Opinion September 3, 2014
C. K. Raju
‘Vedic mathematics’ as a replacement for traditional Indian arithmetic
is hardly an act of nationalism; it only shows ignorance of the history
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
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.
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.
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
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.
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).
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.
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
(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.)