One has heard of
the Kerala School of Mathematics and its lone stellar performer, Madhava of
Sangramagrama. He and his disciples and grand disciples( if one may say so, to
refer to the lineage of disciples) , Parameswara, Neelakantha Somayaji,
Jyeshthadeva, Sankara Varier, Achyutha Pisharoti and others worked on
trigonometry, calculus and geometry centuries before these branches were known
to the western world.

But, Nila
School? This was the topic of a stimulating lecture by Dr. N K Sundareswaran,
Professor, Department of Sanskrit, Calicut University. Hailing from Palakkad,
he was initiated into Sanskrit and Yajurveda by his father in the traditional
manner. Later he graduated in Mathematics and obtained his Master’s and Doctorate
in Sanskrit from Calicut University. He has been teaching and guiding research
for more than a quarter of a century. His doctoral thesis is on Nilakantha
Somayaji’s contributions to astronomy.

He took us
through the main dramatis personae of the Nila School, which in effect,
comprised all the above worthies, excluding Madhava of Sangramagramam. How did
this happen? A lone genius from Irinjalakkuda and all his disciples and
successors from a remote group of villages more than 50 kms. north of the place?

We know about Madhava (c.1340-c1425) mostly
from the work of later mathematicians. Traditionally, he was believed to have
been an Embranthiri ( a Tuluva Brahmin) from Aloor, near Irinjalakkuda in
Trissur district. Most earlier writers had given a convoluted interpretation of
the name ‘Sangramagramam’ to mean Irinjalakkuda/Koodalmanikyam.

But, Prof. Sundareswaran, following Prof. P P
Divakaran (formerly of Tata Institute of Fundamental Research) would prefer to
interpret Sangamagramam to mean Kootallur, a village close to Ponnani. The
literal translation of Sangamagramam is Kootallur. Also, the village and more
particularly, the Namboodiri Illam ( Kutalloor Mana) has a long tradition of
learning even to the present century. It is situated at the confluence of the
rivers Nila and Tootha, which suggest the name Kootallur, a village at the
confluence.

If it is
accepted that Madhava of Sangamagrama belonged to Kootallur, then everything
falls into place, as all the other mathematicians were from neighbouring
villages such as Tripparangodu, Trikkandiyur, Alathiyur etc. (Incidentally,
Prof. PPD suggests that Tirunavaya also used to be and is sometimes still
referred to a Trimurtisangamam on account of the presence, on either bank of
the river, of temples dedicated to the Hindu trinity.)

Madhava’s chief
contribution was the discovery of the infinite series for the trigonometric
functions of sine, cosine, tangent and arctangent. The same series were
developed in Europe for the first time by James Gregory in 1667, more than two
hundred years after Madhava. The world of mathematics has acknowledged this and
the series is now known as Madhava-Gregory-Lleibniz series.( Leibniz only
re-obtained the formula for pi which had already been obtained by Madhava.)

Vatasseri
Parameswara ( c.1380-1460) hailed from Alathiyur, near Tirur and was the direct
disciple of Madhava. He was an astrologer as well and suggested improvements to
the findings of Aryabhata, Bhaskara, Govindasvami and others through his
copious commentaries. He was also known as the father of the Drig ganita system
which is a system of astronomical computations considered more accurate that
the then existing Parahita system. His contribution was in proving theories
through observation. Damodara was the son and pupil of Parameswara and was also
a notable mathematician and astronomer.

Nilakantha
Somayaji ( 1444-1520?) was Damodara’s disciple. Born in Kelalloor mana in
Trikkandiyur, Nilakantha was closely associated with the Sree Rama Temple in
Alathiyur, (which is more famous for its

*upa devata*, Hanuman.
Nilakantha’s
major work was the Tantrasangraha written in 1500 which was principally an
astronomical treatise. His theories are, however, without proofs or
explanations of the logic. For this, we have to turn to his disciple, Jyesthadeva.

Jyesthadeva (c1500-c1575), the
disciple of both Damodara and Nilakantha was the next great mathematician. He
was also from Tripparangodu, another nearby temple-village. His biggest
contribution was the Yuktibhasha, written in Malayalam. It offers detailed
analytical commentary on Nilakantha’s Tantrasangraha. His contribution was in
providing the process and the derivations for arriving at many of his guru’s
theorems.

Sankara Varier, who was a contemporary of Jyeshtadeva, was the sole non-Brahmin mathematician whose works included Yuktideepika and Kriyakarmakari.

The question
came up – did this knowledge travel from Kerala to the West, or were the
scholarships parallel and unconnected?. Calicut Heritage Forum had the
privilege of hosting, a few years ago, Dr.
George Gheverghese Joseph of Manchester University who was posed the same
question. His reply was equivocal, to put it rather bluntly. But his own writing about
there being plenty of opportunities for the Jesuits, who swarmed the area in the
sixteenth century, to carry the new knowledge to the West, betrays his views.
According to him, there was a strong motivation for this transmission: Pope
Gregory XIII had set up a committee to look into modernising the Julian
calendar. The German Jesuit, Clavius was on this committee and he had been
repeatedly requesting his brethren spread over the world for information on how
people constructed calendars in other parts of the world. The Jesuits who were in numbers in Vettathu kingdom ( they had even managed to convert the Vettath King to
Christianity, and Antonio Gomez who replaced Francis Xavier in India was a
frequent visitor to Tanur) could hardly have missed the opportunity to pick up
the astronomically accurate calculations made popular by the Nila school of
mathematicians.

Prof.
Sundareswaran, however, preferred not to comment on this. Instead, he focused
on how knowledge was being transmitted from generation to generation in an
unbroken chain of succession. His concluding statement - that only around 7 per cent of this fund of knowledge had been deciphered, the rest waiting in numerous cadjan leaf manuscripts to be unravelled - reminded one of the poet A K Ramanujam's perceptive observation :

*Even one's own tradition is not one's birthright; it has to be earned, repossessed.*
thanks CK

ReplyDeletewonderful stuff..

If you recall , i asked you a question once about why these mathematicians studied eclipses, and I then went on to study it - This is quite relevant to the Nila school as well, take a look at the first of my outputs.

http://maddy06.blogspot.com/2017/08/eclipses-scriptures-and-mathematicians.html