Introduction to Vedic Mathematics

The “Vedic Mathematics” is called so because of its origin from Vedas. To be more specific, it has originated from “Atharva Vedas” the fourth Veda. “Atharva Veda” deals with the branches like Engineering, Mathematics, sculpture, Medicine, and all other sciences with which we are today aware of.

The Sanskrit word Veda is derived from the root Vid, meaning to know without limit. The word Veda covers all Veda-Sakhas known to humanity. The Veda is a repository of all knowledge, fathomless, ever revealing as it is delved deeper.

It is an ancient technique, which simplifies multiplication, divisibility, complex numbers, squaring, cubing, square roots and cube roots. Even recurring decimals and auxiliary fractions can be handled by Vedic mathematics. Vedic Mathematics forms part of Jyotish Shastra which is one of the six parts of Vedangas. The Jyotish Shastra or Astronomy is made up of three parts called Skandas. A Skanda means the big branch of a tree shooting out of the trunk.

This subject was revived largely due to the efforts of Jagadguru Swami Bharathi Krishna Tirtha Ji of Govardhan Peeth, Puri Jaganath (1884-1960). Having researched the subject for years, even his efforts would have gone in vain but for the enterprise of some disciples who took down notes during his last days. The basis of Vedic mathematics, are the 16 sutras, which attribute a set of qualities to a number or a group of numbers. The ancient Hindu scientists (Rishis) of Bharat in 16 Sutras (Phrases) and 120 words laid down simple steps for solving all mathematical problems in easy to follow 2 or 3 steps.

Vedic Mental or one or two line methods can be used effectively for solving divisions, reciprocals, factorisation, HCF, squares and square roots, cubes and cube roots, algebraic equations, multiple simultaneous equations, quadratic equations, cubic equations, biquadratic equations, higher degree equations, differential calculus, Partial fractions, Integrations, Pythogorus Theoram, Apollonius Theoram, Analytical Conics and so on.

Vedic scholars did not use figures for big numbers in their numerical notation. Instead, they preferred to use the Sanskrit alphabets, with each alphabet constituting a number. Several mantras, in fact, denote numbers; that includes the famed Gayatri Mantra, which adds to 108 when decoded. How fast you can solve a problem is very important. There is a race against time in all the competitions. Only those people having fast calculation ability will be able to win the race. Time saved can be used to solve more problems or used for difficult problems.

Given the initial training in modern maths in today’s schools, students will be able to comprehend the logic of Vedic mathematics after they have reached the 8th standard. It will be of interest to everyone but more so to younger students keen to make their mark in competitive entrance exams. India’s past could well help them make it in today’s world. It is amazing how with the help of 16 Sutras and 13 sub-sutras, the Vedic seers were able to mentally calculate complex mathematical problems.

The 16 Sutras and Sub-sutras are given below with their pronunciation(in bracket) meaning in English :

Sixteen Sutras

1. एकाधिकेन पूर्वेण (Ekadhikena Purvena) : One more than the previous one
2. निखिलम नवश्चरमं दशत: (Nikhilam Navatascaramam Dasatah): All from 9 and last from 10
3. ऊर्ध्वतिर्यग्भ्यां (Urdhva-tiryagbhyam): Criss-cross (Vertically and cross-wise)
4. परावरत्य योजयेत_ (Paravartya Yojayet): Transpose and adjust (Transpose and apply)
5. शून्यम साम्यसमुच्चये (Sunyam Samyasamuccaye): When the samuchchaya is the same, the samuchchaya is zero, i.e it should be equated to zero.
6. आनुरूप्ये (Anurupye): If one is in ratio, the other one is zero
7. संक्लनव्यवकलनाभ्याम् (Sankalana-vyavakalanabhyam): By addition and by subtraction
8. पूरणापूराणाभ्याम् (Puranapuranabhyam): By the completion or non-completion
9. चलनकलनाभ्यां (Calana-Kalanabhyam): By Calculus
10. यावदूनम् (Yavadunam): By the deficiency
11. व्यष्टिसमष्टि: (Vyastisamastih): Specific and General (Use the average)
12. शेषण्यकेन चरमेण (Sesanyankena Caramena): The remainders by the last digit
13. सोपन्त्यद्वयमन्त्यम् (Sopantyadvayamantyam): The ultimate & twice the penultimate
14. एकान्यूनेन पूर्वेण (Ekanyunena Purvena): By one less than the previous one
15. गुणितसमुच्चय: (Gunitasamuccdyah): The product of the sum of coefficients in the factors(The whole product)
16. गुणकसमुच्चय: (Gunakasamuccayah): Set of Multipliers

Thirteen Subsutras

1. आनुरुप्येण (Anurupyena): Proportionately
2. शिष्यते शेषसंज्ञ: (Sityate Sesasanfitah): The remainder remains constant
3. आद्यमाद्येनान्त्यमन्त्येन (Adyamadyenantyainantyena): The first by the first and last by the last
4. केवलै: सप्तकं गुण्यात (Kevalalh Saptakan Gunyat): In case of 7 our multiplicand should be 143
5. वेष्टनं (Vestanam): By osculation
6. यावदूनं तावदूनम् (Yavadunam Tavadunam): Lessen by the Deficiency
7. यावदूनं तावदूनीकृत्यवर्गं च येजयेत (Yavadunam Taradunikrtya Varganca Yojayet): Whatever the extent of its deficiency, lessen it still to that very extent; and also set up the square of that deficiency.
8. अन्त्ययोरेव (Antyayoreva):Only the last terms
9. अन्त्ययोर्दशकेഽपि (Antyayordasake’pi): Whose last digits together total 10 and whose previous part is exactly the same
10. समुच्चयगुणित: (Samuccayaguaitah): The sum of the coefficients in the product
11. लोपस्थानाभ्याम् (Lopanasthapandbhyam): By alternate elimination and retention
12. विलोकनम् (Vilokanam): By observation
13. गुणितसमुच्चय: समुच्चयगुणित: (Gunitasamuccayah Samuccayagunitah): The product of sum of the coefficients in the factors is equal to the sum of the coefficients in the product.

Note: I know there is some mistakes in Devanagari transliteration. I tried my level best to type them with minimal mistakes.