Madhava of Sangamagrama
Mādhava of Sangamagrāma (Mādhavan)[4] (c. 1340 – c. 1425) was an Indian mathematician and astronomer who is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages.
Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry and algebra.
He was the first to use infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity".
However, from scattered references to Madhava found in diverse manuscripts, historians of Kerala school have pieced together information about the mathematician.
In his short work on the moon's positions titled Veṇvāroha, Madhava says that he was born in a house named bakuḷādhiṣṭhita .
But there are several places in Karnataka with samgama or its equivalent kūḍala in their names and with a temple dedicated to Samgamḗsvara, the lord of the confluence.
)[5] There is a small town on the southern banks of the Nila river, around 10 kilometers upstream from Tirunavaya, called Kūḍallūr.
Incidentally there is still existing a Nambudiri (Malayali Brahmin) family by name Kūtallūr Mana a few kilometers away from the Kudallur village.
[7] Thus the most plausible possibility is that the forefathers of Madhava migrated from the Tulu land or thereabouts to settle in Kudallur village, which is situated on the southern banks of the Nila river not far from Tirunnavaya, a generation or two before his birth and lived in a house known as Ilaññippaḷḷi whose present identity is unknown.
c. 1300, a set of fragmentary results[8]), it is clear from citations that Madhava provided the creative impulse for the development of a rich mathematical tradition in medieval Kerala.
The 16th-century text Mahajyānayana prakāra (Method of Computing Great Sines) cites Madhava as the source for several series derivations for π.
[8] In the mid-20th century, the Russian scholar Jushkevich revisited the legacy of Madhava,[10] and a comprehensive look at the Kerala school was provided by Sarma in 1972.
According to a palm leaf manuscript of a Malayalam commentary on the Surya Siddhanta, Parameswara's son Damodara (c. 1400–1500) had Nilakantha Somayaji as one of his disciples.
Among his many contributions, he discovered infinite series for the trigonometric functions of sine, cosine, arctangent, and many methods for calculating the circumference of a circle.
[24] However, they did not combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between the two, or turn calculus into the powerful problem-solving tool we have today.
[25] K. V. Sarma has identified Madhava as the author of the following works:[26][27] The Kerala school of astronomy and mathematics, founded by Madhava, flourished between the 14th and 16th centuries, and included among its members Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
The group is known for series expansion of three trigonometric functions of sine, cosine and arctant and proofs of their results where later given in the Yuktibhasa.
[9] The Kerala school also contributed to linguistics (the relation between language and mathematics is an ancient Indian tradition, see Kātyāyana).
Madhava has been called "the greatest mathematician-astronomer of medieval India",[3] some of his discoveries in this field show him to have possessed extraordinary intuition".
[29] O'Connor and Robertson state that a fair assessment of Madhava is that he took the decisive step towards modern classical analysis.
At the time, the port of Muziris, near Sangamagrama, was a major center for maritime trade, and a number of Jesuit missionaries and traders were active in this region.
