The Vedic Mathematics Sutras

This list of sutras is taken from the book Vedic Mathematics, which includes a full list of the sixteen Sutras in Sanskrit, but in some cases a translation of the Sanskrit is not given in the text and comes from elsewhere.

This formula 'On the Flag' is not in the list given in Vedic Mathematics, but is referred to in the text.

The Sixteen Sutras

         Sutra     Translation
 1 

By one more than the one before
 2    All from 9 and the last from 10
 3 

Vertically and Crosswise
 4 

Transpose and Apply
 5 

If the Samuccaya is the Same it is Zero
 6 

If One is in Ratio the Other is Zero
 7 

 

By Addition and by Subtraction
 8 

 

By the Completion or Non-Completion
 9 

Differential Calculus
10

By the Deficiency
11

Specific and General
12

The Remainders by the Last Digit
13

The Ultimate and Twice the Penultimate
14

By One Less than the One Before
15 The Product of the Sum
16

All the Multipliers

 

Note: The current Shankaracharya of Puri, Jagadguru Swami Nishchalananda Saraswati, has said (in 2008) he will be able to locate all the above sutras in the Vedic texts, but has so far only found one.

See also the article "The Sutras of Vedic Mathematics", by Kenneth Williams, published in the Journal of the Oriental Institute.


The Sub Sutras

           Sub Sutra      Translation
 1   Proportionately
 2 

 The Remainder Remains Constant
 3 

 The First by the First and the Last by the Last
 4   For 7 the Multiplicand is 143
 5 

 By Osculation
 6 

 Lessen by the Deficiency
 7 

 Whatever the Deficiency lessen by that amount and set up the Square of the Deficiency
 8 

 Last Totalling 10
 9 

 Only the Last Terms
10

 The Sum of the Products
11

 By Alternative Elimination and Retention
12

 By Mere Observation
13    The Product of the Sum is the Sum of the Products
14

 On the Flag