Were ancient Indian mathematicians ahead of their time?

The contributions of historical Indian mathematicians were so significant that many of their discoveries preceded similar developments in the Western world by centuries. From the invention of zero to the rules of algebra and trigonometry, Indian students not only solved complex mathematical problems, but also laid the foundations for cutting-edge arithmetic.

Their work was no longer merely theoretical – it contained realistic programs in astronomy, architecture, and exchange, demonstrating a sophistication that was unheard of in the historical world. This raises the question: were historical Indian mathematicians truly ahead of their time? The evidence is clear that they were, as their inventions inspired mathematics and science around the world in ways that are still being discovered today.

One of India’s most important gifts to arithmetic was the concept of zero (zero). Historical civilizations such as the Babylonians and the Mayans used placeholder symbols, but Indian mathematicians were the first to treat 0 as a number with its own individual values. Brahmagupta (seventh century AD) defined the rules for zero in his treatise Brahmasphutasiddhanta, stating that subtracting zero from a number leaves it unchanged and that any number expanded using zero will add up to zero.

This conceptual leap was innovative without it, advanced arithmetic, algebra, and calculus might not have existed. The Arab mathematician al-Khwarizmi later disseminated those ideas to Europe, where they have become the foundation of today’s arithmetic.

Ancient India also perfected the decimal machine, which involved the use of nearby cost notation (in which the place of a digit determines its price). Early styles of this machine appear in texts such as the Bakshali Manuscript (third-fourth century AD), while Aryabhata (fifth century AD) formalized it in his work Aryabhatiya. This machine was far more efficient than Roman numerals or Babylonian base-60 calculations, allowing for faster calculations. When Arab scholars followed suit, the machine spread globally, eventually replacing older numeral structures in Europe by the twelfth century.

Indian mathematicians had made great advances in algebra long before it flourished in the Islamic world and Europe. Aryabhata presented solutions to linear equations, while Brahmagupta developed strategies for solving quadratic equations. Bhaskara II (12th century AD) extended these ideas in Lilavati, in which he discovered indetermined equations and cyclic techniques that foreshadowed calculus.

In trigonometry, Indian scholars added the sine function (jya), which became more accurate than the Greek chord function. Madhava of Sangamagrama (14th century AD) later developed countless collections for trigonometric capabilities – a concept that would be rediscovered centuries later in Europe in the form of the Taylor series.

The Kerala school of mathematics (14th–16th centuries) made discoveries that some historians argue resemble early calculus. Madhava derived the infinite series for π (pi) and used iterative methods to estimate values ​​– strategies that did not appear in Europe until Newton and Leibniz in the seventeenth century. While this does not suggest that Indians “invented” calculus, it does suggest that they were exploring similar mathematical limits much earlier.

Indian mathematicians were also professional astronomers. Aryabhata calculated the rotation of the earth and the length of the year with great accuracy. Varahamihira (6th century AD) compiled mathematical-astronomical expertise in the Pancha-Siddhantika, which blended Greek, Egyptian and Indian ideas. His work was no longer abstract – it was used for calendar making, navigation and temple construction, proving that his knowledge was both deep and realistic.

Despite their brilliance, many Indian contributions have been:

• Misplaced in translation – Sanskrit texts took centuries to reach Europe.
• Attributed to others – Arab scholars like Al-Khwarizmi mediated Indian math to Europe, obscuring its origins.
• Colonial bias – British historians frequently downplayed pre-colonial Indian achievements.

Ancient Indian mathematicians were undoubtedly ahead of their time. Their work formed the backbone of contemporary mathematics, yet their names are less well known than those of Greek or European students. From concepts like 0 to calculus, their innovations are no longer merely theoretical, but have shaped the field. Recognizing their contributions corrects an ancient oversight and reinforces the region of India as the cradle of medical concepts.