broken into (50-2) and (50+2) and the
nationalists on how India lost its mathematical square of the smaller sum (4) subtracted from the square
advantages over the millennia. Thus, our desideratum of the larger (2,500) to reach the answer of 2,496.
lies in highlighting the significance and the vast usage Similarly, division is simplified by multiplying the
of this branch of mathematics. denominator into a base ten number: 44/25 = 176/100 =
1.76. The successors of the Greeks in the history of
Keywords – Vedic Mathematics, Sutras, Vedic system, mathematics were the Hindus. They produced original
concepts and good procedures. They were the first to
Vedas. recognize zero as both a cardinal number and a place
1. INTRODUCTION holder. Bhaskara supplied correct rules for operating
Square one of Vedic mathematics – Isn’t the idea of with irrational numbers. The Hindus created the concept
solving mathematical problems just within the wink of of negative numbers; the earliest known use of negative
an eye fascinating? Veritably, the brownie points here numbers was by Brahmagupta around A.D. 630.
go to Vedic Mathematics inbred in the Vedic Age, Aryabhata went beyond Diophantus in his use of
deciphered towards the beginning of the 20th century, continued fractions to solve indeterminate equations.
by Swami Bharati Krishna Tirthaji. Well, because After Aryabhata and Varahamihira, came Brahmagupta
mathematics, may it be Vedic or modern is not only who was later assessed by Alberuni as the most
about numbers and figures. Many western societies, distinguished mathematician of India. In Brahma-
math is a much dreaded school subject. Vedic math Sphuta-Siddhanta, Brahmagupta has dealt with algebra,
only has 16 rules, each of which is very simple. The arithmetic, geometry and astronomy. Brahmagupta for
Sutras apply to almost every branch of Mathematics the first time dealt with zero and its operations but
making calculations of large numbers easier that was wrongly stated that zero divided by zero is also zero but
nearly impossible in systems like those of the Greeks, is known for arriving at the solution of the
ISSN: 2231-5373 Page 283
2. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017
indeterminate equations of second degree in which he between cardinal and ordinal numbers. The word kha,
excelled Aryabhata. He is the first in the world to have which Indian mathematicians used later to denote zero,
used algebra effectively for astronomical calculations. occurs in Vedic only in the senses of hole, opening
His major achievements were in the field of algebra in vacancy or space. The three greatest landmarks in this
which he carried forward the earlier work of Aryabhata. area are the kuttaka, method of Aryabhata for solving
Medatithi, a seer of the Vedic times, is known to have the linear indeterminate equation ay-bx=c, the bhavana
stated very high numerals, e.g. 10 to the power 22 in a law of Brahmagupta, and the cakravala algorithm
systematic way. His name is associated with hundreds of described by Jayadeva and Bhaskara 2 for solving
verses in the Rig-Veda, Atharvaveda and Yajur Veda. quadratic indeterminate equation Dx2+1=y2.
There is however, no evidence available to show that in
Medhatithi’s time, the large numerals were written as 2. OBJECTIVE
they were spoken. The earliest evidence of the use of the
Objective of the study is the essential facts of Vedic
new system has been found in the Bakhshali manuscript,
Mathematics arousing awareness in the young
whose original composition is said to have been made
generation about the importance of Indian culture
around A.D. 200.Later Aryabhata in his Aryabhatiya,
through so that they feel proud to be a part of such a
Varahamihira in his Pancha Siddhanta, Jainbhadra Gani
diversely rich society. This research bring into notice
and others used the place value system of writing
facts about the growing influence of Vedic mathematics
numerals. In no other country was the decimal system of
in various fields in order to simplify complex
place value notation used so early as in India. The
calculations in order to remove the fear of mathematics
system of place value notation of writing numerals is an
in many students by citing examples of the great
Indian contribution to the world of mathematics that is
mathematicians given by India to the world. Thus, study
reckoned as one of the greatest inventions of all times.
