1. 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, that is beyond their jurisdiction.

2. 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’!

3. 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 (i.e. current) Western methods.

4. And in some very important and striking cases, sums requiring 30, 50, 100 or even more numerous and cumbrous ‘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 little children (of only 10 or 12 years of age) merely look at the sums written on the blackboard and immediately shout out and dictate the answers. 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, slate etc.).

5. On seeing this kind of work actually being performed by the little children, the doctors, professors and other ‘big-guns’ of mathematics are wonder-struck and exclaim: ‘Is this mathematics or magic’? And we invariably answer and say: ‘It is both. It is magic until you understand it; and it is mathematics thereafter’. And then we proceed to substantiate and prove the correctness of this reply of ours!

6. As regards the time required by the students for mastering the whole course of Vedic Mathematics as applied to all its branches, we need merely state from our actual experience that 8 months (or 12 months) at an average rate of 2 or 3 hours per day should suffice for completing the whole course of mathematical studies on these Vedic lines instead of 15 or 20 years required according to the existing systems of the Indian and also of foreign universities.

7. 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 amount of time, energy, and money on and which even now it solves with the utmost difficulty and that also after vast labour involving large numbers of difficult, tedious and cumbersome ‘steps’ of working) 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 that can be conscientiously described as mere ‘mental arithmetic’.

8. It is thus in the fitness of things that the Vedas include 1. 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. 2.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. 3. Gandharva Veda (the science of art and music) and  4. 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.

9. Similar is the case with 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.
   

From the Foreward by Swami Pratyagatmananda Saraswati
Varanasi, 22-03-1965
An extract:

Vedic Mathematics by the late Shankaracharya (Bharati Krsna Tirtha) of Govardhan Pitha is a monumental work. In his deep-layer explorations of cryptic Vedic mysteries relating especially to their calculus of shorthand formulae and their neat and ready application to practical problems, the late Shankaracharya shows the rare combination of the probing insight of revealing intuition of a Yogi with the analytic acumen and synthetic talent of a mathematician.

With the late Shankaracharya we belong to a race, now fast becoming extinct, of diehard believers who think that the Vedas represent an inexhaustible mine of profoundest wisdom in matters of 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 systemic enquiry, but was direct gift of revelation to seers and sages who in their higher reaches of Yogic realisation were competent to receive it from a source, perfect and immaculate.

Whether or not the Vedas are believed as repositories of perfect wisdom, it is unquestionable that the Vedic race lived not as merely pastoral folk possessing a half or a quarter developed culture and civilisation. The Vedic seers were, again, not mere ‘navel-gazers’ or ‘nose-tip gazers’. They proved themselves adepts in all levels and branches of knowledge, theoretical and practical. For example, they had their varied objective science both pure and applied.

Let us take a concrete illustration. Suppose in a time of drought we require rains by artificial means. The modern scientist has his own theory and art (technique) for producing the result. The old seer scientist had his both also, but different from these now availing. He had his science and technique, called Yajna, in which Mantra, Yantra, and other factors must co-operate with mathematical determinateness and precision. For this purpose, he had developed the six auxiliaries of the Vedas in each of which mathematical skill and adroitness, occult or otherwise, play the decisive role. The Sutras lay down the shortest and surest lines. The correct intonation of the Mantra, the correct configuration of the Yantra (in the making of the Vedi etc., e.g. the quadrate of a circle), the correct time or astral conjunction factor, the correct rhythams etc. All had to be perfected so as to produce the desired results effectively and adequately. Each of these required the calculus of mathematics. The modern technician has his logarithmic tables and mechanic’s manuals. The old Yajnik had his Sutras.