The number system which the world uses today originated in India in the first centuries CE. It is usually called the “Arabic numeral system” since the Europeans got it from the Arabs, but in the Middle East it is known as the “Indian system” since the Arabs got it from India. Mathematics emerged as a separate field already in the Vedic period but it was in the Gupta period that the greatest advances were made. The Indians learned from the Greeks, but made seminal contributions of their own. They were the first to make use of decimals and the number zero. They used negative numbers too and they beat Pythagoras to his famous theorem. Indian mathematicians calculated the value of π, pi, with a very high decree of precision, and determined the circumference of the earth and the timing of lunar and solar eclipses. In the 15th century CE, the Kerala school of mathematics developed ideas regarding trigonometric functions.
In India, mathematical knowledge always developed as a result of its application. Already the Harappa civilization, some 2,500 years BCE, used geometry in order to calculate the size of fields and in Vedic culture maths was used to calculate the size of altars and for deciding when to engage in various religious rituals. Likewise, notion of zero and infinity both have their origin in religious speculations. The world as we know it contains no nothing; everything we see around us is something. Yet in Buddhist philosophy, nothingness is a key concept and the goal of mediation is to empty one’s mind. Nothingness, to a Buddhist, is real. Meanwhile, the Jains were fascinated by very large numbers. They told stories of gods who appeared millions of times with millions of years apart. The better you can understand the infinite, they argued, the better you can understand the divine.
The history of mathematics is a great example of a dialogue of civilizations. The Indians learned from the Greeks, taught the Arab world, which in turn taught the Europeans. But at each stage, the knowledge was transformed and improved on. To this day only some ten percent of all the manuscripts on Sanskrit science have been published and much remains to be properly studied. There may be many surprising discoveries to be made.
Incarnations, “Ramanujan: The Elbow of Genius”
Incarnations, “Aryabhata: The Boat of Intellect”
In Our Time, “Indian mathematics”