aims to brim the rich heritage of India thereby bringing
Aryabhata was one of the most scientific innovators of
to the light the various discoveries done by Indian
ancient India. He is the earliest known Hindus author to
mathematicians and the various claims that India lost in
have worked on algebra. Aryabhata expressed high
the hands of others. Even the students at IITs, St James'
numbers by means of syllables. He indicated a method
School, London, have begun to teach the Vedic system
of arriving at a solution of the indeterminate equations
successfully. Our motive is to throw light on claims like
of the first degree. He is also the first to give a concept
our scientists discovered the Pythagoras theorem but we
of kuttakara or pulveriser which was later developed by
gave its credit to the Greeks. Lastly, we want the
others in India. He also quoted the Pythagorean theorem
students to learn simplified techniques for understanding
in one of his verses. Bhaskara anticipated many of the
math and improve their skills.
discoveries in the field of algebra so that his work could
only be surpassed in the European countries after the
17th and 18th centuries. He was the last of the great i) Pertinency of vedic mathematics:
mathematicians of ancient and medieval India. For the
Vedic Mathematics was taken up as a new alternative
Indians of the Vedic times, the performance of a variety
system of mathematics. British mathematicians got
of sacrifices formed a major part of their religion. These
interested in Vedic mathematics. Many lectures on this
sacrifices were performed at certain precalculated times,
were delivered which later on were collected in the book
and in altars of particular sizes and shapes which led
– Introductory Lectures on Vedic Mathematics. After
their builders to understand and deduce certain practical
the visit of Andrew Nicholas to India between 1981 and
geometrical principles. Construction of these altars was
1987, interest in Vedic maths started to develop in India.
handled by people well versed in it and the art of this is
Vedic mathematics has given a new approach to
contained in scriptures known as sulba sutras.
mathematics. To do calculations quickly, the Indian
Baudhayana Sulba Sutra is the oldest and the biggest of
Institute of Technology students are said to use Vedic
them all. It belongs to Krishna of various altars and
Mathematics, St James’ School, London and many other
deals briefly with their shapes and sizes. He describes
schools have started teaching Vedic maths to their
methods for construction of geometrical figures,
students. In India also it is taught in many schools.
combination and transformation of areas, measurement
Students of economics and MBA find it very useful. A
of volumes of areas, and squaring the circle. By 1800
Delhi-based forum known as International Research
mathematics rested upon two foundations, the number
Foundation for Vedic Mathematics and Indian Heritage
system and Euclidean geometry. The 17th centuries
have been giving lectures on Vedic Mathematics since
were the greatest periods of mathematics. What may be
1999 in most of the schools in Delhi. Without a doubt
called the prehistory of zero was expressed in early
there are many advantages of learning Vedic
Vedic by kha which refers to cavities of various sorts
Mathematics. Students develop problem solving ability
and occurs in the Upanishads in the sense of ―space‖.
and it also leads to the development of creative
The Rig-Veda made use of recursion and distinguished
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3. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017
intelligence. Students of Vedic Mathematics can not are multiplied as before. The number on the left is
only do simple calculations of subtraction, addition,
obtained by diagonal cross addition:
multiplication but also very complex calculations such
as algebra, geometry, calculus and trigonometry. Our 105 +05
mind is at work with this mathematics so mental
108 +08
sharpness is associated with it. Vedic math is very
effective and at the same time it is easy to learn. Only 16 113 40
Vedic sutras are used to solve the mathematical
The product is 11340.
problem. Sutras are basically word formulae that
describe normal way of solving mathematical problems. The technique that is useful in all cases is based on the
Instead of learning by repetition, Vedic Mathematics
principle of udhvatiryaka and involves cross
involves logic and understanding the fundamental
concepts. One can do calculations much faster than done multiplication. This was developed in India before 8
by using the conventional method that is taught in
century and is bases on a deep understanding of the
schools. It teaches the students to solve same problem in
different ways. It should indeed be a spirited feeling to place value system of representing numbers.
encourage the system being developed in our own
E.g. 534 with 463
We write down the first number as it is, n reverse the
ii) Exemplification of vedic mathematics: second number;
Perchance, the most striking feature of the Vedic system 534
is its coherence. Instead of a mélange of unrelated
techniques the whole system is bewitchingly interrelated
and unified: the general multiplication method, for 1
example, is easily reversed to allow one-line divisions
and the simple squaring method can be reversed to give
one-line square roots. And these are all easily The first digit of the result is obtained by multiplying the
understood. This unifying quality is hitting the spot vertically overlapping nos 4 and 3.The product is 12; the
making mathematics child’s play and enjoyable. For units digit 2 is written as the units digit of the result and
example: Nikhilam is a special multiplication method 1 is carried over to the second digity.364 is then shifted
which is illustrated as follows: left by a digit. The vertically overlapping numbers are
multiplied and the products added. Any carry from the
Eg: multiply 95 by 98 .note that95 is less than 100 5 previous operation is added to this to obtain the
and 98 is 2 less than 100.let us write the two numbers hundreds digit of the result.
