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सर्वे जनाः सुखिनो भवन्तु

सत्यं वद । धर्मं चर

Vedic Mathematics 

Vedic Mathematics came to light with the invention of Puri Shankaracharya, Swamy Bharati Krishna Tirtha, and the book written by him was first published in 1965. It contains a list of mathematical techniques, which were said to have been retrieved from the vedas and to contain advanced mathematical knowledge.

The vedic mathematics contains metaphorical aphorisms in the form of sixteen sootras and thirteen sub-sootras, which Swamiji interpreted them as significant mathematical tools. The range of their asserted applications spans from topics as diverse as statics and pneumatics to astronomy and financial domains. 

These sootras are primarily a compendium of tricks that can be applied in elementary, middle, and high school, arithmetic and algebra, to gain faster results. The sootras and sub-sootras are abstract literary expressions (for example, “as much less” or “one less than the previous one”) prone to creative interpretations.

According to Swamiji, the sutras and other accessory content were found after years of solitary study of the vedas. They were supposedly contained in the parishishtha—a supplementary text/appendix—of the atharvanaveda. Hence in short it can be said as follows:

  • Vedic Mathematics is the Intuitional use of 16 vedic sootras (Formulae) and 32 sub-sootras (Corollaries) (later only 13 are known or used), from one kalpa in the vedas, in tackling any mathematical problem.
  • vedic Mathematics is a collection of various alternative methods for solving any mathematical problem and developing better control of the number system.
  • It aims at developing mathematical intuition in choosing the best method, on a case-to-case basis, rather than mechanically adhering to only one or few methods.
  • Practice of vedic Mathematics can be a method of mental development, in parallel to solving the mathematics at hand.

The 16 main sutras are:

  1. ekaadhikena poorveNa/एकाधिकेन पूर्वेण | One more than the previous
  2. nikhilam navatah caramam dasatah/निखिलं नवतः चरमं दशतः। All from nine and ultimate from ten
  3. oordhwa tiryagbhyaam/ऊर्ध्व तिर्यग्भ्याम् | With upper slant
  4. paraavartyam yojayet/परावर्त्यं योजयेत् । Transpose and Apply
  5. soonyam saamya samucchaye/सून्यं साम्य समुच्चये । A common factor is the same which is Zero.
  6. (anuroopye) soonyamanyat/(अनुरूप्ये) सून्यमन्यत् । If one is in ratio, the other one is Zero.
  7. sankalana-vyavakalanabhyaam/सङ्कलन व्यवकलनाभ्याम् । By addition and by subtraction
  8. pooranaapooranaabhyaam/ पूरण अपूरणाभ्याम् । By completion or non-completion
  9. chalana-kalanaabhyaam/चलन कलनाभ्याम् । Sequential Motion Differentiation
  10. yavaadoonam/यवादूनम् । The Deficiency
  11. vyastih samastih/ व्यष्टिः समष्टिः । Whole as one and one as whole
  12. sheshanyankena charamena/ शेषण्यङ्केन चरमेण । Remainder by the last digit
  13. sopantyadwayamantyam/सोपन्त्यद्वयमन्त्यम् । Ultimate and twice the Penultimate
  14. ekanyoonena poorvena/एकन्यूनेन पूर्वेण । One less than the Previous
  15. gunita samuchchayah/गुणित समुच्चयः । The whole product is the same.
  16. gunaka samucchayah/गुणक समुच्चयः । Collectivity of Multipliers

Prior to the advent of modern mathematics/ganitam, ancient science included vedic mathematics which is very simple and easy to solve complicated mathematical problems, without using calculators.

SDII-101- vedic Mathematics:


  1. Multiplying two numbers, around a base (power of 10) with Algebraic explanation.
  2. Same, using a sub-base.
  3. Practice session.


  1. Concept of computation of Fraction, in general.
  2. Fractions with denominator ending with 1,3,7 & 9, with conversion, if required.
  3. Binomial Expansion of 1/(1-x) and 1/(1+x) modified for the case of 1/(10x-1) and 1/(10x+1).
  4. Introduction to Vedic One Line Method of computing recurring decimals.
  5. Practice session.


  1. Computation of Recurring Decimals with denominators 19, 29, 39, 49, 59, …
  2. Studying the Periodicity of Recurring Decimals.
  3. Extension of vedic One Line method to compute Recurring Decimals with denominators 21, 31, 41, 51, …
  4. Practice session.


  1. General rules for Divisibility.
  2. Introducing the concept of Osculators. Positive and negative Osculators.
  3. Method of finding Osculators for various numbers ending with 1,3,7 & 9.
  4. Method of finding Divisibility using Osculators.
  5. Algebraic background for Osculation method of testing Divisibility.
  6. Practice session.

Reference Material


Introduction to Vedic Maths by Gautam Mukherjee