{
 "id": "source/karaji-mactutor",
 "class": "source",
 "slug": "karaji-mactutor",
 "label": {
  "ar": "الكرجي — سيرة ماكتوتر الرياضية",
  "en": "Al-Karaji — MacTutor mathematical biography",
  "ur": "الکرجی — میک ٹیوٹر کی ریاضیاتی سوانح"
 },
 "summary": {
  "ar": "سيرة تعرض حساب القوى والمقادير المركبة وحدود الطرق والخلاف في تفسير الابتعاد عن الهندسة.",
  "en": "Biography explaining power arithmetic, composite expressions, methodological limits and differing interpretations of algebra's independence from geometry.",
  "ur": "قوتوں اور مرکب عبارتوں کے حساب، طریقوں کی حدود اور ہندسہ سے الجبرا کی آزادی کی مختلف تعبیرات بیان کرنے والی سوانح۔"
 },
 "stub": false,
 "wings": [],
 "regions": [],
 "periods": [],
 "tags": [],
 "aliases": [],
 "themes": [],
 "data": {
  "kind": "secondary",
  "type": "article",
  "title": "Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji",
  "author": [
   {
    "family": "O'Connor",
    "given": "J. J."
   },
   {
    "family": "Robertson",
    "given": "E. F."
   }
  ],
  "publisher": "MacTutor History of Mathematics, University of St Andrews",
  "issued": {
   "date-parts": [
    [
     1999,
     7
    ]
   ]
  },
  "language": "en",
  "URL": "https://mathshistory.st-andrews.ac.uk/Biographies/Al-Karaji/",
  "open_access": true,
  "reliability_note": "Actual substantive biography, bibliography and July1999 update footer read. The precise birth header is not adopted; names, origins and life dates are uncertain. Technical claims are cited to this biography, including its reports of Crossley, Woepcke, Rashed and al-Samawal; those underlying studies and texts were not independently read. General polynomial division, x^0=1 and fully rigorous modern induction must not be retroactively credited. 'Islamic mathematician' alone is not used as personal Muslim evidence.",
  "status": {
   "review": "published",
   "completeness": 2,
   "generated_by": "Copilot SDK in VS Code"
  },
  "provenance": {
   "generated_by": "Copilot SDK in VS Code",
   "model": "unknown",
   "run": "inventions-p3-b25",
   "source": "Actual mathematical biography, bibliography and update footer read; not search synthesis",
   "extensions": [
    {
     "generated_by": "github-copilot",
     "model": "unknown",
     "run": "inventions-p3-b98",
     "source": "Reread original biography's finite cubic/quartic examples, adjacent-addition translated testimony and limited recursive reasoning. Separate al-Samawal/DSB biographies checked; no primary1972 edition or lost original read. All earlier reliability caveats preserved."
    }
   ]
  }
 },
 "prose": {},
 "degree": 0,
 "contemporaries": [],
 "updated": "2026-11-07",
 "connections": [],
 "related": [],
 "license": {
  "prose": "CC BY-SA 4.0",
  "data": "CC0 1.0"
 }
}