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 young students (of only 12 or 14 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 6 to 9 months at an average rate of 2 or 4 hours per week (including practise time) 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'.