The Legacy Of Kerala Mathematics

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The renowned  poet Kodungallur Kunjikkutan Thampuran in his work   ‘Keralaprathishta’, comments that  Kerala,  with Kanyakumari as  the southern part  and Gokarna, a range of mountains as the northern part    is  a land of virtue  blessed by Lord Siva and Lordess  Parvathi .   Out of such blessings Kerala has contributed much to the world of Mathematics  which emanate from the boundaries of this meritorious land. Mathematics  and Astronomy which are co travelers  got unparalleled growth and developments in the fertile soil of Kerala.  Mathematicians from Kerala made significant inventions regarding planetary movements years before their  European counterparts  Kepler, Kopernicus, Galelio and Newton started similar studies. In Upanishads and Vedas, there were observations regarding planetary movements , their positions and their effect on the day to day life. The major contribution of the  school of mathematics in Kerala  was to support and supplement these observations by structuring  a strong platform of  mathematics. The kerala school of mathematics which can be specified  as the first Indian school of mathematics is the place where the mathematical relation between the movements of the sun, the moon and the earth  was subjected for a deeper study and obtained very decisive results. Along with this,  how the position of planets and heavenly bodies affect whether, environment and the agricultural needs of this land were also the subjects of study in the Kerala school.

The study of mathematics in Kerala was   motivated and intensified from the works of the 4th century   Indian Mathematician Aryabhata.  The nobility and accuracy of the inventions of Aryabhata influenced further research and studies. The commentaries on the works of Aryabhata and Bhaskara oriented Kerala mathematics to a solemn direction and improved its unique growth. The books, ‘Mahabhaskareeyabhaashyam’ by the 8th century mathematician   Govinda Swami and Laghubhaskareeyavivaranam by the 9th  century mathematician   Sankara Narayanan ,   are detailed commentaries on the works of Bhaskara which piloted its further growth. A trigonometric table to calculate the position of heavenly bodies was included in these commentaries. Invoked by  the works of Aryabhata, the kerala school of mathematics turned to a new path of its development through the cryptographical works ‘the katapayadi system’ of the 7th century mathematician Haridathan.  It is  worth to mention that Haridathan authored two books grahakaranibandhanam and mahamarganibandhanam  which explain the mathematical calculations of Astronomy in detail.  Our mathematicians engaged in the mathematical studies of planetary objects by examining  Aryabhateeyam, the mathematical testament of the theory of Astronomy by Aryabhata in length and breadth. Meanwhile other branches of Mathematics  such as trigonometry, number theory, algebra and geometry got recruited   for the purpose of further detailed commentaries on Aryabhateeyam and for the use of common man. The legacy of Kerala school of mathematics is mainly because of the parallel progress of Mathematics and Astronomy to solve the problems raised by Aryabhata and for its elaborate verbalizations.

The first significant mathematician of the kerala school was  Narayana Pandit who was born in 1340 and opened a delusory world of mathematics through his fundamental works beejaganithaavathamsa and ganithakaumudi. He was attracted by the works of Bhaskara II and continued his studies on the path laid by him.  He wrote a dissertation named  Karmapradeepika on Leelavathy of Bhaskara and explained several methods to find square and square roots of numbers along with the procedures to solve a quadratic equation. Madhava  who was born in the  Aloor village of Irinjalakkuta , Trichur known earlier as Samgamagrama was the first  kerala mathematician who gave new colourful dimensions to the study of astronomy with mathematical flavour. He  made profound studies on infinite series and found   approximations to trigonometrical functions in terms of infinite series. Because of his invaluable works he is considered as an eminent preceptor of the middle aged kerala school of mathematics. The ‘infinite tangent series’ he studied was   rediscovered by  Joseph Gregory in Europe after some 300 years in 1667   is an interesting fact to mention. It is  beyond doubt that the contributions of Madhava was far above excellence when his European followers were considered.  It was Madhava who obtained an infinite series approximation  to Pi,  a stunner forever  in the world of Mathematics. The fact, that    only after 400 years a European mathematician   was able to find the same infinite series adds a feather to the cap of the great kerala mathematician Madhava.  It is s an illustrious quantum leap  to declare that it was Madhava who sowed the seeds of Calculus which later started ruling all practical platforms of mathematics.

