Vedic Mathematics In English

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Vedic Mathematics or ‘Sixteen Simple Mathematical Formulae from the Vedas’ was written by His Holiness Jagadguru Sankaracarya Sri Bharati Krsna Tirthaji Maharaja of Covar- dhana Matha, Puri. It deals mainly with various Vedic mathematical formulae and their applications for carrying out tedious and cumbersome arithmetical operations, and to a very large extent, executing them men- tally. In this field of mental arith- metical operations, the works of the famous mathematicians Trachten- berg and Lester Meyers (High Speed Maths) are elementary compared to that of Jagadguruji.

Some people may find it difficult, at first reading to understand the arithmetical operations although they have been explained very lucidly by Jagadguruji. It is not because the explanations are lacking in any manner but because the methods are totally unconventional. Some people are so deeply rooted in the conven- tional methods that they, probably subconsciously, reject to see the logic in unconventional methods.

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HIS HOLINESS JAGADGURU SANKARACARYA SRI BHARATI KRSNA TIRTHAJI MAHARAJA (March 1884-February 1960)” was named as Venkatraman in his early days. As he was extraordinarily proficient in Sanskrit and oratory, he was awarded the title of ‘Saraswati’ by the Madras Sanskrit Association inJuly 1899.

After winning the highest place in the B.A. Examination, he appeared at the M.A. Examination of the American College of Sciences, Roch- ester, New York from Bombay Centre in 1904 and passed in six subjects (Sanskrit, Philosophy, English, Mathe- matics, History and Science) simultan- eously securing the highest honours in all. In 1908, he proceeded to the Sringeri Matha in Mysore to learn at the feet of the renowned late Jagadguru Shankaracharya Maharaj Sri Satcidanandaji. After several years of the most advanced studies, the deepest meditation, and the highest spiritual attainment; he was initiated into the holy order of Sannyasa at Banaras (Varanasi) by Shankaracharya Sri Trivikram Tirthaji of Sharadapeeth on July 4th 1919 and on this occasion he was given the new name, Swami Bharati Krsna Tirthaji. Later, in 1925 Jagadguru Sankaracarya Sri Madhu- sudan Tirthaji of Govardhan Matha, Puri, virtually forced him to accept the Govardhan Math’s Gaddi. In this capacity he continued to. disseminate the holy spiritual teachings of Sanatana Dharma in their pristine purity all over the world for the rest of his life.

 

Author’s Preface
1. In the course of our discourses on manifold and multifarious subjects (spiritual, metaphysical, philosophical, psychic, psychological, ethical, educational, scientific, mathematical, historical, political, economic, social etc., from time to time and from place to place during the last five decades and more, we have been repeatedly pointing out that the Vedas (the most ancient Indian scriptures, nay, the oldest “Religious” scriptures of the whole world) claim to deal with all branches of learning (spiritual and temporal) and to give the earnest seeker after knowledge “ail the requisite instructions and guidance in full detail and on scientifically- nay, mathematically-accurate lines in them all and so on.

2. The very word “Veda” has this derivational meaning, i.e. the fountain-head and illimitable store-house of all knowledge. This derivation, in effect, means, connotes and implies that the Vedas should contain within themselves all the knowledge needed by mankind relating not only to the so-called ‘spiritual’ (or other-worldly) matters but also to those usually described as purely “secular”, “temporal”, or “wordly”; and also to the means required .by humanity as such for the achievement of all-round, complete and perfect success in all conceivable directions and that there can be no adjectival or restrictive epithet calculated (or tending) to limit that knowledge down in any sphere, any direction or any respect whatsoever.

3. In other words, it connotes and implies that our ancient Indian Vedic lore should be all-round, complete and perfect and able to throw the fullest necessary light on all matters which any aspiring seeker after knowledge can possibly seek to be enlightened on.

4. It is thus in the fitness of things that the Vedas include (i) Ayurveda (anatomy, physiology, hygiene, sanitary science, medical science, surgery etc.) not for the purpose of achieving perfect health and strength in the after-death future but in order to attain them here and now in our present physical bodies; (ii) Dhanurveda (archery and other military sciences) not for fighting with one another after our transportation to heaven but in order to quell and subdue all invaders from abroad and all insurgents from within; (iii) Gandharva Veda (the science and art of music); and (iv) Sthapatya Veda (engineering, architecture etc., and all branches of mathematics in general). All these subjects, be it noted, are inherent parts of the Vedas, i.e. are reckoned as “spiritual” studies and catered for as such therein.

5. Similar is the case with regard to the Vedangas (i.e. grammar, prosody, astronomy, lexicography etc..) which, according’ to the Indian cultural conceptions, are also inherent parts and subjects of Vedic (i.e. Religious) study.

