{
  "id": "brahmagupta",
  "domain": "indian-mathematics",
  "type": "Person",
  "title": "Brahmagupta",
  "slug": "brahmagupta",
  "url": "/mathematics/indian-mathematics/brahmagupta/",
  "born": "598 CE",
  "born_place": "Bhillamāla (Bhinmal), Rajasthan, India",
  "died": "c. 668 CE",
  "position": "Head of astronomical observatory, Ujjain",
  "summary": "Indian mathematician and astronomer. First to give systematic rules for arithmetic with zero and negative numbers. Author of the Brāhmasphuṭasiddhānta (628 CE).",
  "key_contributions": [
    "First systematic arithmetic rules for zero (BSS Ch. 18, 628 CE)",
    "Rules for negative numbers",
    "Brahmagupta's formula for area of cyclic quadrilateral",
    "Brahmagupta–Fibonacci identity",
    "Study of Pell's equation (chakravāla method)"
  ],
  "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": "150–181" },
    { "tier": 1, "citation": "Colebrooke, H.T. (1817). Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara. John Murray, London." },
    { "tier": 2, "citation": "O'Connor, J.J. and Robertson, E.F. (2000). Brahmagupta. MacTutor.", "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Brahmagupta/" },
    { "tier": 3, "citation": "Joseph, G.G. (2011). The Crest of the Peacock. 3rd ed. Princeton University Press.", "pages": "223–248" }
  ],
  "relationships": [
    { "type": "major_work", "target": "brahmasphutasiddhanta", "label": "Brāhmasphuṭasiddhānta (628 CE)" },
    { "type": "concept_introduced", "target": "zero", "label": "Zero arithmetic rules" },
    { "type": "influenced_by", "target": "aryabhatiya", "label": "Āryabhaṭa (disputed and extended)" },
    { "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": "1.2"
}