The Mathematics of Medieval Islam: Epistemological Foundations, Structural Innovations and the Scientific Legacy of the Arabic Tradition (8th–14th Centuries)

This article undertakes a historical-epistemological and mathematical analysis of the body of knowledge produced by scholars of the medieval Islamic world between the 8th and 14th centuries — a period commonly designated in historiography as the Golden Age of Islam. Countering Eurocentric narratives that reduced this tradition to a role of preserving and transmitting the Greek legacy, this study demonstrates, through rigorous analysis of primary sources and specialized secondary literature, that medieval Arabic mathematics constituted an autonomous, innovative intellectual tradition that structurally transformed the universal mathematical corpus. The investigation is organized around eight central thematic axes: (1) the systematization of algebra by Muḥammad ibn Mūsā al-Khwārizmī and its elaborations by Abū Kāmil, al-Karajī, al-Samawʾal, and Omar Khayyam; (2) arithmetic and the decimal positional numeral system; (3) contributions to plane and spherical trigonometry; (4) advances in number theory; (5) combinatorics and the arithmetic triangle; (6) geometry with proto-non-Euclidean consequences; (7) contributions to proto-calculus; and (8) applied mathematics in optics, astronomy, and geodesy. It is concluded that the Arabic mathematical tradition constituted a generative — rather than merely transmissive — link in the history of universal mathematics.