• Article outlines achievements of Indian Scholars in the field of Mathematics for e.g. the earth is round, concept of zero and benefits, rules for solving quadratic equations and importance of negative numbers etc.

Specialists in the field of Mathematics are now among the most sought after in financial and technological world. Many of today’s leading digital technologies – Artificial Intelligence (AI), Machine Learning (ML), Data Science (DS), Big Data (BD), and Cyber Security (CS) – need strong foundational knowledge of mathematics. As in other walks of life, ancient India has had a great mathematical tradition.

The intellectual superiority of Indians, more particularly of Tamil Brahmans, and their resultant success in the Western world is largely attributable to their mathematical prowess. It is only imperative that we recapitulate our mathematical past and build our success stories of the future on it.

This article was published in Bharatiya Vidya Bhawan Journal.

At the UNESCO recognised World Heritage Site of Bhimbetka near Bhopal, there are enchanting rock paintings that date back to the Paleolithic, Mesolithic and Neolithic periods adorning a multitude of caves that actually formed dwellings for primitive people belonging to various ages. The paintings demonstrate the lifestyle and mundane everyday activities of our ancestors. Not only are humans depicted as hunters and food gatherers, the paintings also feature fighters, elephants bearing metal weapons, riders on horses, and battle scenes where rulers carry spears, swords, arrows, and bows. In some caves there are marks which give the impression of counting; maybe of animals that our ancestors had started rearing. Thus may have started India’s tryst with Ganitam or Mathematics.

As far back as 1200 BC, mathematical knowledge formed a part of a larger body of knowledge known as Vedas. From the third century BC, there is also written evidence of the Brahmi numerals that preceded Hindu-Arabic numeral system.

Aryabhatta, a colossus in the field of mathematics, was the first to proclaim that the earth is round, that it rotates on its axis, orbits the sun and is suspended in space - 1000 years before Copernicus published his heliocentric theory. He is also acknowledged for calculating p (Pi) to four decimal places: 3.1416 and the sine table in trigonometry.

Centuries later, in 825 CE, the Arab mathematician, Mohammed Ibna Musa credited the value of Pi to the Indians, ‘This value has been given by the Hindus.’ And above all, his most spectacular contribution was the concept of zero without which modern computer technology would have been non-existent.

The invention of ‘Zero’ gave a sudden boost to the mathematical mechanics that enabled the ancient Indians to study higher mathematics over 3000 years ago and make seminal contributions in the study of trigonometry, algebra, arithmetic and negative numbers among other areas, well before similar advances were made in Europe, with its influence meanwhile spreading to China and the Middle East.

The discovery of Zero also greatly helped in the evolution of the decimal system, which led to the expression of numbers as multiples of 10. The placeholder symbol for nothing made Zero itself a part of the numeral system and allowed numbers to be written efficiently and reliably. In turn, this allowed for effective record[1]keeping that meant important financial calculations could be checked retroactively, ensuring the honest actions of all concerned. The discovery of ‘Zero’ paved the route for what they call democratisation of mathematics.

In the seventh century, the first written evidence of the rules for working with zero were formalised in the Brahmasputha. In his seminal text, the astronomer Brahmagupta introduced rules for solving quadratic equations and for computing square roots. He also demonstrated rules for working with negative numbers by placing Zero in between the series of positive numbers and that of the negative numbers. He wrote down rules that have been interpreted by translators as: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”.

The importance of negative numbers was lost on European mathematicians as they jettisoned the idea as absurd and useless for a long time even as Indian and Chinese mathematicians could recognise early on that debts were best depicted by negative numbers. Brahmagupta also knew that “The product of a debt and a fortune is a debt” – a positive number multiplied by a negative is a negative.

Gottfried Wilhelm Leibniz, a European Mathematician gave due recognition to the Indian concept of negative numbers and to use zero in a systematic way in the development of calculus, the very important branch of mathematics used to measure rates of changes, which is important in almost every branch of science, notably underpinning many key discoveries in modern physics. The Indian mathematician, Bhaskara had, however, already discovered many of Leibniz’s ideas over 500 years earlier. He had also made major contributions to algebra, arithmetic, geometry and trigonometry during that time.

The Sulvasutras contain elaborate descriptions of construction of vedis and enunciate various geometric principles. These were composed in the first millennium BC, the earliest Baudhayana Sulvasutra dating back to about 800 BC. Even as it did not seem to have gone very far in comparison to the Euclidean geometry evolved in the seventh century BC. It was, however, an important stage of development in India too. The Sulvasutra geometers were also aware of the principle that is now known as the Pythagoras theorem, over 200 years before.

Coming to the measurement of time, according to the Vedic literature, one Ahoratri (also called Hora or hour) comprised 60 Nadis; 60 Vinadis equalled one Nadi and one Vinadi equalled 6 Pranas. In another ancient Indian system a day of 24 hours would be measured thus: 18 winks of eye was equal to one Kasta; 30 Kastas would equal to 1 Kala; 30 Kalas equaled to 1 Muhurta and 30 Muhurtas made a day. It is worth mentioning that the Almanac produced by the Kashmiri Pandits is the oldest one and their predictions about the solar and lunar eclipses was 100 percent accurate.

Aryabhatiya, written in 499, is basic to the tradition, and even to the later works of the Kerala school of Madhava of Astronomy and Astrology both. It consists of 121 verses divided into four chapters - Gitikapada, Ganitapada, Kalakriyapada and Golapada.

Starting with Aryabhata (476-550), the founding father of scientific astronomy in India, and extending to Bhaskara II (1114-1185) and beyond, the essential continuity of the ancient Indian tradition was carried over centuries by Varahamihira in the sixth century, Bhaskara I and Brahmagupta in the seventh century, Govindaswami and Sankaranarayana in the ninth century, Aryabhata II and Vijayanandi in the 10th century, Sripati in the 11th century, Brahmadeva and Bhaskara II in the 12th century, and Narayana Pandit and Ganesa from the 14th and 16th centuries respectively.

In another chapter devoted to mathematics per se, are particular procedures to find square roots and cube roots, as also an approximate expression for the value of ‘pi’ at 3.1416. The genius of Srinivasa Ramanujan, a globally renowned mathematician, inspires not only us as a nation, but the mathematicians of the whole world.

And finally the concept of infinity postulated in this universally acclaimed mantra of Isopanishad: Om purnamadah purnamidam purnat purnamudachyate, purnasya purnamaday, purnameva vashishyate (The invisible is infinite, the visible too is infinite; from the infinite, the visible universe of infinite extension has come out. The infinite remains the same even though the infinite universe has come out of it).

Also read

1. Renowned Mathematicians of India

2. The man who knew infinity

3. A brief history of Indians Maths

4. Talks on Maths in Metrical form

5. The Story of Pythagoras

This article was first published in the Bhavan’s Journal, 31 March 2021 issue. This article is courtesy and copyright Bhavan’s Journal, Bharatiya Vidya Bhavan, Mumbai-400007. eSamskriti has obtained permission from Bhavan’s Journal to share.