[Dr. C K Raju, a mathematician by training, is a highly learned person
doing research for ages on oriental roots of science and mathematics, and
much else.
If I correctly recall, he considers that European colonisers have severely
distorted the history of science and mathematics to deny the orient of its
due credit.
He is considered a maverick by some. But that's somewhat beside the point
here.
The original author of the 'Vedic Mathematics' has quite clearly averred in
his introduction to the book that this is his own creation and not to be
found in any of the Vedas.
The other relevant point is that though it is labelled as "mathematics", it
deals, in a limited way, exclusively with its only one branch, the most
primary one, the arithmetic. It essentially offers some trick methods for
quick mental calculations.
The Trachtenberg system, named after its creator, is another school, or
rather another set of trick methods, of the same genre - understandably
quite well-known the world over.]
Nothing Vedic in 'Vedic Maths'
C. K. RAJU
Advocating 'Vedic mathematics' as a replacement for traditional Indian
arithmetic is hardly an act of nationalism; it only shows ignorance of the
history of mathematics
Gujarat has made it compulsory for school students to read the texts of
Dinanath Batra, endorsed by Prime Minister Narendra Modi. According to news
reports, Mr. Batra has now proposed a non-governmental education commission
which will Indianise education through, for instance, Vedic mathematics.
The Minister for Education has also mentioned Vedic mathematics as part of
her agenda.
*Ignorant of tradition*
One appreciates the desire of these people to work for Indian traditions.
But where in the Vedas is "Vedic mathematics" to be found? Nowhere. Vedic
mathematics has no relation whatsoever to the Vedas. It actually originates
from a book misleadingly titled *Vedic Mathematics *by Bharati Krishna
Tirtha. The book admits on its first page that its title is misleading and
that the (elementary arithmetic) algorithms expounded in the book have
nothing to do with the Vedas. This is repeated on p. xxxv: "Obviously these
formulas are not to be found in the present recensions of Atharvaveda." I
have been pointing this out since 1998. Regrettably, the advocates of
"Vedic mathematics," though they claim to champion Indian tradition, are
ignorant of the actual tradition in the Vedas. Second, they do not even
know what is stated in the book -- the real source of "Vedic mathematics."
Third, they are unaware of scholarly writing on the subject. When education
policy is decided by such ignorant people, they only end up making a
laughing stock of themselves and the Vedas, and thus do a great disservice
to the very tradition which they claim to champion.
Everyone learns how to add, subtract, multiply and divide in school. Why
should we replace those algorithms with "Vedic mathematics"? Will that
Indianise education? No. The standard arithmetic algorithms actually
originated in India, where they were known by various names such as
* patiganita*(slate arithmetic). However, the word "algorithm" comes from
"algorithmus": the Latinised name of al Khwarizmi of the 9th century House
of Wisdom in Baghdad. He wrote an expository book on Indian arithmetic
called *Hisab al Hind*. Gerbert d'Aurillac (later Pope Sylvester II), the
leading European mathematician of the 10th century, imported these
arithmetic techniques from the Umayyad Khilafat of Córdoba. He did so
because the primitive Greek and Roman system of arithmetic (tied to the
abacus), then prevailing in Europe, was no match for Indian arithmetic.
However, accustomed to the abacus (on which he wrote a tome), Gerbert was
perplexed by algorithms based on the place-value system, and foolishly got
a special abacus (apices) constructed for these "Arabic numerals" in 976
CE. Hence the name "Arabic numerals" -- because a learned pope amusingly
thought there was some magic in the shape of the numerals which made
arithmetic efficient.
Later, Florentine merchants realised that efficient Indian arithmetic
algorithms conferred a competitive advantage in commerce. Fibonacci, who
traded across Islamic Africa, translated al Khwarizmi's work, as did many
others, which is why they came to be known as algorithms. Eventually, after
600 years, Indian algorithms displaced the European abacus and were
introduced in the Jesuit syllabus as "practical mathematics" circa 1570 by
Christoph Clavius. These algorithms are found in many early Indian texts,
such as the *Patiganita *of Sridhar or the *Ganita Sara Sangraha *of
Mahavira, or the*Lilavati *of Bhaskara II. So, advocating "Vedic
mathematics" as a replacement for traditional Indian arithmetic is hardly
an act of nationalism. On the contrary, it only shows ignorance of the
history of mathematics. Spreading this ignorance among future generations
will weaken the nation, not strengthen it.
The techniques of "Vedic mathematics" are designed for mental arithmetic,
traditionally used by lower caste artisans such as carpenters or by people
like Shakuntala Devi. There are many other such systems of mental
arithmetic today. If that is what we intend to promote, we should first do
a systematic comparison. We should also be honest and refrain from using
the misleading label "Vedic" which is the main selling point of Bharti
Krishna Tirtha's system, and which attracts gullible people who infer value
just from the wrapper.
*Suppressing real Mathematics*
Promoting the wrongly labelled "Vedic mathematics" suppresses the
mathematics that really does exist in the Vedas. For example, Yajurveda
17.2 elaborates on the decimal place value system (the basis of Indian
algorithms) and some of those names for numbers are still in use, though
terms such as arab (arbudam) have changed meaning. That passage shows that
the place value system extends back to Vedic times, and it was a late
acquisition only in mathematically backward Europe.
Likewise, the theory of permutations and combinations is built into the
Vedic metre (and Indian music in general), as explained in various texts
from Pingala's* Chandahsutra *to Bhaskar's *Lilavati*. The *aksa sukta *of
the Rgveda gives a beautiful account of the game of dice, which is the
foundation of the theory of probability. The romantic story of Nala and
Damayanti in the Mahabharata further relates dice to sampling theory (to
count the number of fruits in a tree).
More details are in my article on "Probability in Ancient India" available
online and published in the Elsevier *Handbook of the Philosophy of
Statistics*. However, all these scholarly efforts are jeopardised, for they
too are viewed with suspicion.
We need to change the Western and colonial education system, especially
with regard to mathematics. Traditional Indian *ganita* has much to offer
in this process, but "Vedic mathematics" is definitely not the right way.
Wrong solutions like "Vedic mathematics" persist because an insecure
political dispensation values the politically loyal over the learned who
are loyal to the truth. ("Merit" apparently is important only in the
context of reservations.) Such political processes are historically known
to damage real traditions.
As I wrote over a decade ago in my book *The Eleven Pictures of Time*,
those who attain or retain state power through religion are the worst
enemies of that religion, whatever be the religion they claim to represent:
Christianity, Islam, or Hinduism.
*(C.K. Raju is author of *Cultural Foundations of Mathematics*. He was
professor of mathematics, and Editorial Fellow of the Project of History of
Indian Science, Philosophy and Culture.)*
--
Peace Is Doable
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