Myths and reality : On `Vedic mathematics' S.G. Dani School of Mathematics Tata Institute of Fundamental Research (An updated version of the 2-part article in Frontline, 22 October and 5 November 1993) We in India have good reasons to be proud ing an awareness of our past achievements, on of a rich heritage in science, philosophy and cul- the strength of authentic information, a more ur- ture in general, coming to us down the ages. In gent need has also arisen to confront and ex- mathematics, which is my own area of special- pose such baseless constructs before it is too isation, the ancient Indians not only took great late. This is not merely a question of setting the strides long before the Greek advent, which is record straight. The motivated versions have a a standard reference point in the Western his- way of corrupting the intellectual processes in torical perspective, but also enriched it for a society and weakening their very foundations in long period making in particular some very fun- the long run, which needs to be prevented at all damental contributions such as the place-value costs. system for writing numbers as we have today, The so-called ” Vedic mathematics” is a case introduction of zero and so on. Further, the sus- in point. A book by that name written by Ja- tained development of mathematics in India in gadguru Swami Shri Bharati Krishna Tirthaji the post-Greek period was indirectly instrumen- Maharaja (Tirathji, 1965) is at the centre of this tal in the revival in Europe after ”its dark ages”. pursuit, which has now acquired wide follow- Notwithstanding the enviable background, ing; Tirthaji was the Shankaracharya of Govard- lack of adequate attention to academic pursuits han Math, Puri, from 1925 until he passed away over a prolonged period, occasioned by sev- in 1960. The book was published posthumously, eral factors, together with about two centuries but he had been carrying out a campaign on of Macaulayan educational system, has unfor- the theme for a long time, apparently for sev- tunately resulted, on the one hand, in a lack of eral decades, by means of lectures, blackboard awareness of our historical role in actual terms demonstrations, classes and so on. It has been and, on the other, an empty sense of pride which known from the beginning that there is no evi- is more of an emotional reaction to the colonial dence of the contents of the book being of Vedic domination rather than an intellectual challenge. origin; the Foreword to the book by the General Together they provide a convenient ground for Editor, Dr. A.S.Agrawala, and an account of the extremist and misguided elements in society to genesis of the work written by Manjula Trivedi, ”reconstruct history” from nonexistent or con- a disciple of the swamiji, make this clear even cocted source material to whip up popular eu- before one gets to the text of the book. No one phoria. has come up with any positive evidence subse- That this anti-intellectual endeavour is quently either. counter-productive in the long run and, more im- There has, however, been a persistent pro- portant, harmful to our image as a mature soci- paganda that the material is from the Vedas. In ety, is either not recognised or ignored in favour the face of a false sense of national pride associ- of short-term considerations. Along with the ob- ated with it and the neglect, on the part of the vious need to accelerate the process of creat- knowledgeable, in countering the propaganda, 1 even educated and well meaning people have while edifice in mathematics (as also in many tended to accept it uncritically. The vested in- other areas). Harish Chandra’s work is held terests have also involved politicians in the pro- in great esteem all over the world and sev- paganda process to gain state support. Several eral leading seats of learning of our times leaders have lent support to the ”Vedic mathe- pride themselves in having members pursu- matics” over the years, evidently in the belief ing his ideas; (see, for instance, Langlands, of its being from ancient scriptures. In the cur- 1993). Even among those based in India, several rent environment, when a label as ancient seems like Syamdas Mukhopadhyay, Ganesh Prasad, to carry considerable premium irrespective of its B.N.Prasad, K.Anand Rau, T.Vijayaraghavan, authenticity or merit, the purveyors would have S.S.Pillai, S.Minakshisundaram, Hansraj it going easy. Gupta, K.G.Ramanathan, B.S.Madhava Rao, Large sums have been spent both by the V.V.Narlikar, P.L.Bhatnagar and so on and also Government and several private agencies to sup- many living Indian mathematicians have carved port this ”Vedic mathematics”, while authentic a niche for themselves on the international math- Vedic studies continue to be neglected. People, ematical