Madhava of Sangamagrama - Kerala Mathematician

Our country, India, was rich in the field of mathematics from very early periods dating back to B.C. 3000 or more. Numbers with decimal system, geometry, astronomy and related fields had developed during those periods as per the excavations made at places such as Mohenjadaro and Harappa on the banks of river Sindh. Vedas also provide light into the application of various mathematical methods. Connected with yagas (a ritual to please Gods) and other rituals, determination of suitable time, construction of yaga place, etc. are decided using mathematical methods. The counting numbers including zero (0,1,2, ......,9) which are now used throughout the world are said to have originated here. It is referred sometimes as Arabic numerals, since the Europeans got them from Arabs who had commercial relationships with India from very early periods. Through this connection Arabs got these numerals from India.

When talking about Indian mathematicians the name of Arya bhata I (475 – 550 AD) comes first. According to certain historians the birth place of Arya bhata was in Kerala, though he later shifted to Patna. However after this there is a big gap in the mathematical history of Kerala. However, Kerala has a golden history of Mathematics between 14 and 17 centuries. There are various names already identified as Mathematicians belonging to Kerala, such as Sangamagrama Madhavan, Vadassery Parameswaran, Kelallur Neelakanta Somayaji, Chithrabhanu, Narayanan, Jyeshtadevan, Puthumana chomathiri, Achutha Pisharoti, Sankara Variyar, Sakara varman and so on. Only through some of the known works certain details about these great people are known.

Four works related to Kerala mathematics and astronomy of those periods are generally considered as 'Thantra samgraha' of Neelakantan, 'Yukthi bhasha' of Jyeshtadevan, 'Karana paddhathy' of Puthumana chomathiri and 'Sadrathna mala' of Sankara varman.

One of the names among the Kerala Mathematicians whose works are well recognised is that of Sangama grama Madhavan. His name is connected with the village to where he belonged. It is Sangama Gramam, it is related to the name of a temple 'Sangameswara kshethram' near Irinjalakkuda in Thrissur district. His life period is considered to be during 1350 to 1425 AD. Much biographical details of Madhavan are not available. He belonged to Embranthiri community, a sub- group of Brahmin community. It is believed that these people migrated from coastal Karnataka regions. In his book 'Venvaroham' certain mentions are there about his village and house. This information helped to identify the village as Sangama gramam. The house name as indicated in the above work is 'Ilaininna palli' (Two houses with slightly modified names are still there near Irinjalakkuda Railway station at Kallettumkara in Irijalakkuda).

Sangamagrama Madhavan is one of the greatest names among the ancient Indian astronomers. He is recognised also as a pure mathematician. His known works include 'Venvaroham', 'Lagnaprakaram', 'sphutachandrapthi', 'Mahagyanayana prakaram', 'Madhyayanayanaprakaram', 'Aganitham' and 'Aganitha panchangam'. Most of this works are based on Vararuchi's 'Chandravakya Padhathi'. Vararuchi's method only could calculate the position of moon to the nearest minute, where as Madhavan did it to seconds correctness, which is described in 'Venvaroham'. The mathematical principles involved in this method were far advanced than what were available during those periods. He has used the principles of integration and infinite series.

From the works of Madhavan's disciples and successors in the field such as Neelakantan, Jyeshtadevan, Narayanan and Sankara Varier more references to Madhavan's contributions are available. Some of them are very important results in modern mathematics. His results include the derivation of infinite series for circular and trigonometric functions (it is popular as Gregory series for arc-tangent), infinite series for the mathematical constant 'Pi' (the ratio of the circumference of a circle to its diameter) and the Newton Power series expansion for sine and cosine (This is known in Newton's name because in Europe this appeared in 1676 in a letter written by Newton to the Secretary of Royal Society).

Similarly the series related to the value of 'Pi' invented by Madhavan in the 14th century was re-invented by Gregory in 1671 and Leibniz in 1673. The infinite series for arc-tangent was developed by James Gregory of Scotland in the year 1667 and hence it is known as Gregory series, but now having seen that the same was invented about two and a half century back by Madhavan, the series has been re-named as Madhava – Gregory series. Similarly the Newton's power series expansion for sine and cosine is now known as Madhava – Newton series.

Madhavan is referred to in certain references as 'Golavid' meaning 'a learned man about the globe', mainly because of his works in the field. His works have highly influenced the works of Parameswaran, Neelakantan, Jyeshtadevan and others. Madhavan can be even considered as the introducer of topic Mathematical Analysis, since his attempts in this field are notable. His intuitive approach in solving problems can be compared with that of great Sreenivasa Ramanujan (1887 – 1920).

Further studies are needed to find out the Madhavan's total contributions in the field of Mathematics. One thing is certain that he stood above all mathematicians of his period and had shown his intuitive powers in the formation of theories and solving them. He had discovered several results in trigonometry and infinite series much earlier than these were rediscovered by European Mathematicians.