## It uses short and efficient aphorisms to express principles and rules

In the light of the Human Resources Development Minister Smriti Irani

bringing to the forefront the need for some Indianisation of the school

curriculum, together with the inclusion of Vedic Maths, it is necessary

for a greater understanding of what this subject is about. To date,

there has been a groundswell of grassroots interest in this,

particularly in India, but there has also been serious criticism of its

“Vedicness.”

bringing to the forefront the need for some Indianisation of the school

curriculum, together with the inclusion of Vedic Maths, it is necessary

for a greater understanding of what this subject is about. To date,

there has been a groundswell of grassroots interest in this,

particularly in India, but there has also been serious criticism of its

“Vedicness.”

This criticism was recently highlighted in an article in

Sept. 3) which, unfortunately, was a misunderstanding of what this

approach to Maths is really about and what constitutes the Vedas.

*The Hindu*by Professor C.K. Raju (“Nothing Vedic in ‘Vedic Maths,’”Sept. 3) which, unfortunately, was a misunderstanding of what this

approach to Maths is really about and what constitutes the Vedas.

**A holistic approach**Vedic Maths is concerned with a universal structure of Maths revealed

through a personal approach to problem-solving and other fields of human

activity. It is described by a small collection of aphorisms called

*sutras*.

*Sutras*express

naturally occurring mental processes by which mathematical problems can

be solved with the least effort. Vedic Maths does not advocate the sole

use of blanket methods through which students can reduce problems to

merely mechanical responses to given stimuli. Instead, it encourages an

intelligent and holistic approach — one that engenders reason and

develops strategic thinking. There are blanket methods as well as

special case methods. If you find that a problem can be solved by an

easier or different method from what is commonly taught, then that is

used as a valid method, even if the problem is solved just by

inspection. The

*sutras*describe such principles and methods.

For example, if you want to add 324 and 199, an easy approach is to add

200 instead of 199 to 324 and take off one, resulting in 523. This is a

naturally occurring mental method and uses the fact that 199 is

deficient from 200 by one. Such special cases are not normally taught

but most people will naturally adopt them by understanding numbers. This

comes under the pithy sutra, deficiency. This example shows that there

are often simple methods which follow the path of least action and

reflects Sir Isaac Newton’s observation, “Nature abhors the pomp of

superfluous causes.”

200 instead of 199 to 324 and take off one, resulting in 523. This is a

naturally occurring mental method and uses the fact that 199 is

deficient from 200 by one. Such special cases are not normally taught

but most people will naturally adopt them by understanding numbers. This

comes under the pithy sutra, deficiency. This example shows that there

are often simple methods which follow the path of least action and

reflects Sir Isaac Newton’s observation, “Nature abhors the pomp of

superfluous causes.”

Each

recognition of the same underlying thought pattern at work has the

effect of unifying diverse aspects of Maths. An example of this is the

meaning ‘transpose and adjust’. It occurs wherever there is an action

by which something is transferred to something else with a resulting

adjustment. Such is the case when an architect transposes a previously

used plan to a new situation or a doctor adjusts a common prescription

to suit the needs of an individual. The mathematical applications of

this

polynomial division, matrices, analytic geometry, calculus, and many

others.

*sutra*covers a wide range of applications, and therecognition of the same underlying thought pattern at work has the

effect of unifying diverse aspects of Maths. An example of this is the

*Paravaryta Yojayet sutra*,meaning ‘transpose and adjust’. It occurs wherever there is an action

by which something is transferred to something else with a resulting

adjustment. Such is the case when an architect transposes a previously

used plan to a new situation or a doctor adjusts a common prescription

to suit the needs of an individual. The mathematical applications of

this

*sutra*are manifold such as for transformations, equations,polynomial division, matrices, analytic geometry, calculus, and many

others.

Vedic Maths is not historical and is not about mathematical tricks; it provides insights into the very nature of the subject

and the human psyche

It must be emphasised that Vedic Maths highlights the mental processes

and principles that take place in the mind of anyone engaged in

mathematical activity. These processes are not random and haphazard but

are reasonable, ordered and yet highly flexible.

and principles that take place in the mind of anyone engaged in

mathematical activity. These processes are not random and haphazard but

are reasonable, ordered and yet highly flexible.

