{"id":"bhaskara-ii","domain":"indian-mathematics","type":"Person","title":"Bhāskara II","slug":"bhaskara-ii","url":"/mathematics/indian-mathematics/bhaskara-ii/","born":"1114 CE","born_place":"Vijjadavida, India","died":"c. 1185 CE","position":"Head of astronomical observatory, Ujjain","summary":"Completed the chakravāla method for Pell's equation. Worked with concepts anticipating differential calculus (maxima/minima). Wrote Līlāvatī and Bījagaṇita.","key_contributions":["Completed chakravāla method (Pell's equation)","Derivative-like concept: quantity vanishes at maximum","Proposed a/0 = infinity","Pythagorean theorem rearrangement proof"],"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":"181–211"},{"tier":1,"citation":"Colebrooke, H.T. (1817). Algebra, with Arithmetic and Mensuration. John Murray."},{"tier":2,"citation":"Katz, V.J. (1995). Ideas of calculus in Islam and India. Mathematics Magazine, 68(3), 163-174."},{"tier":3,"citation":"Joseph, G.G. (2011). The Crest of the Peacock. 3rd ed. Princeton University Press."}],"relationships":[{"type":"extended","target":"brahmagupta","label":"Brahmagupta's Chakravāla method"},{"type":"anticipated","target":"derivative","label":"Derivative — maxima/minima"},{"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"}