and their deviations from 100 with a line separating the 534
two as follows:
95 05
98 02
Note that the deviation has 2 digits. The product of 95
and 98 is obtained by multiplying the numbers to the 33+1=34)
right of the line. Then a cross a cross subtraction is
Thus the overlapping digits 3 and 3 as well as 4 and 6
carried out diagonally, to give 93 which occupies the
are multiplied and the two products are added to give
thousands and hundreds places, 9310 is the required
33.The addition of carry 1 gives 4 as second digit of the
result and as a carry of 3.The process is repeated by
Another e.g. Indicating the nikhilam for numbers
again shifting 364 to the left as shown:
greater than the base; 534
For numbers close to some power of 10 eg: if we want 364
to multiply 105 n 108 the we proceed as follows; 531
To the right of the number we write its difference from =242(5*3+3*6+4*4=49
100 with a positive sign. Now the numbers on the right 49+3=52)
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4. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017
Thus the overlapping are multiplied and added, we get proof or explanation of a method beforehand is not
49, to which we add the carry over 3.The third digit of essential in the Vedic methodology. The Vedic system
the product is therefore 2 and 5 is carried over to the appears to be effective over all ability ranges: the able
fourth digit. child loves the choice and freedom to experiment and
The number 364 is again shifted left and the same the less able may prefer to stick to the general methods
but loves the simple patterns they can use. Artistic types
operation is repeated as shown:
love the opportunity to invent and have their own unique
534 input, while the analytic types enjoy the challenge and
scope of multiple methods because the Vedic system
uses these ultra-easy methods mental calculation is
4531 preferred and leads naturally to develop mental agility.
And this in turn leads to growth in other subjects. In the
Vedic system 'difficult' problems or huge sums can often
(42+5=47) be solved immediately. These striking methods are just a
part of a complete system of mathematics which is far
The addition of the products of overlapping digits gives
more systematic than the modern 'system'. Vedic
42 and to this we add the carry 5 to give 7 as the fourth
Mathematics manifests the coherent and unified
digit of the result, and as 4 as the carry. Again, 364 is
structure naturally inherent in mathematics and the
shifted to the and repeat the operation.
methods are direct. Vedic mathematics, a set of
supposedly ancient techniques that help even the most
364 numerically challenged to conquer difficult sums, is
surging in popularity as government ministers claim that
they could hold the key to better education
As only 5 and 4 are vertically overlapping their product iv) The field of vision:
yields 20.The carry 4 is added to give 24.The fifth digit
The debate has raised an uncomfortable question for
of the result is thus 4,and 2 will be carried over to the
Hindu nationalists on how India lost its scientific and
sixth digit. Once again shifting 364 to the left by a digit
mathematical advantages over the following millennia.
