Iranian Journal for the History of Islamic Civilization

Iranian Journal for the History of Islamic Civilization

Mechanisms of Knowledge Transmission in the Mathematical Sciences within the Teacher–Student Educational Tradition (3rd–5th Centuries AH / 9th–11th Centuries CE)* *

Document Type : Research Paper

Authors
1 Postdoctoral Researcher, Postdoctoral Researcher, Department of History and Civilization of Islamic Nations, Faculty of Theology and Islamic Studies, University of Tehran, Tehran, Iran
2 Professor, Department of History and Civilization of Islamic Nations, Faculty of Theology and Islamic Studies, University of Tehran
Abstract
The third to fifth centuries AH mark the formative period of informal scientific networks in the history of Islamic mathematics – an era when mathematical knowledge was transmitted not through centralized institutions but through master–disciple relationships. Adopting a descriptive-analytical method and historical approach, this study examines the following question: in the absence of formal educational structures, what mechanisms sustained the transmission and continuity of mathematical knowledge within scholarly ties between masters and students? Four main mechanisms are explored: study circles (ḥalaqāt) as the primary setting for instruction and debate; scholarly journeys (riḥalāt) as a means of transferring knowledge and connecting intellectual centers across regions; scholarly titles (alqāb) as tools for consolidating prestige, competence, and academic standing; and licensure (Eǰāzeh) as a device for legitimizing knowledge transmission and affirming the scholarly bond between master and disciple. Although classical classifications of the mathematical sciences include arithmetic, geometry, astronomy, and theoretical music, this study – because it focuses on computational mathematics and the astronomical sciences – excludes theoretical music from its scope. The findings reveal that the transmission of mathematical knowledge during this period resulted from an interplay between pedagogical models derived from religious sciences and the epistemological and practical demands of the mathematical disciplines. This interaction enabled Muslim mathematicians, without relying on formal institutions, to teach, train disciples, and sustain scientific traditions. The synergy among study circles, scholarly journeys, titles, and licensure not only reinforced the continuity of scholarly chains but also facilitated the production, reproduction, and expansion of mathematical knowledge within Islamic civilization
Keywords
Subjects

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Volume 59, Issue 1
(Spring & Summer 2026)
September 2026
Pages 73-99

  • Receive Date 18 May 2026
  • Revise Date 04 July 2026
  • Accept Date 07 August 2026