Kerala School of Astronomy and
Mathematics: Contributions and Contemporary Relevance
A National Seminar on
“Kerala School of Astronomy and Mathematics : Contributions and
Contemporary Relevance” in collaboration with Amrita Darshanam
International Centre for Spiritual Studies, Amrita Vishwa Vidyapeetham
was organised on November 4th5th, 2016, at Amritapuri Campus, Kollam,
Kerala.


The Kerala School of Astronomy represents the unbroken lineage of
astronomical works from Kerala, India between the 4th century CE and
the 20th century CE. The tradition was introduced in Kerala by
Vararuchi in the 4th century CE through his Chandravākyas. These
vakyas enable us to directly compute the true longitudes of the moon
on any day using simple mathematical calculations, without resorting
to the more involved procedures outlined in the siddhāntic texts. The
vakya system of computing longitudes is simply ingenious. The
Ganitanirṇaya of Puliyoor Puruṣottaman Nambūtiri, published in
1940,is widely considered as the final major work from this school.
During the span of its 1600year history, intellectual activity in
this field waxed and waned, reaching its low ebb in the 5th and 6th
centuries CE. The tradition reached its zenith in the 14th and 15th
centuries. Some of the major personalities who arose during that
fruitful period include Mādhava of Saṅgmagrāma (c. 13401425 CE),
Parameśvara of Vaṭasseri (c. 13601460 CE), and Nilakaṇṭha
Somayājī of Kelallur (c 14431560 CE).
About 350 works by over 115 authors have been identified related to
the Kerala School of Astronomy and Mathematics. The available
manuscripts cover subjects like the mean and true position of planets,
the computation of eclipses, and the timing of moonrises and sunrises,
etc. The scope of subjects covered in these documents is surprising.
There is at least one work, for example, which explains the
construction and working principle of the clock. The hallmarks of the
Kerala School of Astronomy and Mathematics can be summarized as
follows:
1.) gave high
importance to correcting the theoretical values ascribed to observed
data,
2.) adhered to Aryabhaṭa’s system,
3.) enjoyed royal patronage
4.) used the Malayalam language
5.) provided proofs for theorems and formulae
6.) dealt with the epistemology of astronomy
7.) and employed a traditional system of teaching and learning.
In the inaugural
session, Chairperson, Amrita Darshanam, welcomed the gathering and
introduced the dignitaries. The benedictory speech was delivered by
Swami Sivamrita Chaitanya. Felicitation Addresses were given by
Brahmachari Sudeep, Director, Amritapuri Campus and Principal, Amrita
School of Arts and Science, Amritapuri Campus. Sri Pratapanand Jha
from Indira Gandhi National Centre for the Arts (IGNCA) highlighted
the scope of the Vedic Heritage Portal project of the IGNCA under the
aegis of the Ministry of Culture Government of India. The highlight of
the inaugural session was the keynote address by Prof.
Ramasubramanian, IIT, Mumbai. Setting a perfect stage for the two days
National Seminar, Prof. Ramasubramanian gave a scholarly introductory
exposition of the subjects of astronomy and mathematics. He
highlighted the following points, illustrating contributions by
astronomers and mathematicians from Kerala:

Introduction of Vakya
System of computation of planetary longitudes by Vararuchi in 4th
century which enormously simplified the calculations involved.

Madhava in 14th
century enunciated the verses that present infinite series expansion
for pi and other trigonometric functions like sine and cosine.

Nilakantha Somayaji
in 15th century introduced a planetary model wherein there was a clear
recognition of the fact that the 5 planets (mercury, venus, mars,
jupiter and saturn) move around the sun and the sun in turn moves
around the earth.
The second day of the
national seminar commenced with the presentation of Prof. M. S.
Sriram, Madras University. He spoke on ‘Karanapaddhati: A theoretical
Guide–book for Preparing Karana and Vakya Texts’. Prof. Sriram
stressed the importance of Karanapaddhati composed by the great Kerala
astronomer Putumana Somayāji as a unique work. Prof. M. D. Sreenivas,
Centre for Policy Studies, Chennai, presented his paper on “the Work
of Kerala School of Astronomy and Mathematics: A Scientific Revolution
Prior to European Renaissance". Prof. T.G. Sarachandran, Deputy
Director [Retd.], Collegiate Education, Kottayam, focused on the
fascination of geometry in Indian Mathematics, with special reference
to Kerala Mathematics. Dr. Vanishri Bhat, a scholar from Bengaluru
presented a paper on "Proof for an Infinite Series by Śaṅkara in his
Kriyākramakarī". In the postlunch session Prof. Ramasubramanian, IIT,
Mumbai. Prof. Ramasubramanian demonstrated with examples explaining
how the true longitude of sun could be determined on any given day.
The two day national
seminar concluded with a panel discussion about the contributions and
contemporary relevance of the Kerala School of Astronomy and
Mathematics. Prof. Ramasubramanian, Prof. M. S. Sriram, Sh.
Pratapanand Jha shared their views under the Chairmanship of Prof. M.
D. Srinivas. The points highlighted by the panel were:

Though there is
greater awareness in the past 2025 years regarding the contribution
of the Kerala School of Astronomy and Mathematics, there is a lack of
resource materials which can be accessed by students and researchers.

