{"id":"madhava","domain":"indian-mathematics","type":"Person","title":"Mādhava of Saṅgamagrāma","slug":"madhava","url":"/mathematics/indian-mathematics/madhava/","active":"c. 1340 – c. 1425 CE","location":"Saṅgamagrāma, Kerala, India","founded":"Kerala School of Astronomy and Mathematics","summary":"Discovered infinite series for π, sine, cosine ~250 years before Gregory/Leibniz/Newton. No original writings survive; known through successors (Nīlakaṇṭha, Jyeṣṭhadeva).","key_contributions":["π/4 = 1-1/3+1/5-1/7+... (Mādhava-Leibniz series)","arctan(x) series (Mādhava-Gregory series)","sin(x), cos(x) infinite series (Taylor series equivalent)","π to 11 decimal places"],"added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Plofker, K. (2009). Mathematics in India. Princeton University Press.","pages":"217–253"},{"tier":1,"citation":"Sarma, K.V. (ed./transl.) (2008). Gaṇita-Yukti-Bhāṣā of Jyeṣṭhadeva. Springer."},{"tier":2,"citation":"Katz, V.J. (1995). Ideas of calculus in Islam and India. Mathematics Magazine, 68(3), 163-174."},{"tier":2,"citation":"Bressoud, D. (2002). Was calculus invented in India? The College Mathematics Journal, 33(1), 2-13."},{"tier":3,"citation":"Joseph, G.G. (2011). The Crest of the Peacock. 3rd ed. Princeton University Press."}],"relationships":[{"type":"anticipated","target":"limit","label":"Limit — infinite series techniques"},{"type":"successor_to","target":"bhaskara-ii","label":"Bhāskara II"},{"type":"part_of_tradition","target":"indian-mathematics-overview","label":"Indian Mathematics"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.5"}