Vedic Mathematics is a form of mathematics, which was in practice in the prehistoric India. Vedic Mathematics is basically a set of Algorithms to solve frequently encountered Mathematical problems. Many ancient Hindu saints and others (including Shankaracharyas) contributed to this amazing mathematical idea.
Recently, Vedic mathematics has increasingly gained popularity all over the world as a simple technique to carry out algebraic and geometric operations by hand.
The concepts of Vedic Mathematics were studied in detail and revised by Jagadguru Swami Bharathikrishna Tirthaji of Puri Jaganath. He did extensive researches on the topic for a whole lifetime and many of the results were published by his desciples in the book, Vedic Mathematics, in the 1960s.
Vedic Mathematicians used Sanskrit alphabets to represent big numbers. It has been found that many of the Sanskrit Mantras represent numbers. (The famous Gayatri Mantra is said to have a number representation 108, while added after decoding).
A Few Simple Examples
Note: (x)(y) represents a number obtained by concatenating the digits of x with those of y.
To multiply a positive integer with 9, 99, 999, ...
Result= (Original number -1) (Digits obtained by subtracting 9 from each of these new digits).
Example: 999x343=342657
i.e, 342 and (9-3)(9-4)(9-2)
To calculate the square of any number ending with five:
((x)(5))^2 = (x)(x+1)(25)
Examples: 15^2 = ((1)(1+1))25 = 225.
95^2 = (9(9+1))25 = 9025.