Infinite series for pi, sine and arctangent
AI-drafted · awaiting admin review
Madhava of Sangamagrama in Kerala (c. 1350–1425) found infinite series for sine, cosine, arctangent and pi about 250 years before Newton, Gregory and Leibniz.
India first (well documented)Mathematics & astronomy
Indian claim
The series known as Gregory's, Leibniz's and Newton's were found first by Madhava and the Kerala school.
Evidence for the Indian claim
- Later Kerala texts, Nilakantha Somayaji's Tantrasangraha (c. 1500) and Jyeshthadeva's Yuktibhasa (c. 1530), give the series and clearly attribute them to Madhava.
- The Yuktibhasa gives derivations, not just results, and Madhava added correction terms that make the pi series converge fast.
- Madhava computed pi correct to 11 decimal places (MacTutor).
Commonly credited to
Newton (sine and cosine, 1669), James Gregory (arctangent, 1671) and Leibniz (series for pi/4, 1673–74) discovered these series in Europe.
Evidence for the other claim
- No work of Madhava himself containing the series survives; they are known through his followers.
- The European discoveries were made without any documented knowledge of the Kerala texts.
What historians and scientists say
Historians accept that the Kerala school had these series about two and a half centuries before Europe. Many now call them the Madhava–Leibniz, Madhava–Gregory and Madhava–Newton series.