results in no overlap and therefore the sixth digit of the
Dina Nath Batra said ―Muslim invasions and British
result is only the carry 2.thus 534*463=247242.In
colonial rule were to blame. The ancient knowledge had
modern teaching we usually have one way of doing a
been neglected because we’ve been slaves of the
Mohammedans and the British for 2,000 years. Nalanda
and other places of wisdom were destroyed‖, he said. St
iii) Leg –up: James' School, London, and other schools began to
teach the Vedic system, with notable success. Today this
The Vedic system has many special methods, when a
remarkable system is taught in many schools and
calculation has some special characteristic that can be
institutes in India and abroad, and even to MBA and
used to find the answer more easily. This flexibility adds
economics students. When in 1988, Maharishi Mahesh
to the fun and gives pupils the freedom to choose their
Yogi brought to light the marvels of Vedic
own approach. This in turn leads to the development of
math; Maharishi Schools around the world incorporated
creativity and intuition. The Vedic system does not
it in their syllabi. At the school in Skelmersdale,
insist on a purely analytic approach as many modern
Lancashire, UK, a full course called "The Cosmic
teaching methods do. This makes a vast difference to the
Computer" was written and tested on 11 to 14 year old
attitude which students have towards mathematics. The
pupils, and later published in 1998. According to
ease and simplicity of Vedic Mathematics means that
Mahesh Yogi, "The sutras of Vedic Mathematics are the
calculations can be carried out mentally. A flexible,
software for the cosmic computer that runs this
mental system has leg up over the unpliable ones. Pupils
universe."The difference created by Vedic mathematics
can invent their own methods and are not limited to the
is that it had developed the system of tens, hundreds,
one 'correct' method. This leads to more creative,
thousands, etc., and the basis of carrying the remainder
interested and intelligent pupils. It also leads to
of one column of numbers over to the next. This made
improved memory and greater mental agility. All these
for smooth sailing calculations of large numbers that
features of Vedic math encourage students to be creative
was nearly impossible in other systems, as found with
in doing their math. Being naturally creative students
the Greeks, Romans, Egyptians and even Chinese. The
like to devise their own methods of solution. The Vedic
rising popularity of Vedic maths is partly because of a
system seeks to cultivate intuition, having a conscious
renewed campaign by the nationalist Prime Minister,
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5. International Journal of Mathematics Trends and Technology (IJMTT) – Volume 47 Number 4 July 2017
Narendra Modi, to lay India’s claim to the cornerstones beauty-a beauty cold and austere, like that of sculpture.
of human knowledge. He marked India’s successful In our legwork, we have tried to bring into account the
mission to Mars last year by claiming its ancient Vedic antiquity of mathematics and then of Vedic mathematics
scientists had conceived of air travel thousands of years in an effort to create awareness about the rich culture of
before the Wright Brothers made their first flight. Not which we should be proud as Indians so that the Golden
only is this, the techniques of Vedic mathematics used in Bird is able to witness many more Aryabhatas and
the processors used in electronic devices. As proposed Bhaskaras in the upcoming years. With a presentation of
by the IEEE, we know that the ever increasing demand the various views on the topic, we have reached to the
in enhancing the ability of processors to handle the conclusion that the methods of Vedic mathematics are
complex and challenging processes has resulted in the quite simple and easy to understand but the views of
integration of a number of processor cores into one chip. various authors regarding the fact that there is no solid
Still the load on the processor is not less in generic evidence to prove that these actually form a part of the
system. This load is reduced by supplementing the main Vedas. But, certainly, this method has gained popularity
processor with Co-Processors, which are designed to not only in solving high school mathematics problems
work upon specific type of functions like numeric but has emerged immense growth leading to the
computation, Signal Processing, Graphics etc. The speed formation of actual multipliers and various other real life
of ALU depends greatly on the multiplier Vedic applications. Along with the above mentions pros and
Mathematics as by employing these techniques in the cons of the topic, we have tried to describe the
computation algorithms of the coprocessor will reduce simplicity of Vedic mathematics to the fullest by
the complexity, execution time, area, power etc. highlighting the closeness of Vedic mathematics with
the theory of Integration Simplification. The two are
v) Anonymity between vedic mathematics and similar in the aspect of saving precious resources like
time and reducing complexity to make things more
integration simplification:
efficient. Vedic Mathematics is a branch of
One fresh thought, one new thought can change your life mathematics; nevertheless the applications of the two in
forever. Perception, simplicity and evaluation have led their respective fields and the motives behind them are
to the spurting out of a methodology that has its roots in similar thereby leading to the involvement of the
the blend of pragmatism and idealism thereby refraining efficient and wise utilisation of resources and
from complexity. The process of Integration exhilaration of more efficacious techniques in the
simplification, in the light construction of reality, is respective areas for their upliftment. Thus, by bringing
based on the psychological concept of differentiation, to the brim, all the necessary facts regarding our topic
assimilation, integration and accommodation. ,we wrap us as proud Indians of a diverse Indian society
Disintegration refers to the misapplication of resources and hope that India gets the acknowledgements of the
like time. Integration refers to harmonizing towards a future discoveries and we are able to witness much
common purpose. It is a pragmatic approach of solving a more inventiveness down the line.
problem or preventing a problem in an interactive
manner .Complexity means distracted effort whereas
simplicity is a focused effort. Well, generalizing the
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