 Vattasseril Parameswaran born at Alathur in 1370 is another keral mathematician who studied mathematical facts in astronomy in depth. In his book ‘Karmadeepika’ which is an explanatory note on Mahabhaskareeyam, he presented several invaluable information regarding movements of planets, shapes of their orbits, mathematical methods to determine their position and eclipses. In the interpretation of Aryabhateeyam, Parameswara described several methods for the calculation of time based on the length of the shadow of an object. In ‘Leelavathybhashyam’, a rendition of Leelavathy of Bhaskara II he elaborated the theory of Calculus initiated by Madhava. Several  mathematical results  regarding tides were presented in Sidhanthadeepika another commentary to Mahabhaskareeyabhaashyam. Trigonometrical relations which help to find the tide-table were studied explicitly  in this work.

Another Kerala mathematician who followed the legacy of Madhava was Neelakantasomayaji born at thrikkantiyoor near Tirur in 1440. He, a maestro in astronomy and philosophy was a deciple of Damodara, son of Parameswara. Thanthrasamgraha , authored by Somayaji is considered to be a very fundamental book on astronomy during that period. In this work he gave scientific explanations for the movement of planets along their orbits and reasons for their  elliptic shapes. The coordinate wise representation of positions of the sun, the earth and the moon was also mentioned  there. The practical use of mathematics in astronomy, distance between the sun, the earth and the moon and scientific explanations for the  solar system were brought in through his works Golasaram, Sidhanthadarppanam, Chandrachayaganitham and Grahanirnayam.

This divine land of kerala witnessed the mathematical talent of the great mathematician Jyeshtadeva through his dogmatic work Yukthibhasha after Neelakantasomayaji. Yukthibhasha which expounded the mathematical results of Thanthrasamgraha in simplex language popularized mathematics and astronomy through its  432 stanzas .  The intricacies of the solar system, the science behind the elliptic shapes of orbits which was to be explained by Kepler after 100 years, the position of planets during eclipses , the rising and setting of the sun and the moon, the amount of light reflected by the moon and the  procedures to find the tide-table were some of the major subjects of study in Yukthibhasha. The fact that the European mathematics community headed by Coppernicus,  , Kepler, Tychobrahe and  Galelio was able to find similar results only after 100 years from  the incomparable  contributions made by the  Kerala Mathematicians makes us  tingle with pride.

Several other mathematicians including Achuthappisharadi who authored Karanottam dealing with the lattitude – longitude studies, Uparagakriyakarmam dealing with the lunar- solar eclipses, Chithrabhanu authored Kriyakarmakari also added fame to the Kerala legacy of Mathematics. 

During the period from 14th to  16th  century Indian mathematics was enriched with  the contributions from the Kerala school of Mathematics. Kerala sowed the seeds for many fabulous inventions and findings in Mathematics which the entire world observed with great astonishment later. We must say that the lack of a suitable  language of communication decelerated further studies and the spreading of the already known results before the general public. We painfully realize  that the so-called  mathematical discoveries of the west especially that from Europe are nothing but the extension of the findings of the  Kerala School. Yet it is  an unchallengeable dominion  that with  the contributions of Madhava, Neelakanta, Parameswara, Sankaravaryar,  Jyeshtadeva and a host of mathematicians,  Kerala got established itself  in the mathematical and astronomical atlas of the world. Its our obligation  to proclaim, propagate and promote the Kerala legacy of Mathematics.

References: G.G.Joseph, A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact, Sage India, 2009. Kim Plofker, Mathematics in India, Pinceton University Press, 2009. C.S.Seshadri, Studies in the History of Indian Mathematics, Hindusthan Book Agency ,2010. G.G.Joseph, Kerala Mathematics: History and Its Possible Transmission to Europe,BR Publishing Corporation, 2011.

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