scene (see Narasimhan, 1991). Ignor- especially children, are encouraged to learn and ing all this while introducing the swamiji’s name spread the contents of the book, largely on the in the ”brief history” would inevitably create a baseless premise of their being from the Vedas. warped perspective in children’s minds, favour- With missionary zeal several ”devotees” of this ing gimmickry rather than professional work. cause have striven to take the ”message” around What does the swamiji’s ”Vedic mathematics” the world; not surprisingly, they have even met seek to do and what does it achieve? In his pref- with some success in the West, not unlike some ace of the book, grandly titled ” A Descriptive of the gurus and yogis peddling their own ver- Prefatory Note on the astounding Wonders of sions of ”Indian philosophy”. Several people Ancient Indian Vedic Mathematics,” the swamiji are also engaged in ”research” in the new ”Vedic tells us that he strove from his childhood to mathematics.” study the Vedas critically ” to prove to ourselves To top it all, when in the early nineties the (and to others) the correctness (or otherwise)”of Uttar Pradesh Government introduced ”Vedic the ”derivational meaning” of ”Veda” that the mathematics” in school text books, the contents ” Vedas should contain within themselves all of the swamiji’s book were treated as if they the knowledge needed by the mankind relating were genuinely from the Vedas; this also nat- not only to spiritual matters but also those usu- urally seems to have led them to include a list ally described as purely ’secular’, ’temporal’ or of the swamiji’s sutras on one of the opening ’worldly’; in other words, simply because of the pages (presumably for the students to learn them meaning of the word ’Veda’, everything that is by heart and recite!) and to accord the swamiji worth knowing is expected to be contained in a place of honour in the ” brief history of In- the vedas and the swamiji seeks to prove it to be dian mathematics” described in the beginning of the case! the textbook, together with a chart, which cu- It may be worthwhile to point out here that riously has Srinivasa Ramanujan’s as the only there would be room for starting such an enter- other name from the twentieth century! prise with the word ’science’! He also describes For all their concern to inculcate a sense how the ” contemptuous or at best patronising of national pride in children, those respon- ” attitude of Orientalists, Indologists and so on sible for this have not cared for the simple strengthened his determination to unravel the fact that modern India has also produced sev- too-long-hidden mysteries of philosophy and eral notable mathematicians and built a worth- science contained in ancient India’s Vedic lore, 2 with the consequence that,”after eight years of to do so, but when Prof.K.S.Shukla, a renowned concentrated contemplation in forest solitude, scholar of ancient Indian mathematics, met him we were at long last able to recover the long in 1950, when the swamiji visited Lucknow to lost keys which alone could unlock the portals give a blackboard demonstration of his ”Vedic thereof.” mathematics”, and requested him to point out The mindset revealed in this can hardly be the sutras in question in the Parishishta of the said to be suitable in scientific and objective Atharva Veda, of which he even carried a copy inquiry or pursuit of knowledge, but perhaps (the standard version edited by G.M.Bolling and one should not grudge it in someone from a to- J.Von Negelein), the swamiji is said to have tally different milieu, if the outcome is positive. told him that the 16 sutra demonstrated by him One would have thought that with all the com- were not in those Parishishtas and that ”they oc- mitment and grit the author would have come curred in his own Parishishta and not any other” up with at least a few new things which can (Shukla, 1980, or Shukla, 1991). What justifica- be attributed to the Vedas, with solid evidence. tion the swamiji thought he had for introducing This would have made a worthwhile contribu- an appendix in the Atharva Veda, the contents tion to our understanding of our heritage. In- of which are nevertheless to be viewed as from stead, all said and done there is only the author’s the Veda, is anybody’s guess. In any case, even certificate that ”we were agreeably astonished such a Parishishta, written by the swamiji, does and intensely gratified to find that exceedingly not exist in the form of a Sanskrit text. though mathematical problems can be easily and Let us suppose for a moment that the author readily solved with the help of these ultra-easy indeed found the sutras in some manuscript of Vedic sutras (or mathematical aphorisms) con- the Atharva Veda, which he came across.