Semischolarly
material highlighting the contributions of Kerala School of Astronomy
and Mathematics, and articles on research in this area should be
published and made available to students and researchers.

There are revived
manuscripts which are yet to be studied. Research opportunities in
this area are plenty.

The syllabi in
schools and colleges can incorporate Indian system of mathematics and
astronomy.

Indian system of
mathematics can enhance creativity and intuition in students, as there
could be several methods to arrive at the solutions.

Indian medical
education system should make indigenous systems mandatory.

More research should
be taken up in the areas of mathematics and astronomy.

Research should be
linked to education.

Sanskrit could be
made mandatory in schools.

Most of the
mathematics taught in schools are of Indian origin. This should be
made clear to the students, so that they could feel proud about their
tradition.

Ancient Indian texts
in mathematics and astronomy could be translated and made accessible
to students.
Math phobia in students can be addressed by making available
simplified methods in local languages.

Scholars should write
text books involving creative usage of verses. Mathematical solutions
could be memorized easily if they are in verses.

Universities should
be flexible to include subjects like astrology and astronomy and make
them at par with other popular subjects.

Researchers should
demand access to manuscripts. Demand for manuscripts could bring about
policy matters which help revive and preserve ancient manuscripts.

Topic 
View / Download 
View 
01 
The Work of Kerala School
of Astronomy and Mathematics  A Scientific Revolution Prior to
European Renaissance by Prof. M. D. Sreenivas, CPS, Chennai 
Abstract 
Video 
02 
An Appraisal of the Poetic
Features of Karaṇapaddhati by Prof. Ramasubramanian, IIT Bombay,
Mumbai 
Abstract 
Video (part 01)
Video (part 02) 
03 
Karanapaddhati: A
Theoretical Guidebook for Preparing Karaṇa and Vākya texts Prof.
M.S. Sriram, Madras University, Chennai 
Abstract 
Video (part 01)
Video (part 02) 
04 
The Fascination of Geometry
in Indian Mathematics, with Special Reference to Kerala
Mathematics by Prof. TG Sarachandran, Deputy Director [Retd.],
Collegiate Education, 
Abstract 
Video 
05 
Significance of Moon
Sentences in Indian Astronomy by Prof. S.Gopalakrishnan Unnithan,
Principal [Retd.], Sree Ayyappa College Chengannur, Bengaluru 
Abstract 
Video 
06 
Proof for an Infinite
Series by Śaṅkara in his Kriyākramakarī, Dr. Vanishri Bhat,

Abstract 
Video 
07 
Exposition on Planetary
Models by Bhāskara, Mādhava and Nīlakaṇṭha Somayājī by Dr.
Upadyayula K.V. Sarma, Amrita University 
Abstract 
Video 
08 
Encoding Systems in Vedic
Mathematics by Lakshmipriya K, Amrita School ofArts and Sciences,
Kochi 
Abstract 
Video 
09 
A Comparison between
Geometric Constructions as Described in ‘Baudhāyana Śulbasūtra’
and the Elements by Sindhurani P.J., Cochin University of Science
and Technology, Cochin 
Abstract 
Video 
10 
Astounding Indian
Intellectual Tradition of Vedic Mathematics as a Febrifuge for
Mathematics Anxiety  Application of ‘Antyayordashake’pi’ Sūtra by
Dr. Smitha S, Sree Narayana Training College, Thiruvananthapuram 
Abstract 
Video 
11 
Kerala School of
Mathematics with Special Reference to the Work of Saṅgamagrāma
Mādhava by Prof. V.P.N.Nampoori, Inter University Centre for
Studies on Kerala Legacy of Astronomy and Mathematics, CUSAT 
Abstract 

12 
Ᾱryabhaṭīya Bhāṣa of
Nīlakaṇṭha Somayājī  Salient Features by Dr. N.K Sundareswaran,
Calicut University Kottayam 
Abstract 

13 
Understanding Vākyas
through Karaṇapaddhati by Dr. Venkateswara Pai, IISER Pune 
Abstract 

14 
Interpolation and Inverse
Interpolation: Kerala’s Golden Contributions by Prof. V. Madhukar
Mallayya, Mohandas College of Engineering and Technology,
Trivandrum 
Abstract 

15 
The Śulba Literature in
Kerala Vedic Tradition  A Study by D.S.Sivanandan, Amrita
University 
Abstract 

16 
The Study of Lunar Motion
in Indian Astronomy by Prof. Madhavan, Thiruvananthapuram 
Abstract 

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