Vedic Mathematics

Vedic mathematics is a system of mathematics consisting of a list of 16 basic sutras, or aphorisms , that allegedly encompass all mathematics. They were presented by a Hindu scholar and mathematician, Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja, during the early part of the 20th century (Trivedi, 1965).

Tirthaji and the rediscovery of Vedic Mathematics

The ancient system of Vedic Mathematics was rediscovered from the Sanskrit texts known as the Vedas, between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960). At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics. They could find no mathematics in the translation and dismissed the texts as rubbish. Bharati Krsna, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas. According to his research all of mathematics is based on sixteen Sutras, or word-formulae.

Bharati Krsna wrote sixteen volumes expounding the Vedic system but these were unaccountably lost and when the loss was confirmed in his final years he wrote a single book: Vedic Mathematics, currently available. It was published in 1965, five years after his death.

Background Information on the Vedas

The word "veda" has two basic meanings. The first, a literal translation of the Sanskrit word, is "knowledge" (Veda). The second, and most common meaning of the word, refers to the sacred ancient literature of Hinduism, the Vedas, a collection of hymns, poetry and Hindu ceremonial formulas (Veda). Believed to be one of the oldest human written records, the Vedas date back over 4000 years Traditionally, they were passed down orally and adapted from generation to generation by sacred sages called rishis, before eventually emerging written in Vedic, an ancient form of Sanskrit, during the 3rd century BCE (Veda).

The Vedas are divided into four main sections: the Rig-veda, Sama-veda, Yajur-veda and the Atharva-veda, known collectively as the Samhitas (Veda). The first three, the Rig-veda, Sama-veda, and Yajur-veda are basically ritual handbooks that were used by priests during the Vedic period (1500-500 BCE) (Veda). Vedic mathematics is apparently part of the fourth Veda, Atharva-veda, which is distinct from the others in several ways. First, unlike the religious focus of the other Vedas, the Atharva-veda contains hymns, spells and magical incantations for personal and domestic use (Veda). Also, the Atharva-veda, which was written later than the other Vedas, was not always considered authoritative, but only became so after being accepted by the Brahmans, the highest order of Hindu priests (Veda). Collectively, the Vedas do include information about a huge range of subjects, spanning religion, medicine, architecture, astronomy.

Applications of Vedic Mathematics

The most notable application of Vedic mathematics is in education. Vedic mathematical strategies may prove to be a useful resource for teachers and students, who may find elements of it easier and more accessible to teach and learn than conventional mathematics. In particular, these strategies may be an invaluable resource to students that already struggle with mathematics, and could benefit from alternative approaches.

Sutras of Vedic Mathematics

Merely 16 Sutras and 13 Sub-Sutra form the basis of Vedic Mathematics. These sutras can be used to solve all types of Mathematical Problems!!!

These sutras had been long lost in the cryptic Vedas where the mathematical solutions were hidden in Sanskrit Verses for centuries. Sri Bharati Krsna Tirthaji's "Vedic Mathematics" recently discovered these techniques again and given it to all of us to use.

The 16 sutras, or rules, and 14 sub-sutras can be used to solve complex mathematical problems mentally, leaving your fellow students and colleagues in awe

The 16 Sutras of Vedic Mathematics:

Sutra 1 : By one more than the one before

Sutra 2: All from 9 and the last from 10

Sutra 3: Vertically and crosswise

Sutra 4 : Transpose and apply

Sutra 5 : If the Samuccaya is the same it is zero

Sutra 6 : If one is in ratio the other is zero

Sutra 7: By addition and by subtraction

Sutra 8: By the completion or non-completion

Sutra 9: Differential calculus

Sutra 10: By the deficiency

Sutra 11: Specific and general

Sutra 12: The remainders by the last digit

Sutra 13: The ultimate and twice the penultimate

Sutra 14: By one less than the one before

Sutra 15: The product of the sum

Sutra 16: All the multipliers

The 13 Sub-sutras:

SS 1: Proportionately

SS 2: The remainder remains constant

SS 3: The first by the first and the last by the last

SS 4: For 7 the multiplicand is 143

SS 5: By osculation

SS 6: Lessen by the deficiency

SS 7: Whatever the deficiency lessen by that amount and set up the square of the deficiency

SS 8: Last totaling 10

SS 9: Only the last terms

SS 10: The sum of the products

SS 11: By alternative elimination and retention

SS 12: By mere observation

SS 13: The product of the sum is the sum of the products