Person · Kerala school astronomer-mathematician
Madhava of Sangamagrama
Also known as Mādhava of Sangamagrāma, Mādhavan, Sangamagrama Madhava, Golavid
Madhava of Sangamagrama (c. 1340–c. 1425) was the astronomer-mathematician credited with founding the Kerala school of astronomy and mathematics. Almost none of his own writing survives: his infinite series for sine, cosine, arctangent and pi are known mainly because Nilakantha Somayaji's Tantrasangraha and Jyeshthadeva's Malayalam Yuktibhasa name him as their source, centuries before Gregory and Leibniz. His pupil Parameshvara began the teacher-to-pupil chain that carried the school into the seventeenth century.
- Date
- c. 1340 – c. 1425
- Function
- Science & medicine
- Confidence
- Mixed / layered
Worth knowing
The series π/4 = 1 − 1/3 + 1/5 − 1/7 … is now often called the Madhava–Leibniz series, and Madhava also gave correction terms for the error left after stopping at n terms. A faster series he derived from it gives pi correct to eleven decimal places from its first 21 terms.
Which results are Madhava's own and which his successors' is debated, because most of his works are lost and the series survive in later texts. 'Sangamagrama' is usually identified with Irinjalakuda, but the Wikipedia biography argues for Kudallur on the Nila; his dates are inferred from those of his pupil Parameshvara.
Connections (5)
- Associated withSangamagrama
Later Kerala astronomers almost always call him 'Sangamagrama Madhava', so the place-name is the one fixed fact of his biography. His own lunar treatise, the Venvaroha, says he was born in a house called bakuladhishthita vihara, Sanskrit for the Malayalam Ilaññippaḷḷi, and a manuscript at the Oriental Institute, Baroda, calls him Mādhavan Ilaññippaḷḷi Emprān. Where Sangamagrama lay is argued: the common view says Irinjalakuda, while the Wikipedia biography prefers Kudallur on the Nila.
- Traditional linkSangameshwara / Bharata, Irinjalakuda
The usual identification of Sangamagrama with Irinjalakuda rests largely on this temple: its presiding deity is worshipped as Sangameswara, lord of the confluence, so Sangamagrama can be read as the village of Sangameswara. The Kerala school article accepts the identification and places the school's founding at Irinjalakuda. The Madhava biography calls the ground for it thin, notes that there is no river confluence near the town, and proposes Kudallur on the Nila instead.
- Teaching lineageNilakantha Somayaji
Nilakantha Somayaji's Tantrasangraha of about 1500 is the main early text that names Madhava as the source of the infinite series for sine and arctangent. The tie between them is a documented chain of pupils: Madhava taught Parameshvara, and Parameshvara's son Damodara counted Nilakantha among his disciples, according to a palm-leaf Malayalam commentary on the Surya Siddhanta. Without Nilakantha's attributions, Madhava's share in the Kerala series would be largely invisible.
- TransmissionJyeshthadeva
Jyeshthadeva, a disciple of Nilakantha, wrote the Yuktibhasa in Malayalam around 1530, and it is there that Madhava's arctangent series appears with a derivation and proof rather than as a bare verse result. The text spells out the iteration — multiply by the square of the sine, divide by the square of the cosine, then divide the terms by the odd numbers — that yields what is now called the Madhava–Gregory–Leibniz series, more than a century before Gregory.
- PrecursorBhaskara II
Madhava's power series grew out of the older Sanskrit astronomical tradition rather than breaking with it. The Wikipedia account notes that he extended results already found in the work of Bhaskara II, and that mathematical astronomy in Kerala had long run on the Aryabhatiya tradition and Haridatta's Parahita system. What Madhava and his successors did not do was unite derivative and integral under general ideas, so the comparison with European calculus is partial.
Sources
Wikipedia, "Madhava of Sangamagrama"; "Kerala school of astronomy and mathematics". K. V. Sarma, A History of the Kerala School of Hindu Astronomy (1972).
Open Madhava of Sangamagrama in the repository →