Kerala School of Astronomy and Mathematics: Contributions and Contemporary Relevance

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 1600-year 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. 1340-1425 CE), Parameśvara of Vaṭasseri (c. 1360-1460 CE), and Nilakaṇṭha Somayājī of Kelallur (c 1443-1560 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:

1. Introduction of Vakya System of computation of planetary longitudes by Vararuchi in 4th century which enormously simplified the calculations involved.
2. Madhava in 14th century enunciated the verses that present infinite series expansion for pi and other trigonometric functions like sine and cosine.
3. 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 post-lunch 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:

1. Though there is greater awareness in the past 20-25 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.
2. Semi-scholarly 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.
3. There are revived manuscripts which are yet to be studied. Research opportunities in this area are plenty.
4. The syllabi in schools and colleges can incorporate Indian system of mathematics and astronomy.
5. Indian system of mathematics can enhance creativity and intuition in students, as there could be several methods to arrive at the solutions.
6. Indian medical education system should make indigenous systems mandatory.
7. More research should be taken up in the areas of mathematics and astronomy.
8. Research should be linked to education.
9. Sanskrit could be made mandatory in schools.
10. 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.
11. 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.
12. Scholars should write text books involving creative usage of verses. Mathematical solutions could be memorized easily if they are in verses.
13. Universities should be flexible to include subjects like astrology and astronomy and make them at par with other popular subjects.
14. 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 Guide-book 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