## Mathematics In Ancient India

The history of mathematics in ancient India is rich and varied, and it stretches back to the Indus Valley Civilization, one of the world’s oldest urban civilizations, which existed around 2500 BCE. Evidence of early mathematical understanding is found in the Indus Valley’s sophisticated architecture and urban planning, which involved complex calculations related to geometry and measurement.

In the Vedic period (1500 – 500 BCE), the religious texts known as the Vedas were composed, and they contained references to mathematics, particularly geometry and algebra. It was largely due to the requirements of the Vedic rituals, which involved constructing elaborate altars with precise measurements. The “Shulba Sutras” are part of these texts, containing geometric principles and techniques for constructing altars.

In the post-Vedic period, the development of mathematics in India continued and flourished. The ancient text “Baudhayana Sulbasutra,” dated to around 800 BCE, contains geometric knowledge, including the approximation of the square root of 2 and rules for obtaining Pythagorean triples (a set of three positive integers a, b, and c that fit the rule a^2 + b^2 = c^2).

## The Decimal System

The decimal system, also known as the base-10 system or decimal number system, is a positional numeral system employing ten as the base and requiring ten different numerals, the digits from 0 to 9. It also uses a decimal separator to represent fractions. The invention and development of the decimal system was a significant breakthrough in mathematics that facilitated easier calculation and was essential for the progress of science and commerce.

The decimal system is historically attributed to the ancient Indian mathematicians, who developed the concept around the 5th century CE or possibly earlier. Before the decimal system, numbers were often represented using other systems, such as the Roman numeral system, which was cumbersome for calculations.

## The Zero

One of the most revolutionary aspects of the decimal system is the introduction of zero as a digit and its concept. Ancient Babylonians had a placeholder symbol to denote the absence of a value in a positional number system. Still, it was in India that the symbol evolved to become a number in its own right. Brahmagupta, an Indian mathematician and astronomer who lived in the 7th century CE, is often credited with comprehensively explaining the mathematical rules and properties of zero.

In the yogic culture, zero, also called “Shunya” or “Shoonya”, holds significant philosophical meaning, symbolizing the state of emptiness or voidness. This concept is deeply rooted in Eastern spiritual philosophies, including Buddhism, Hinduism, and Jainism.

In the context of Yoga, as interpreted by teachers like Sadhguru, “Shunya” represents a state of meditativeness where one is not identified with anything—no thoughts, emotions, biases, or preconceived notions. It is a state of pure consciousness or ultimate awareness, where one transcends the physical limitations and experiences the infinite nature of existence.

In this sense, zero is not just a numerical value or a mathematical concept but a state of being one aspires to attain through spiritual practices. It’s a state where the individual ego dissolves, and one experiences a sense of unity with the universe. This state of “Shoonya” or “emptiness” doesn’t mean an absence. Rather it means presence in its purest form, unclouded by the mind’s interpretations or attachments.

Zero, or “Shunya,” is the basis for creation in the yogic culture. It signifies that everything comes from nothingness and eventually returns to nothingness. This understanding can be related to the fundamental principles of quantum physics, which suggest that particles can pop in and out of existence from what appears to be a void.

The invention of zero by the ancient Indians was not by accident. They experienced with a deep perception and understood Shoonya the Yogic way.

### The Numerals

Brahmagupta’s works were later translated into Arabic, and from there, the decimal system spread to the Islamic world and then to Europe. The Italian mathematician Fibonacci, who grew up in North Africa and was taught mathematics by Arab teachers, was instrumental in spreading the system throughout Europe after his return to Italy.

Today’s Arabic numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) were originally designed in India and are sometimes more accurately referred to as Hindu-Arabic numerals due to their origin. The use of these numerals has become so widespread due to the power and utility of the decimal system that they are now standard in almost every country around the world. The decimal system remains a foundational element of mathematics, science, engineering, and commerce.

### The Value of Pi

Pi is a mathematical constant representing the ratio of a circle’s circumference to its diameter. It’s an irrational number, which means it cannot be expressed as a simple fraction, and its decimal representation never ends or repeats. Its approximate value is 3.14159.

In the 5th century, the mathematician Aryabhata wrote the “Aryabhatiya,” providing significant mathematical and astronomical knowledge. He introduced the concept of sine in trigonometry, gave methods to calculate the areas of triangles, circles, and spheres, and accurately calculated the approximate value of pi.

The concept of Pi and its value has been recognized and used for thousands of years. As early as 1900 BCE, the ancient Babylonians approximated Pi as 3.125, while the ancient Egyptians, a little later, approximated Pi as 3.16.

The first theoretical calculation of the value of Pi was that of the Indian mathematician and astronomer Aryabhata in the 5th century CE. He used the word “asana” (approaching) to suggest that the ratio of the circumference to the diameter is a constant and provided a value of 3.1416, remarkably close to the modern value.

The 12th-century mathematician Bhaskara II (also known as Bhaskaracharya) made significant contributions to mathematics, including explaining the concept of what is now known as differential calculus. His works “Lilavati” and “Bijaganita” are famous for their mathematical content, including algebra, equations, and trigonometry.