6. As a direct and unshirkable consequence of this analytical and grammatical study of the real connotation and full implications of the word “Veda” and owing to various other historical causes of a personal character (into details of which we need not now enter), we have been from our very early childhood, most earnestly and actively striving to study the Vedas critically from this stand-point and to realise and prove to ourselves (and to others) the correctness (or otherwise) of the- derivative meaning in question.

7. There were, too, certain personal historical reasons why in our quest for the discovering of all learning in all its departments, branches, sub-branches etc., in the Vedas, our gaze was riveted mainly on ethics, psychology and metaphysics on the one hand and on the “positive” sciences and especially mathematics on the other.

8. And the contemptuous or, at best patronising attitude adopted by some so-called Orientalists, Indologists, antiquarians, research-scholars etc., who condemned, or light hearredly, nay irresponsibly, frivolously and flippantly dismissed, several abstruse-looking and recondite parts of the Vedas as “sheer-non-sense’v=or as “infant-humanity’s prattle”, and so on, merely added fuel to the fire (so to speak) and further confirmed and strengthened our resolute determination to unravel the too-long hidden mysteries of philosophy and science contained in ancient India’s Vedic lore, with the consequence that, after eight years of concentrated contemplation in forest-solitude, we were at long last able to recover the long lost keys which alone could unlock the portals thereof.

9. And we were agreeably astonished and intensely gratified to find that exceedingly tough mathematical problems (which the mathematically most advanced present day Western scientific world had spent huge lots of. time, energy and money on and which even now it solves with the utmost difficulty and after vast labour involving large numbers of difficult, tedious and cumbersome “steps” of workirig) can be easily and readily solved with the help of these ultra-easy Vedic Sutras (or mathematical aphorisms) contained in the Parisista (the Appendix-portion) of the Atharvaveda in a few simple steps and by methods which can be conscientiously described as mere “mental arithmetic”.

10. Ever since (i.e. since several decades ago), we have been carrying on an incessant and strenuous campaign for the India-wide diffusion of all this scientific knowledge, by means of lectures, blackboard- demonstrations, regular classes and so on: in schools, colleges, universities etc., allover the country and have been astounding our audiences everywhere with the wonders and marvels not to .say, miracles of Indian Vedic mathematics.

11. We were thus able to succeed in attracting the more-than-passing attention of the authorities of several Indian universities to this subject. And, in 1952, the Nagpur University not merely had a few lectures and blackboard-demonstrations given but also arranged for our holding regualr classes in Vedic mathematics (in the University’s Convocation Hall) for the benefit of all in general and especially of the University and college professors of mathematics, physics etc.

12. And, consequently, the educationists and the cream of the English educated section of the people including the highest officials (e.g. high- court judges, ministers etc.,) and the general public as such were all highly impressed nay, thrilled, wonder-struck and flabbergasted! And not only the newspapers but even the University’s official reports described the tremendous sensation caused thereby, in superlatively eulogistic terms; and the papers began to refer to us as “the Octogenarian Jagadguru Sankaracarya who had taken Nagpur by storm with his Vedic mathematics”; and so on !

13. It is manifestly impossible, in the course of a short note (in the nature of a “trailer”), to give a full, detailed, thorough-going, compre- hensive and exhaustive description of the unique features and startling characteristics of all the mathematical lore in question. This can and will be done in the subsequent volumes of this series (dealing seriatim and in extenso with all the various portions of all the various branches of mathematics). 14. We may, however, at this point, draw the earnest attention of everyone concerned to the following salient items thereof:

(i) The Sutras (aphorisms) apply to and cover each and every part of each and every chapter of each and every branch of mathematics (including arithmetic, algebra, geometry-plane and solid, ‘trigonometry -plane and spherical, conics-geometrical and analytical, astronomy, calculus-differential and integral etc.). In fact, there is no part of mathematics, pure or applied, which is beyond their jurisdiction; (ii) The Sutras are easy to understand, easy to apply and easy to remember; and the whole work can be truthfully summarised in one word “mental” !

(iii) Even as regards complex problems involving a good number of mathematical operations (consecutively or even simultaneously to be performed), the time taken by the Vedic method will be a third, a fourth, a tenth or even a much smaller fraction of the time required according to modern Western methods;

(iv) And, in some very important and striking cases, sums requiring 30,50,100 oreven more numerous.and cumbersome “steps” of working (according to the current Western methods) can be answered in a single and simple step of work by the Vedic method! And children of even 10 or 12 years of age merely look at the sums written on the blackboard (on the platform) and immediately shout out and dictate the answers from the body of the convocation hall (or other venue of the demonstration). And this is because, as a matter of fact, each digit automatically yields. its predecessor and its successor! and the children have merely to go on tossing off (or reeling off) the digits one after another (forwards or backwards)by mere mental arithmetic (without needing pen or pencil, paper or slate etc.)!

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Weight 0.46 kg
Dimensions 21.59 × 13.97 cm
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