Author: Piali Banerjee

Publication: Mumbai Mirror

Date: July 29, 2008

URL: http://www.mumbaimirror.com/net/mmpaper.aspx?page=article§id=2&contentid=20080729200807290216155316003718

Subsets of calculus existed in the Ganita-Yukti-Bhasa
two centuries before Isaac Newton published his work, according to a recently
published translation of the manuscript

Prof K Ramasubramanian of IIT-Bombay has news
for us that we'd all love to hear. 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.

Q.: How old is the Ganita-Yukti-Bhasa?

A.: 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.

Q.: What is the Ganita-Yukti-Bhasa about?

A.: 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.)

Q.: And the Tantra Sangraha?

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

Q.: How much of Tycho Brahe's theory existed
in this ancient manuscript?

A.: 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.

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

A.: 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.

Q.: Could you give an example?

A.: 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.

Q.: How is it different?

A.: 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.

Q.: So what's the relevance of these findings?

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

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

A.: 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.

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

A.: 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.

Q.: What are you working on next?

A.: I'm working on other works of Nilakantha.