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for The Mumbai Mirror on Aug. 16, 2008Prof K Ramasubramanian of IIT-Bombay has some interesting news. His recently released two-volume translation of the Ganita-Yukti-Bhasa by Jyesthdeva points to the fact that some subsets of calculus existed in Indian manuscripts almost two centuries before Isaac Newton published his work. And that an Indian mathematician and astronomer Nilakantha Somayaji spoke, in parts, about a planetary model, credited to Tycho Brahe almost a century later.

Chak de India? “Let’s not get over-excited,” laughs Ramasubramanian. “Let’s present the facts instead.”

Presenting excerpts of a conversation with the professor - a physicist and Sanskrit scholar, who has been working on the history of science for years now.

How old is the Ganita-Yukti-Bhasa?

It was published some time between 1530 and 1540. However, what’s important is that the material in this book is far older. For, the author makes it clear that his manuscript only explains in detail the work described in the Tantra Sangraha by Nilakantha Somayaji. So the work spoken about is actually much older, as Nilakantha in the 15th century.

What is the Ganita-Yukti-Bhasa about?

It is divided into 15 chapters. Seven chapters are devoted to mathematics, and eight to astronomy. (By the way, it’s written in Malayalam, not Sanskrit. And I’ve translated it along with M D Srinivas and M S

Sriram.)

And the Tantra Sangraha?

The Tantra Sangraha is a treatise on astronomy and related mathematics in elegant verse form, in Sanskrit. It consists of 432 verses.

How much of Tycho Brahe’s theory existed in this ancient manuscript?

Well, in the Tantra Sangraha, Nilakantha talks about a planetary model where five planets, which can be seen with the naked eye – Mercury, Venus, Mars, Jupiter and Saturn – move around the sun, which in turn moves around the earth. The fact remains that a century later, Tycho Brahe published the same planetary model and was credited for it, since no one knew of Nilakantha’s work.

The Ganita-Yukti-Bhasa also points to the fact that first work on calculus began in India?

Well, the Ganita-Yukti-Bhasa attributes its mathematical models work to Madhava, who lived from 1340 to 1420. That’s way ahead of Newton. But it would be too sweeping a statement to say that this was the first work on calculus. Yes, some of the notions described in the book form a subset of calculus. That’s a fact.

Could you give an example?

The infinite series for the pi, the arc tangent, the sine and cosine functions. The value of the pi, for instance – expressing quantity in the form of an infinite series, came two centuries before calculus was formally developed by Newton and Leibniz. In a different context, perhaps, and expressed in a different way. But it did exist. Obtaining a fast convergent from a slow convergent is a major development in mathematical analysis. This too existed in this book, though in a different way.

How is it different?

Madhava and Nilakantha don’t take a formalistic approach to mathematics, the way we do now, having followed Euclid’s method of mathematics. Euclid’s method is a formal, deductive approach. This is a different approach. Now we need to question whether the formalistic approach is the only approach, or the ‘correct’ approach. And it’s a very fundamental question.

So what’s the relevance of these findings?

It’s not to show the superiority of Indian mathematicians. I’m only interested in presenting the correct history of the evolution of mathematics.

Can we get credit for the work of our ancient mathematicians?

Our mathematicians haven’t got their due credit due to two reasons. One is that the western world is largely ignorant of ancient Indian work. The second is that some very tall and inappropriate claims have been made about Indian work, in the past. For instance, there was a claim that differential equations existed in Vedic mathematics. Such tall claims only put us back and we’re not taken seriously.

Can saving the Sanskrit language in India put things right to some extent?

I don’t think the Sanskrit language is under threat in India. The language can be saved. It’s Sanskrit scientific texts that really need saving.

What are you working on next?

I’m working on other works of Nilakantha.