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.]

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 theLilavati 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.)