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Sriram Sundaram

Indian Civilization is the most holistic civilization of all, we know in the whole world. The study
of Indian civilization, which encompasses all spheres of creative human endeavors like art, literature,
science, philosophy and culture is know as Indology. Indology is an active area of research in India and
abroad. Many noted scholars including scientists, historians, linguists and so on, have ventured into
this vast ocean of holism. Before getting into the subject of the article, its important to set a convention
which will be followed through out the article.
Notation : The system of B.C. (Before Christ) and A.D.(Anno Domini) nomenclature would be used
while mentioning the time periods in this article in contrast to the relatively new system of notation
used by historians B.C.E.(Before the Current or Common Era) and C.E.(Current or Common Era).

In Indian Civilization, as Prof. B. M. Deb (A Mathematician turned Theoretical Chemist and an
ardent student of civilizations) aptly points out in his monumental work [1], which was recently pub-
lished, “everything is connected to everything else”[1]. In this article I intend to give a very small
glimpse onto how Mathematics was illustrated in ancient times (say, since 4th century A.D.) in India
and a humble effort to let you all know the extent of contribution of our ancestors have made into all
the spheres of human endeavors.

Many of the modern basic mathematics concepts and foundation that we know today, dates back
to Kerala School Of Astronomy and Mathematics (4th Century A.D. - 1650 A.D.). Kerala School of
Astronomy and Mathematics, founded by Madhava of Sangamagrama was situated near, now known
Cochin-Trissur side of Kerala, was home for many noted and revered scholars of the time. Unknown to
the rest of the world, including the rest of India, Kerala School of Astronomy and Mathematics was far
ahead of mathematics developed in the rest of the world. The prominent scholars who were responsible
for the brilliant and outstanding contributions of the school include Madhava of Sangamagrama (1340
A.D. - 1455 A.D.), Parameswara (1360 A.D. - 1455 A.D.), Nilakantha Somayaji (1443 A.D. - 1560 A.D.),
Jyesthadeva (1500 A.D. - 1610 A.D.), Acyuta Pisarati (1550 A.D. - 1621 A.D.) and Melputtur Narayana
Bhattathiri (around 1587 A.D.) ([1] and references therein.). The School reached its peak of brilliance
and got flourished between 14th and 16th A.D., though the roots of initiation goes back to the work of
Aryabhata I (5th century A.D.). The original research seems to have ended with Narayana Bhattathiri
due to further foreign invasion, battles and so on which cropped up in Kerala. The originality and the
content of the kind of works that has come up from Kerala School of Astronomy and Mathematics, how
the works got transmitted to the outside world including Greeks, Arabs and Europeans are still subjects
of research and extensive investigation. These Mathematicians and astronomers came up with many
important, basic and original concepts including [1], :

• Revolutionary ideas of Calculus.

• Infinite series expansion of functions, e.g : Power series, Taylor series, Trigonometric series.
(Madhava-Newton power series. rediscovered in Europe at the time of Newton.)

• Differentiation Theory

• Integration Theory, including numerical integration.

• The idea that area under the curve is its integral.

• Used their intuitive understanding of integration in deriving the areas of curved surfaces and
volumes enclosed by them .

• Detailed astronomical calculations and observations.

• Heliocentric planetary model.

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Most of us would not have heard the names of all the scholars I mentioned above. But, I am sure that,
we all have heard the name Melputtur Narayana Bhattathiri. The great eminent scholar who composed
the most revered and scholarly Sanskrit work Narayaneeyam. Melputtur Narayana Bhattathiri was a
mathematical linguist. He was one among the most renowned mathematicians and student of Acyuta
Pisharati of Kerala School of Astronomy and Mathematics. Narayana Bhattathiri’s other famous schol-
arly works includes setting up an axiomatic system elaborating on the classical system of Panini (The
world’s first linguist, grammarian, who came up with the ever revered glorious work, Ashtadyayi - a
treatise on Sanskrit Grammar around 700 B.C.). Elaborating on the same can be yet another series of
articles.

One can clearly see that the Mathematics was expressed in the form verses or slokhas, i.e Mathe-
matics, Art and Literature went hand in hand. One golden example for the same outside Kerala School
of Astronomy and Mathematics, to illustrate the fact that, this system was practiced in all parts of An-
cient and Medieval India, is Hemachandra’s (Acharya Hemachandra, Born in Dhandhuka, in present-
day Gujarat, 1088 A.D. - 1173 A.D., was a Jain scholar, poet, and polymath who wrote on grammar,
philosophy, prosody, and contemporary history.) poetry. It is through Hemachandra’s poetry in San-
skrit, that the now known, famous Fibonnaci sequence (1, 1, 2, 3, 5, 8, 13, ...) first came into light. It was
presented around 1150 A.D., about fifty years before the well revered Mathematician Fibonacci. A par-
ticular pattern of placing the long and short syllable in Sanskrit poetry, led to the discovery of Fibonacci
sequence. Oh No! Now, among the modern Mathematicians, its known as Hemachandra - Fibonacci
Sequence [2].

Last but not the least, we should not forget that the works by reverent scholars like Newton, Leibniz,
and so on by no doubt are original, outstanding and brilliant. Ultimately, as we can clearly see, our
ancestors practiced broad and open minded learning.

To conclude for this issue, as a student from Kerala, it is a matter of guilt for me that only after
17 years of my school/college, I realized that the real academic culture of Kerala is this holisitc and we
had such a rich cultural and scholarly past with hands on every strand of creative human endeavor.
Let’s go back, see and learn from our glorious past, where “overall”intellectual human development
had emphasis. For the same one has to go through authentic resources carefully, in this era of getting
information on a single click 1. (to be continued.)

References

[1] B. M. Deb, The Peacock in Splendour - Science, Literature and Art in Ancient and Me-
dieval India, Viswa-Bharati Publishing, 2015.

[2] Online Video lectures of Prof. Manjul Bhargava published in Youtube.

1A small piece of information : In this modern era, it is heartening to note that nice initiatives such as “The Murty Classical
Library of India”is happening, where many scholars from different parts are working together to reproduce the Classic Indian
literature works by giving an English translation alongside the original Indic script.

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