The men who knew infinity - India`s lost history of mathematical genius

  • By MINT editorial
  • May 2016
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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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Also  read
1. Brief history of Indian Mathematics
2. Vedic Maths - Every child deserves it