Madhava of Sangamagrama

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Madhava of Sangamagrama : biography

Irinjalakuda was once known as ‘Irińńāţikuţal’. Sangamagrāmam (lit. sangamam = union, grāmam = village) is a rough translation to Sanskrit from Dravidian word ‘Irińńāţikuţal’, which means ‘iru (two) ańńāţi (market) kǖţal (union)’ or the union of two markets. "Madhava" also means "Love War" sangamagramian

Kerala School of Astronomy and Mathematics

The Kerala school of astronomy and mathematics flourished for at least two centuries beyond Madhava. In Jyeṣṭhadeva we find the notion of integration, termed sankalitam, (lit. collection), as in the statement:

ekadyekothara pada sankalitam samam padavargathinte pakuti,

which translates as the integration a variable (pada) equals half that variable squared (varga); i.e. The integral of x dx is equal to x2 / 2. This is clearly a start to the process of integral calculus. A related result states that the area under a curve is its integral. Most of these results pre-date similar results in Europe by several centuries. In many senses, Jyeshthadeva’s Yuktibhāṣā may be considered the world’s first calculus text.

The group also did much other work in astronomy; indeed many more pages are developed to astronomical computations than are for discussing analysis related results.

The Kerala school also contributed much to linguistics (the relation between language and mathematics is an ancient Indian tradition, see Katyayana). The ayurvedic and poetic traditions of Kerala can also be traced back to this school. The famous poem, Narayaneeyam, was composed by Narayana Bhattathiri.

Influence

Madhava has been called "the greatest mathematician-astronomer of medieval India", or as "the founder of mathematical analysis; some of his discoveries in this field show him to have possessed extraordinary intuition." O’Connor and Robertson state that a fair assessment of Madhava is that he took the decisive step towards modern classical analysis.

Possible propagation to Europe

The Kerala school was well known in the 15th and 16th centuries, in the period of the first contact with European navigators in the Malabar Coast. 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. Given the fame of the Kerala school, and the interest shown by some of the Jesuit groups during this period in local scholarship, some scholars, including G. Joseph of the U. Manchester have suggested

that the writings of the Kerala school may have also been transmitted to Europe around this time, which was still about a century before Newton. While no European translations have been discovered of these texts, it is possible that these ideas may still have had an influence on later European developments in analysis and calculus. (See Kerala school for more details). 

This is due to wrong understanding of the authors concerned. It was almost impossible for the Jesuits in the 16th century, who are experts with the eminence of Madhava or his disciples, to study Sanskrit and Malayalam and to transmit them to European mathematicians, instead of they themselves claiming the credit for the discovery.

Madhava’s works

K.V. Sarma has identified Madhava as the author of the following works:

  1. Golavada
  2. Madhyamanayanaprakara
  3. Mahajyanayanaprakara
  4. Lagnaprakarana (लग्नप्रकरण)
  5. Venvaroha (वेण्वारोह)
  6. Sphutacandrapti (स्फुटचन्द्राप्ति)
  7. Aganita-grahacara (अगणित-ग्रहचार)
  8. Candravakyani (चन्द्रवाक्यानि)

Historiography

Although there is some evidence of Mathematical work in Kerala prior to Madhava (e.g., Sadratnamala c. 1300, a set of fragmentary results), it is clear from citations that Madhava provided the creative impulse for the development of a rich mathematical tradition in medieval Kerala. However, most of Madhava’s original work (except a couple of them) is lost. He is referred to in the work of subsequent Kerala mathematicians, particularly in Nilakantha Somayaji’s Tantrasangraha (c. 1500), as the source for several infinite series expansions, including sinθ and arctanθ. The 16th-century text Mahajyānayana prakāra cites Madhava as the source for several series derivations for π. In Jyeṣṭhadeva’s Yuktibhāṣā (c. 1530),