The ancient civilization of Bharat, present-day India, served as the cradle of numerous intellectual and scientific advancements. Vedic Mathematics, an ancient mathematical system, is one such gift to the world. Developed by the scholars of Bharat thousands of years ago, Vedic Mathematics showcased their remarkable understanding of mathematical concepts and problem-solving techniques.
In the first part of this article, we delve into the brilliance of Vedic Mathematics as compared to the contemporary Western mathematical systems of that time.
1. The Roots of Vedic Mathematics:
Vedic Mathematics derives its name from the Vedas, sacred texts from ancient Bharat. Scholars believe that Vedic Mathematics dates back to at least 1500 BCE. The knowledge was transmitted orally from one generation to another and was eventually compiled in texts known as the Vedangas. These texts contained a wide range of topics including arithmetic geometry algebra and calculus.
2. Efficient Problem-Solving With Sutras:
Vedic Mathematics is renowned for its concise and efficient problem-solving techniques. The system revolves around a set of operative principles known as sutras. These sutras provide a simplified yet comprehensive approach to solving mathematical problems. The sutras offer both general techniques and specific methods tailored to various mathematical operations, making calculations quicker and easier.
3. Basic Fundamental Concepts Of Vedic Mathematics:
a. Ekadhikena Purvena: This sutra enables the multiplication of numbers ending with nine by adding the number being multiplied with the next higher number, followed by appending one at the end.
b. Nikhilam: This sutra is useful for multiplication by a close number known as a base, followed by an adjustment by the difference between the base and the actual number.
c. Paravartya Yojayet: This sutra aids in solving division problems by reversing the digits of the divisor and adjusting the quotient accordingly.
d. Anurupyena: This approach facilitates proportionately compressing and expanding numbers when solving mathematical problems.
4. Comparison With Western Mathematical Systems:
During the time when Vedic Mathematics flourished, the Western world was primarily focused on Greek and Roman mathematical systems. While these systems were robust, Vedic Mathematics showcased a level of sophistication and efficiency that surpassed its Western counterparts. Vedic Mathematics possessed numerous techniques for complex operations like multiplication division squares cubes and square roots, providing a streamlined approach that could solve problems in significantly less time.
5. Modern Applications And The Legacy Of Vedic Mathematics:
The legacy of Vedic Mathematics extends far beyond ancient times. Today, its techniques find applications in various scientific and mathematical pursuits. The efficiency of Vedic Mathematics has been acknowledged and embraced by modern mathematicians engineers and computer scientists. Its ability to simplify complex calculations and improve mental math skills has made it popular globally. Additionally, Vedic Mathematics serves as a historical testament to the advanced knowledge and intellectual achievements of Ancient Bharat.
In ancient India, there were several important scriptures that played a significant role in teaching Mathematics. These texts provided profound insights and laid the foundation for various mathematical principles and formulas.
In the second part of this article, let’s delve into a few of these scriptures and explore the formulae they mentioned, along with their Sanskrit references and translations.
1. “Vedanga Jyotisha” (1400–1200 BCE) – Authored by Lagadha. This scripture is a part of the Vedangas which are texts associated with the study of the Vedas. It contains astronomical calculations and mathematical formulae. One noteworthy formula mentioned in this text is the calculation of the approximate number of lunar days in a solar year, known as the “Tithi Equation”.
2. “Sulba Sutras” (800–500 BCE) – These mathematical treatises are attributed to ancient Indian scholars called “Sulba Sutracara.” The Sulba Sutras primarily focus on geometry and provide instructions for the construction of altars and fireplaces used in Vedic rituals. One well-known formula mentioned in these texts is the “Pythagorean theorem” for right-angled triangles, which is described as the “diagonal rope” in the Baudhayana Sulba Sutra.
3. “Bakhshali Manuscript” (200–400 CE) – This ancient mathematical text is named after the village of Bakhshali in present-day Pakistan. It contains various mathematical operations, including arithmetic and algebraic techniques. One remarkable formula mentioned in this manuscript is the “Quadratic equation” in its operation general form (ax^2 + bx + c = 0) which appears as a verse on page 122 of the manuscript.
4. “Lilavati” (1150 CE) – Authored by Bhaskara II also known as Bhaskaracharya this mathematical treatise is dedicated to his daughter Lilavati. It covers a wide range of topics including arithmetic algebra and geometry. One notable formula mentioned in this book is the “Bhaskara’s formula” for solving quadratic equations, which is explained in the chapter named “Lilavati” itself.
5. “Ganita Sara Sangraha” (850–1250 CE) – This mathematical work was composed by Mahaviracharya, an Indian mathematician from the Jain tradition. The text covers various aspects of mathematics, including arithmetic algebra and geometry. It contains several formulae, but one prominent formula mentioned is the “Rule of Three” or “Proportionality Rule” which enables the calculation of an unknown quantity based on two known quantities.
Note: Many ancient scriptures and books were burnt down by invaders in Bharat that is India today, one eminent example is ancient Nalanda University that was brutally destroyed and burnt by Muslim invader ‘Bakhityar Khilji’ and the lakhs of books kept the fire burning for about three months but fortunately, thanks to ancient Indian tradition of deep learning and reciting the scripture and mantras, that made it possible for them to pass on the knowledge to the next generations, also rewrote many important lost scriptures, few, if not in lakhs must have been restored. Nevertheless, these ancient Indian scriptures served as a remarkable foundation for mathematical principles and their authors made significant contributions to the world of Mathematics.
Vedic Mathematics stands as a testament to the brilliance and intellectual prowess of ancient Bharat. With its concise and efficient problem-solving techniques, Vedic Mathematics has left an indelible mark on the world of mathematics. By comparing it with Western mathematical systems at that time, we can appreciate its advanced nature and its potential to revolutionize calculations. The legacy of Vedic Mathematics continues to thrive, holding relevance even in the modern world.
