September 3, 2014
Updated: September 3, 2014 15:52 IST
Illustration by Satwik Gade.
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.)
http://www.thehindu.com/opinion/op-ed/nothing-vedic-in-vedic-maths/article6373689.ece
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The Fraud of Vedic Maths
14 August 2010
Those who seriously still think ancient India had devised a parallel mathematical system need to acquaint themselves with an inventive Shankaracharya called Bharti Krishna Tirthaji.
BY Hartosh Singh Bal
The sutras, unfortunately, only reveal how little Tirathji knew of maths. But his quest was still forgivable
In 1965, a book titled Vedic Mathematics was published in English. Since then, the subject has become an industry that shows no sign of diminishing. In its latest manifestation, parents who know no better are shelling out serious money in the hope that their children will become scientific geniuses. They really shouldn’t bother. The subject amounts to nothing more than a few cheap parlour tricks, and there is nothing Vedic about it. But the story of how it came to be makes for a fantastical tale.
Bharti Krishna Tirthaji was born in 1884 with some talent for science and mathematics. But he eventually paid heed to a passion for Sanskrit and philosophy, and joined the Sringeri math in Mysore to study under its Shankaracharya. In 1925, he became a Shankaracharya himself. All through these years, he’d kept up his interest in science and mathematics. Many scholars before him had dismissed the Atharva Veda as arcane and difficult to understand, but Tirathji decided to spend time studying it in the belief that he could excavate the knowledge that he felt must lie there.
After eight years of ‘deep’ contemplation, he claimed to have found 16 sutras which explained all of mathematics. He, it is said, then wrote 16 volumes on Vedic mathematics, one on each sutra. Mysteriously, just before their publication, the manuscripts were lost. But in 1960, the last year of his life, Tirathji managed to rewrite one volume which was published in 1965 as Vedic Mathematics.
As stories go, this is not a bad one, but the evidence does nothing to support it. The 16 sutras expounded by Tirathji do not appear in any known edition of the Atharva Veda. Tirathji’s defenders have claimed that Tirathji was so immersed in Vedic thought that he was able to glean what the Vedic seers had in mind even if it was not explicitly so stated anywhere in the Vedic corpus. If one were to actually concede this meeting of minds between Tirathji and the ancient Vedic seers, it would have the unfortunate consequence of implying that not just Tirathji but even these seers were limited in their mathematical understanding.
All the sutras largely do is make the burden of addition and multiplication faster (though never nearly as fast as the cheapest pocket calculator), and even that, they do at a cost. Students studying the traditional method of multiplication should ideally understand (and bad teachers themselves fail to grasp this) what multiplication is, how it works, and how it is in essence an act of repeated addition. Tirathji’s methods are just rules that make mathematics seem like a bunch of tricks which are easy to implement but difficult to understand.
Take, for example, the multiplication of 9 and 7. Line them along with their difference from 10. That is:
9–10 = –1 and 7–10 = –3
9–1
7–3
——
6 3
You obtain the answer in the following fashion: the unit’s digit is the two differences multiplied together, –1 x –3 = 3 and the other digit 6 is just either of the diagonals added together, that is, 9–3 = 7–1 = 6. This method can be extended to much larger numbers. It is a neat trick, but it does not make multiplication easier to fathom, quite the contrary.
Let us then set Tirathji’s claims aside. The 16 sutras expound all of mathematics no more than astrology expounds all of modern astronomy. So what drove him and his followers (who brought out the book) to make a claim so extreme based on so little?
The answer lies in Tirathji’s times. The man was an early nationalist, and he worked with GK Gokhale in 1905 when the latter was president of the Indian National Congress. Among Gokhale’s initiatives was an effort to spread education among the Indian masses. Tirathji was caught between his devotion to the math and Gokhale’s vision. In 1908, he actually left the math to head a National College in Rajamahendri.
Three years later, he went back to the math, but the experience would have left Tirathji with little choice but to confront the message that Englishmen such as Macaulay had so forcefully fashioned, that the ancient history and knowledge of India were worth nothing when set against the most elementary aspects of Western thought.
To men like Tirathji, it was clear that if the secret of Western domination over India lay anywhere, it lay in the knowledge of the sciences, and mathematics stood at the heart this knowledge. What better answer to such hubris than to show that in fact all of mathematics had already been revealed in the Vedas?
The sutras, unfortunately, only reveal how little Tirathji knew of mathematics. Today, they only symbolise the strivings of a colonised mind searching for some self-respect, and we can find their equivalent in the Sangh Parivar’s absurd attempts to search for the technology of the jet engine in the udankhatola of The Ramayan. At least Tirathji’s quest was far more understandable and forgivable, given his times, but that we Indians should still take it seriously only shows the extent to which our creative imagination remains colonised. How much better off we would be if we could forgo the portentous name given to these tricks and learn to enjoy them as a Shankaracharya’s fancy.
http://www.openthemagazine.com/article/art-culture/the-fraud-of-vedic-maths
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Neither Vedic Nor Mathematics
http://www.sacw.net/DC/CommunalismCollection/ArticlesArchive/NoVedic.html
We, the undersigned, are deeply concerned by the continuing attempts to thrust the so-called `Vedic Mathematics' on the school curriculum by the NCERT.
