The Hindu: ‘Everything Vedic in ‘Vedic Maths’

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
This criticism was recently highlighted in an article in 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 approachVedic 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.”
Each sutra covers a wide range of applications, and the
recognition 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

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.
The sutras also reflect deeper philosophical truths concerning
human nature, our perception of the world and our relationship with it.
For example, one sutra states Vyashti Samashti, Specific
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.”
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.
Prof. Raju claims that Bharati Krishna Tirtha’s book “Vedic Mathematics” states that the sutras are
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 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,” Tirthaji states that he found all 16 sutras in the Sthapatya-Veda in
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.
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 Tirthaji’s book was
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.
Offering a new orientationProf. 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 Tirthaji
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.
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.
(James Glover is a fellow of the Institute of Mathematics and its Applications. He is the author of Vedic Mathematics for Schools, 1-3.)

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