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Illustration: Jayachandran/Mint
Illustration: Jayachandran/Mint

The men who knew infinity: India’s lost history of mathematical genius

Many Indian discoveries have been wrongly attributed to European scholars

It was roughly a century ago that J.E. Littlewood, a renowned British mathematician, noted that every positive integer was a personal friend of Srinivasa Ramanujan. The Man Who Knew Infinity, a biopic on Ramanujan—a legendary mathematician born in 1887 in modern Tamil Nadu—released in India on Friday reminded his admirers of this dollop of history. A man with no formal training in mathematics, he would go on to secure several remarkable breakthroughs in his short life of 32 years.

Although a bright star, Ramanujan is just one among many distinguished Indian names who have made stellar contributions to the field of mathematics. The heritage of Indian mathematics is tremendously rich and diverse. The first comprehensive use of the place value system of arithmetic was found in Āryabhaṭīya (499CE), a famous work of Aryabhata. The trigonometric function “sine" traces its origin to jya-ardha series, a table of half-chords of a unit radius circle, compiled by him. Other prominent Indian names in mathematics include, chronologically, Varahamihira, Brahmagupta, Bhaskara I, Bhaskara II and Madhava.

Many of the discoveries which are attributed to European scholars had previously been worked out in India—in some cases centuries earlier. One of the most glaring examples is the Pythagorean theorem. There is no evidence to suggest that Pythagoras, the Greek mathematician, ever arrived at this theorem. The theorem, however, finds a place in Baudhayana’s Śulbasūtras, which dates back to about 800 BC—more than 200 years before Pythagoras was born. Pell’s equation, attributed by 18th century Swiss mathematician Leonhard Euler to 17th century English mathematician John Pell was originally solved by Bhaskara II, a 12th century Indian mathematician-astronomer.

Similarly, much of the work on calculus was done in India by the Kerala School of Mathematics—much before Isaac Newton and Gottfried Wilhelm Leibniz came into the picture—founded by Madhava in the 14th century CE. The entire list of wrong attributions is a much longer one. This is not an attempt to illegitimately usurp every work in the field of mathematics and claim it as Indian. The immense contributions of mathematicians from Europe, the Arab world, China and Africa cannot be wished away. Nor is this an effort to “Hinduize" or “saffronize" the achievements of India’s past. In fact, both the Jain and Buddhist traditions are inextricable parts of this heritage. For instance, Sūryaprajñapti, a Jain text had arrived to a close estimate of the value of π in the fourth century BC itself. A network of pearls described in the Buddhist text Avataṃsaka Sūtra as one where “in each pearl one can see the reflections of all the others, as well as the reflections within the reflections and so on" was worked upon by mathematicians in the US. The arrangement is exactly, they found, that of circles in what is known as Schottky groups. See the pictures here.

An important difference between the Indian tradition and the Greco-Western tradition of mathematics is the emphasis on proofs placed by the latter. This divergence is most distinctly observed in arguments between Ramanujan and his mentor G.H. Hardy at Trinity College, Cambridge. For Ramanujan, an equation had no meaning unless it expressed a thought of God. This fits in with the evolution of mathematics in India in a multi-disciplinarian framework. A regular osmotic process has sustained between Indian mathematics and other fields like astronomy, physics, linguistics, spiritualism and music.

Manjul Bhargava, a Princeton University mathematician of Indian origin and recipient of the prestigious Fields Medal, is one of the finest exponents of such cross-disciplinarian synergies. One of his favourites is how the number of rhythms in Sanskrit poetry consisting of long and short syllables—corresponding to beats on a musical instrument—can be calculated using the Hemachandra numbers, popularly known as the Fibonacci numbers after an Italian mathematician despite being first documented by the Indian polymath.

Barring the work of a few exceptions like Ramanujan, Indian advances in mathematics have seen an unprecedented decline in the last few centuries. Foreign conquests and colonization of the country seem to be the immediate factors contributing to the decline. Kerala remained untouched by the conflicts that had engulfed the northern parts of India, perhaps explaining why the mathematical tradition continued there longer than elsewhere else in the country.

Not much effort has been expended since independence on the revival of this great tradition. The cross-disciplinarian approach has been almost entirely done away with in the schools. A greater culture of commerce, trade and exchange of ideas that reinforced the intellectual quests of Indians in the past has also been lost; this is on the mend only in the last three decades. It is high time Indians took up this project.

A recovery of this great Indian tradition would involve a restoration of India’s glorious history. Mathematical concepts should be taught to students along with their histories. As Bhargava notes, “...knowing the correct history of mathematics was useful in my own research, because if you learn from the original source how an idea came about, that can give you great insight." A beginning can be made by correcting the name and the origin of the so-called Pythagorean theorem in school textbooks.

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