The

human nature, our perception of the world and our relationship with it.

For example, one

and General. A simple application is in finding a mean, which provides a

single number that represents the whole. It describes the principle in

which something of the whole is reflected in the part or individual — a

wide-ranging law or principle permeating throughout nature. For example,

oak trees have characteristics common to all trees of that genre and

yet each oak tree is different from every other. The commonality is

reflected in each individual. The same principle occurs in the Egyptian,

Hermetic, Platonic, Hindu, Judaic, Islamic and Christian teachings

often expressed as “As above, so below.”

*sutras*also reflect deeper philosophical truths concerninghuman nature, our perception of the world and our relationship with it.

For example, one

*sutra*states*Vyashti Samashti*, Specificand General. A simple application is in finding a mean, which provides a

single number that represents the whole. It describes the principle in

which something of the whole is reflected in the part or individual — a

wide-ranging law or principle permeating throughout nature. For example,

oak trees have characteristics common to all trees of that genre and

yet each oak tree is different from every other. The commonality is

reflected in each individual. The same principle occurs in the Egyptian,

Hermetic, Platonic, Hindu, Judaic, Islamic and Christian teachings

often expressed as “As above, so below.”

To the outsider or casual onlooker, Vedic Maths appears to be a

collection of arithmetic maths tricks and algebraic methods but this is

very far from the truth about the system. Critics of Vedic Maths have

not examined what it is really about —like judging a soup by reading the

ingredients of the label on the tin rather than tasting what is inside.

collection of arithmetic maths tricks and algebraic methods but this is

very far from the truth about the system. Critics of Vedic Maths have

not examined what it is really about —like judging a soup by reading the

ingredients of the label on the tin rather than tasting what is inside.

Prof. Raju claims that Bharati Krishna Tirtha’s book “Vedic Mathematics” states that the

not to be found in the Vedas. In fact, the general editor of the text

states that this work “deserves to be regarded as a new

connection with astronomy. It is quite feasible that this is not a

published source. Nevertheless, the indication is that Prof. Raju thinks

the Vedas are a fixed set of texts from antiquity and that they are

published and can be searched through. But this is not so. Yes, there

are ancient texts commonly accepted as Vedic but there are other

treatises, or expressions, which may constitute Vedas — those that are

not published or even translated from the original Sanskrit language.

*sutras*arenot to be found in the Vedas. In fact, the general editor of the text

states that this work “deserves to be regarded as a new

*Parishishta*[appendix to the Vedas] by itself” since it is not to be found in any known or published*Parishishtas*. However, on page 231 of “Vedic Metaphysics,” Tirtha*ji*states that he found all 16*sutras*in the*Sthapatya-Veda*inconnection with astronomy. It is quite feasible that this is not a

published source. Nevertheless, the indication is that Prof. Raju thinks

the Vedas are a fixed set of texts from antiquity and that they are

published and can be searched through. But this is not so. Yes, there

are ancient texts commonly accepted as Vedic but there are other

treatises, or expressions, which may constitute Vedas — those that are

not published or even translated from the original Sanskrit language.

More importantly, such critics rely on only one narrow interpretation of

what constitutes the Vedas. Clearly, in India, there is a great emotive

connection with the understanding that Vedas are ancient texts forming

the basis for culture, laws, morals, religion and philosophy. But to

understand really what the Vedas are, we should seek out authority on

the matter rather than rely on mathematicians, journalists, historians,

and so forth. In 1965, the same year that Tirtha

published, Shankaracharya Shantananda Saraswati, famous for his profound

understanding of Vedic philosophy, the spread of meditation and his

connections with seekers of spiritual knowledge from the West, said,

“The Veda should not be taken in a very restricted sense. The Veda means

knowledge and it is not entirely Indian. It manifests in many ways in

different lands. Any nation or race or group of people who have learned

to live a civilised life; who have evolved or appreciated ethics or

morals, govern themselves according to laws, they too have seen the

Vedas. It may be different, but nevertheless, it is the Veda. The West is

neither entirely destitute of Vedas…They and many others too have

some part of the universal knowledge.” Here Vedas mean universal

knowledge and are not restricted to a hoary past. Vedas are living

knowledge and not something from history. Part of the civilised life, to

which the Shankaracharya refers, is the use and development of reason.

