India gave world its mathematical language: US prof

Long before Newton formulated his laws or Fibonacci counted his rabbits, Indian scholars were quietly laying down the rules of mathematics. They worked with fire altars, verses of poetry and the very structure of language itself. From this grew ideas that shaped how we count, calculate and even programme machines today.

Yet most schoolchildren are taught a different story. At a conference, South Asia’s Manuscript Heritage and Mathematical Contributions, Prof Manjul Bhargava, Fields Medallist and Professor of Mathematics at Princeton University, spoke of a quiet erasure. “The irony,” he said, “is that the number system travelled from India to the Arab world, then westwards, only to return to us as ‘Arabic numerals’.”

The story of India’s role in mathematics, he said, extended far beyond Aryabhata’s zero. “The Baudhayana Sulbasutras, written around 800 BCE, were manuals for building fire altars used in religious rites. In them, scholars explain that if you draw a square on the diagonal of a rectangle, its area equals the sum of the squares on the sides. Today, we call this the Pythagorean theorem. In other words, Indian scholars knew it long before Pythagoras,” he said.

Around the 5th century BCE, grammarian Panini composed the Astadhyayi, a system of rules that could generate all correct Sanskrit sentences. His grammar worked almost like an algorithm, a logical framework so advanced that modern computer scientists compare it to the foundations of programming languages. In 628 CE, mathematician-astronomer Brahmagupta extended the concept of zero further than anyone before him. In his Brahmasphutasiddhanta, he treated zero as a number in its own right and laid out rules for its use. He also gave the earliest version of the quadratic formula and discussed negative numbers, which he called “debts”.

The cross-pollination of art and science played its role too. The study of Sanskrit poetry, with its long and short syllables, inspired explorations of patterns and sequences. This led scholars such as Pingala and Virahanka to ideas resembling the binomial triangle and the Fibonacci sequence, centuries before these concepts surfaced in Europe.

Perhaps the most remarkable advance came from the Kerala school in the 14th century, as Prof Bhargava explained. Madhava of Sangamagrama and his disciples pushed maths into the infinite. They developed infinite series for sine, cosine and pi, laying down the early ideas of limits and convergence, concepts that were later formalised in Europe as calculus.

Prof Bhargava argued recovering this history was not a matter of pride, but honesty. “When children in India learn mathematics, they should know that much of the very language of numbers and patterns comes from their own heritage,” he said.