Unscientific maths?

By S.G. Dani

Important words, like other important things, are often vulnerable to misuse by elements inclined to derive undeserved benefits from their glory.

Practitioners of many a trade have found it advantageous to use the adjective `scientific', even when their basic tenets and methods are quite inconsistent with the scientific method. `Vedic' is one such word, the use of which promises dividends, especially in the context of the peculiar weakness of the popular mind in India. Also, the users seldom seem to be called upon to justify themselves on account of the pious way such claims tend to be approached.

The so called `Vedic Mathematics' (VM for short) is a case in point. It is well-acknowledged that, as being practised, it is based on a book of Swami Sri Bharati Krishna Tirthaji, who was the Shankaracharya at Puri from 1925 until his passing away in 1960.

As commonly understood and implicitly assumed, the adjective `Vedic' means being from the `Vedas' or the civilisation around their time. While there are variations on the estimates of the period involved, by any reckoning they are at least 2500 years old. In what sense do the contents of the book belong there? Neither has Tirthaji nor have the proteges provided any evidence or clue in this respect that a rational mind can appreciate.

The book has a preface grandiosely titled `A Descriptive Prefatory Note on the Astounding Wonders of Ancient Indian Mathematics'. All one finds there is a lot of raving and ranting, followed by a vague statement to the effect that `exceedingly tough mathematical problems' can be easily solved with the help of some `sutras' in the Parishishta (Appendix) of the Atharvaveda. There is no substantiation or elaboration concerning their being genuinely from the Vedas.

It cannot be that it did not occur to Tirthaji to include such details in the preface or elsewhere in the book.

He was, in fact, confronted by Professor K.S. Shukla, a doyen in the studies on ancient Indian mathematics, to show the sutras, to which Tirthaji is said to have replied that they are not in any standard Parishishta, but only in his `own Parishishta to the Atharvaveda'!

The book also contains a short biographical sketch and an account of the genesis of the work written by Ms. Manjula Trivedi, a disciple of Tirthaji. She mentions that the `Revered Guruji used to say that he reconstructed the 16 mathematical formulae from the Atharvaveda after assiduous Tapas for about eight years in the forests surrounding Sringeri'. They were not found in any version of the Vedas. They were `reconstructed'.

Contrary to what is made out, `Vedic Mathematics' is no `system' of solving problems in mathematics or even just arithmetic. It is only an assortment of tricks, based on simple algebraic principles. It is thoroughly lacking in coherence or harmony.

As one goes along the text of the book, one is introduced to various tricks to solve certain special problems, and while doing so Tirthaji gives names to some of the operations. `Ekadhikena Purvena', which means `by one more than the previous one', is an operation which involves something or the other to be done with something or the other that happens to be `previous' in one or the other sense. Lo and behold: you have a sutra for the problem. Mind you, the string of words does not by itself enable you to solve the problem and in most instances even the operation it connotes needs to be supplemented by several others. These one has to learn. It only enables you remember something of the operation.

In the style of how matters proceed in the book, `hold the bucket' can be said to be a sutra for milking a cow! From a mathematical point of view, the sutras of VM are of little value. To some extent, they serve as memory aids to the practitioners. Other than that, their sole role has been as props to the false pretense of antiquity.

The main positive contribution of Tirthaji's book lies in highlighting some tricks with which certain specific calculations can be done faster. In this sense, it is comparable to Trachtenberg's methods of `high speed' computation.

The main drawback of such methods is that they are very problem- specific and depend heavily on identifying special features which may be exploited to attack the problems.

Secondly, speed in computing mentally, which is the sole feature to which they contribute to some extent, has become largely redundant in the computer age.

(The writer is a Senior Professor at the Tata Institute of Fundamental Research, Mumbai.)

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