This includes Maths. And people’s personal experience of revelation or

realisation in Maths seems to be connected with that “wow” moment when

something is suddenly seen to be true.

what constitutes the Vedas. Clearly, in India, there is a great emotive

connection with the understanding that Vedas are ancient texts forming

the basis for culture, laws, morals, religion and philosophy. But to

understand really what the Vedas are, we should seek out authority on

the matter rather than rely on mathematicians, journalists, historians,

and so forth. In 1965, the same year that Tirtha

*ji*’s book waspublished, Shankaracharya Shantananda Saraswati, famous for his profound

understanding of Vedic philosophy, the spread of meditation and his

connections with seekers of spiritual knowledge from the West, said,

“The Veda should not be taken in a very restricted sense. The Veda means

knowledge and it is not entirely Indian. It manifests in many ways in

different lands. Any nation or race or group of people who have learned

to live a civilised life; who have evolved or appreciated ethics or

morals, govern themselves according to laws, they too have seen the

Vedas. It may be different, but nevertheless, it is the Veda. The West is

neither entirely destitute of Vedas…They and many others too have

some part of the universal knowledge.” Here Vedas mean universal

knowledge and are not restricted to a hoary past. Vedas are living

knowledge and not something from history. Part of the civilised life, to

which the Shankaracharya refers, is the use and development of reason.

This includes Maths. And people’s personal experience of revelation or

realisation in Maths seems to be connected with that “wow” moment when

something is suddenly seen to be true.

**Offering a new orientation**Prof. Raju’s expertise and knowledge of the history of Indian

mathematics is of the highest standard. He points out that India has a

brilliant past with regard to the development of Maths. So much so that

even now there are research programmes, for example at IIT in Mumbai,

looking into the vast knowledge-base of the mathematics of Kerala

spanning nearly a 1,000 years. But the history of Maths is not what

Vedic Maths is about at all. These

*sutras*of Tirtha

*ji*

reveal the real deal; they show the principles and laws behind

mathematics and mathematical activity as it happens in the present.

Vedic Maths is not historical and is not about mathematical tricks. It

provides deep insights into the very nature of the subject and the human

psyche. Neither is it exclusive. Although Tirthaji sets out alternative

methods for some topics, he does not exclude more widely known methods.

Rather it expresses underlying laws and mental patterns of all methods.

It provides us with an entirely new orientation — one that humanises

mathematics, thereby reducing the fear of numbers and mathematical concepts.

Vedic Maths unifies diversity, uses short and efficient aphorisms to

express principles and rules of working, produces and encourages easy

routes for problem-solving develops strategic thinking, describes what

happens in the mind as mathematics happens, and points to underlying

spiritual truths.

express principles and rules of working, produces and encourages easy

routes for problem-solving develops strategic thinking, describes what

happens in the mind as mathematics happens, and points to underlying

spiritual truths.

Ms Irani has every right to explore the avenues which this new and

attractive approach to Maths offers. It will be interesting to see how

this unfolds in schools. Having taught Vedic Maths for more than 30

years in the U.K. and other countries, I have seen students of all ages

finding nothing but delight in this system. Moreover, they have

benefited from it.

attractive approach to Maths offers. It will be interesting to see how

this unfolds in schools. Having taught Vedic Maths for more than 30

years in the U.K. and other countries, I have seen students of all ages

finding nothing but delight in this system. Moreover, they have

benefited from it.

*(James Glover is a fellow of the Institute of Mathematics and its Applications. He is the author of*Vedic Mathematics for Schools, 1-3

*.)*