As has been pointed out earlier on several occasions, the so-called 'Vedic Mathematics' is neither 'Vedic' nor can it be dignified by the name of mathematics. 'Vedic Mathematics', as is well-known, originated with a book of the same name by a former Sankracharya of Puri (the late Jagadguru Swami Shri Bharati Krishna Tirthaji Maharaj) published posthumously in 1965. The book assembled a set of tricks in elementary arithmetic and algebra to be applied in performing computations with numbers and polynomials. As is pointed out even in the foreword to the book by the General Editor, Dr. A.S. Agarwala, the aphorisms in Sanskrit to be found in the book have nothing to do with the Vedas. Nor are these aphorisms to be found in the genuine Vedic literature.
The term "Vedic mathematics'' is therefore entirely misleading and factually incorrect. Further, it is clear from the notation used in the arithmetical tricks in the book that the methods used in this text have nothing to do with the arithmetical techniques of antiquity. Many of the Sanskrit aphorisms in the book are totally cryptic (ancient Indian mathematical writing was anything but cryptic) and often so generalize to be devoid of any specific mathematical meaning. There are several authoritative texts on the mathematics of Vedic times that could used in part to teach an authoritative and correct account of ancient Indian mathematics but this book clearly cannot be used for any such purpose. The teaching of mathematics involves both the teaching of the basic concepts of the subject as well as methods of mathematical computation. The so-called "Vedic mathematics'' is entirely inadequate to this task considering that it is largely made up of tricks to do some elementary arithmetic computations. Many of these can be far more easily performed on a simple computer or even an advanced calculator.
The book "Vedic mathematics'' essentially deals with arithmetic of the middle and high-school level. Its claims that "there is no part of mathematics, pure or applied, which is beyond their jurisdiction'' is simply ridiculous. In an era when the content of mathematics teaching has to be carefully designed to keep pace with the general explosion of knowledge and the needs of other modern professions that use mathematical techniques, the imposition of ``Vedic mathematics'' will be nothing short of calamitous.
India today has active and excellent schools of research and teaching in mathematics that are at the forefront of modern research in their discipline with some of them recognised as being among the best in the world in their fields of research. It is noteworthy that they have cherished the legacy of distinguished Indian mathematicians like Srinivasa Ramanujam, V. K. Patodi, S. Minakshisundaram, Harish Chandra, K. G. Ramanathan, Hansraj Gupta, Syamdas Mukhopadhyay, Ganesh Prasad, and many others including several living Indian mathematicians. But not one of these schools has lent an iota of legitimacy to `Vedic mathematics'. Nowhere in the world does any school system teach "Vedic mathematics'' or any form of ancient mathematics for that matter as an adjunct to modern mathematical teaching. The bulk of such teaching belongs properly to the teaching of history and in particular the teaching of the history of the sciences.
We consider the imposition of `Vedic mathematics' by a Government agency, as the perpetration of a fraud on our children, condemning particularly those dependent on public education to a sub-standard mathematical education. Even if we assumed that those who sought to impose `Vedic mathematics' did so in good faith, it would have been appropriate that the NCERT seek the assistance of renowned Indian mathematicians to evaluate so-called "Vedic mathematics" before making it part of the National Curricular framework for School Education. Appallingly they have not done so. In this context we demand that the NCERT submit the proposal for the introduction of `Vedic mathematics in the school curriculum to recognized bodies of mathematical experts in India, in particular the National Board of Higher Mathematics (under the Dept. of Atomic Energy), and the Mathematics sections of the Indian Academy of Sciences and the Indian National Science Academy, for a thorough and critical examination. In the meanwhile no attempt should be made to thrust the subject into the school curriculum either through the centrally administered school system or by trying to impose it on the school systems of various States.
We are concerned that the essential thrust behind the campaign to introduce the so-called 'Vedic mathematics' has more to do with promoting a particular brand of religious majoritarianism and associated obscurantist ideas rather than any serious and meaningful development of mathematics teaching in India. We note that similar concerns have been expressed about other aspects too of the National Curricular Framework for School Education. We re-iterate our firm conviction that all teaching and pedagogy, not just the teaching of mathematics, must be founded on rational, scientific and secular principles.
S.G.Dani Professor of Mathematics, Tata Institute of Fundamental Research, Mumbai
Madhav M. Deshpande Professor of Sanskrit and Linguistics Department of Asian Languages and Cultures, University of Michigan
Indranil Biswas Professor of Mathematics at TIFR.
Nirmala B. Limaye Professor of Mathematics University of Mumbai
B.V. Limaye Professor of Mathematics Indian Institute of Technology Bombay
Alladi Sitaram, Indian Statistical Institute, B'lore
S. Ramasubramanian, Indian Statistical Inst.,B'ore
V. Pati, Indian Statistical Inst., B'lore
G. Misra, Indian Statistical Inst., B'lore
Jishnu Biswas, Indian Statistical Inst., B'lore
D. P. Sengupta, Indian Inst. of Science(Retd.), B'lore
Alladi Uma, Dept. of English, Univ. of Hyderabad
M. Sridhar, Dept. of English, Univ. of Hyderabad
Amitava Bhattacharya
S.Subramanian, Tata Institute of Fundamental Research Mumbai
Professor Nitin Nitsure,Tata Institute of Fundamental Research, Mumbai
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