Vedic Mathematics Or ‘Sixteen Simple Mathematical Formulae from The Vedas’ (For One-line Answers to All Mathematical Problems)

Email

Whatsapp

Facebook

Pinterest

Twitter

Copy link

Vedic Mathematics by the late Sankaracarya (Bharati Krsna Tirtha) of Govardhana Pitha is a monumental work. In his deep-layer explorations of cryptic Vedic mysteries relating specially to their calculus of shorthand formulae and their neat and ready application to practical problems, the late Sankaracarya shews the rare combination of the probing insight and revealing intuition of a Yogi with the analytic acumen and synthetic talent of a mathematician. With the late Sankaracarya we belong to a race, now fast becoming extinct, of die-hard believers who think that the Vedas represent an inexhaustible mine of profoundest wisdom in matters both spiritual and temporal; and that this store of wisdom was not, as regards its assets of fundamental validity and value at least, gathered by the laborious inductive and deductive methods of ordinary systematic enquiry, but was a direct gift of revelation to seers and sages who in their higher reaches of Yogic realization were competent to receive it from a Source, perfect and immaculate. But we admit, and the late Sankaracarya has also practically admitted, that one cannot expect to convert or revert criticism, much less carry conviction, by merely asserting one's staunchest beliefs. To meet these ends, one must be prepared to go the whole length of testing and verification by accepted, accredited methods. The late Sankaracarya has, by his comparative and critical study of Vedic mathematics, made this essential requirement in Vedic studies abundantly clear. So let us agree to gauge Vedic mysteries not as we gauge the far-off nabulae with the poet's eye or with that of the seer, but with the alert, expert, scrutinizing eye of the physical astronomer, if we may put it as that.

That there is a consolidated metaphysical background in the Vedas of the objective sciences including mathematics as regards their basic conceptions is a point that may be granted by a thinker who has looked broadly and deeply into both the realms.

In our paper recently published 'The Metaphysics of Physics' we attempted to look into the mysteries of creative emergence as contained in the well-known cosmogenic Hymn (Rg. X.190) with a view to unveiling the metaphysical background where both ancient wisdom and modern physics may meet on a common basis of logical understanding, and compare notes, discovering, where possible, points of significant or suggestive parallelism between the two sets of concepts, ancient and modern. That metaphysical background includes mathematics also; because physics as ever pursued is the application of mathematics to given or specified space-time-event situations. There we examined Tapas as a fundamental creative formula whereby the Absolute emerges into the realms of measures, variations, limits, frame-works and relations. And this descent follows a logical order which seems to lend itself, within a framework of conditions and specifications, to mathematical analysis. Ratri in the Hymn represents the Principle of Limits, for example, Rtanca Satyanca stand for Becoming (Calana-kalana) and Being (vartana-kalana) at a stage where limits or conditions or conventions do not yet arise or apply. The former gives the unconditioned, unrestricted how or thus of cosmic process; the latter, what or that of existence. Tapas, which corresponds to Ardhamatra in Tantric symbolism, negotiates, in its role specially of critical variation, between what is, ab-initio, unconditioned and unrestricted, and what appears otherwise, as for instance, in our own universe of logico-mathematical appreciation.

This is, necessarily, abstruse metaphysics, but it is, nevertheless, the starting background of both physics and mathematics. But for all practical purposes we must come down from mystic nabulae to the terra firma of our actual apprehension and appreciation. That is to say, we must descend to our own pragmatic levels of time-space-event situations. Here we face actual problems, and one must meet and deal with these squarely without evasion or mystification. The late Sankaracarya has done this masterly feat with an adroitness that compels admiration.

Vedic Maths is concerned with a universal structure of mathematics revealed through a personal approach to problem-solving and other fields of human activity. It is underpinned by a small collection of sutras. These pithy aphorisms express naturally occurring mental processes by which mathematical problems can be solved with the least effort. Vedic Maths does not advocate sole use of blanket methods which reduce problems to merely mechanical responses to given stimuli. Instead, it encourages an intelligent and holistic approach one which engenders reason and develops strategic thinking. Each sutra has many applications and leads to a unified and integrated approach to mathematics.

Background of Text

The text of Vedic Mathematics was bequeathed by Shankaracarya Sri Bharati Krishna Tirthaji to his disciples shortly before his passing in 1960. After some time it was published, first by Banares Hindu University in 1965 and very shortly after, following requests for a large number of copies from the School of Economic Science & Philosophy in London, by Motilal Banarsidass, Delhi, the renowned indological publishers.

Since then, interest has grown around the world in the unique approach set out by Tirthaji, not only for highly efficient methods of calculation, particularly in arithmetic and algebra, but also for the wide-ranging application of each of the sutras, together with their depth of meaning. Since 1965, Motilal has sold over one million copies of the book and there has been a wealth of development in the scope of the system.

The sub-title is 'Sixteen simple Mathematical Formulae from the Vedas' indicates there are 16 sutras and we have to trust that Tirtha provided this list in the manuscript as reported by his close disciple Srimati Trivedi. We can assume that the text was compiled sometime in the 1950s.

In one of the introductions, written by Smti. Manjula Trivedi, she stated that Tirthaji, "used to say that he had written sixteen volumes (one for each sutra) and that the manuscripts of the said volumes were deposited at the house of one of his disciples. Unfortunately, the said manuscripts were lost irretrievably...." Since these manuscripts are nowhere to be found it is not possible to determine their extent, whether a few notes on each sutra or many pages. To add to the perplexity, Tirthaji himself states, "It will be our aim in this and the succeeding volumes to bring this long-hidden treasure trove of mathematical knowledge within easy reach...." This implies that the text we have is the first and that he intended to provide or write later volumes. It is possible that since he wrote this volume late in life he was unable to produce any subsequent volumes.

The general editor was Dr V.S. Agrawala who held a senior position at Banares Hindu University. He was a renowned scholar in the fields of Indian history, culture and also Sanskrit, but was not a mathematician. The manuscript was given to him in 1964 by Srimati Trivedi. At that time, Dr Agrawala was deeply engaged in his own writings and editing of other books and, although he gives a beautiful forward revealing deep understanding of the meaning of Veda, it is unlikely that he could have spent much time engaging with the text. He was aging and it turned out to be the last year of his own life. He gave the manuscript to the head of Mathematics at BHU, Dr. Brij Mohan, to go through and verify the calculations. Unfortunately, this task was not carried out with sufficient care and diligence. Consequently, early editions of the book contain a significant number of arithmetic and algebraic errors. Some of these may have been typographical in nature but these should have been checked prior to publication.