Vedic Mathematics is a system of mathematics that finds its roots in ancient Indian scriptures known as the Vedas. The term “Vedic” is derived from the word “Veda,” which means knowledge. This mathematical system is based on 16 Sutras (formulas) and 13 Sub-Sutras (sub-formulas) that simplify arithmetic operations, algebra, geometry, calculus, and other branches of mathematics.

**Historical Background**

The origins of Vedic Mathematics can be traced back to ancient Indian texts, particularly the Atharva Veda. However, the modern compilation and popularization of these methods were primarily the work of Bharati Krishna Tirthaji Maharaja (1884-1960), a scholar and monk who rediscovered and compiled the Vedic Sutras in the early 20th century.

The Vedic Maths Sixteen Sutras

S.No | Sutra | Meaning |
---|---|---|

1 | Ekadhikena Purvena | By one more than the previous one |

2 | Nikhilam Navatashcaramam Dashatah | All from 9 and the last from 10 |

3 | Urdhva-Tiryagbyham | Vertically and crosswise |

4 | Paravartya Yojayet | Transpose and adjust |

5 | Shunyam Saamyasamuccaye | When the sum is the same that sum is zero |

6 | Anurupye Shunyamanyat | If one is in ratio, the other is zero |

7 | Sankalana-vyavakalanabhyam | By addition and by subtraction |

8 | Puranapuranabyham | By the completion or non-completion |

9 | Chalana-Kalanabyham | Differences and Similarities |

10 | Yavadunam | Whatever the extent of its deficiency |

11 | Vyashtisamasthi | Part and Whole |

12 | Shesanyankena Charamena | The remainders by the last digit |

13 | Sopaantyadvayamantyam | The ultimate and twice the penultimate |

14 | Ekanyunena Purvena | By one less than the previous one |

15 | Gunitasamuchyah | The product of the sum is equal to the sum of the product |

16 | Gunakasamuchyah | The factors of the sum is equal to the sum of the factors |

**Key Concepts and Sutras**

Vedic Mathematics simplifies complex mathematical problems into simple calculations. Here are a few fundamental Sutras:

**Ekadhikena Purvena**: By one more than the previous one.- Used for finding the square of numbers ending in 5.
- Example: To find $2_{2}$, take 2 (the preceding number of 5) and multiply it by one more than itself (3), then append 25. Thus, $2_{2}=2×3$ with 25 appended = 625.

**Nikhilam Navatashcaramam Dashatah**: All from 9 and the last from 10.- Useful for multiplication of numbers close to bases of 10, 100, 1000, etc.
- Example: To multiply 98 by 97, base is 100. Subtract each number from 100 to get complements (2 and 3). The result is (100 – (2+3)) | (2×3) = 9506.

**Urdhva-Tiryakbyham**: Vertically and crosswise.- Used for general multiplication.
- Example: To multiply 12 by 13, multiply vertically (1×1, 2×3) and crosswise (1×3, 2×1), then sum the results appropriately.

**Applications and Benefits**

Vedic Mathematics is not only about speed but also about understanding the relationships between numbers. It provides:

**Enhanced Speed and Accuracy**: The methods are designed to be faster than conventional techniques, reducing the steps involved in calculations.**Mental Agility**: Encour

ages mental calculation and reduces dependency on calculators.

**Improved Problem-Solving Skills**: The techniques promote logical thinking and problem-solving skills.**Accessibility**: The methods are simple and can be grasped by young students, making learning mathematics more enjoyable and less intimidating.

**Practical Examples**

**Squaring Numbers Ending in 5**:**Example**: $7_{2}$- Step 1: Identify the number preceding 5, which is 7.
- Step 2: Multiply 7 by one more than itself (8), which gives $7×8=56$.
- Step 3: Append 25 to the result, thus $7_{2}=5625$.

**Multiplication Using Nikhilam Sutra**:**Example**: $96×94$- Base is 100.
- Step 1: Subtract each number from 100 (100 – 96 = 4, 100 – 94 = 6).
- Step 2: Add the complements to the base and then multiply the complements: $(100−(4+6))∣(4×6)=90∣24=9024$.

**Using Urdhva-Tiryakbyham for Multiplication**:**Example**: $21×23$- Step 1: Multiply vertically the leftmost digits: $2×2=4$.
- Step 2: Multiply crosswise and add: $(2×3)+(1×2)=6+2=8$.
- Step 3: Multiply vertically the rightmost digits: $1×3=3$.
- Combine the results: 483.

**Learning Vedic Mathematics**

Many resources are available for those interested in learning Vedic Mathematics, including books, online courses, and workshops. Key texts include Tirthaji’s “Vedic Mathematics” and various educational websites offering tutorials and exercises.

## About His Holiness

His Holiness Jagadguru Shankaracharya Shri Bharati Krishna Tirthaji Maharaja is the founder father of Vedic Maths and was the ecclesiastical head of most of Hindu India and was the apostolic successor of the first Shankaracharya ( 9th Century; India’s greatest philosopher).