ESHS/HSS Annual Meeting

Perspectives on the Integration of Muslim Mathematical Productions into the History of Calculus: Steps Towards a Rebuilding of Narratives

• In Event: Euclid and Geometry Across Traditions

English Abstract

Muslim mathematical production between the 7th and 14th centuries is often integrated into the history of mathematics by focusing primarily on two areas: the original development of algebra—mostly limited to Al-Khwarizmi’s works—and the preservation and transmission of Greek productions prior to the 3rd century CE. Both classic and recent works (e.g. Bressoud, 2019; Kline, 1985), while focusing on the history of calculus, takes as a starting point the exhaustion method developed in Greece from Eudoxus to Archimedes, and then shifts to the the symbolic algebra of Viète and Descartes' La Géométrie. The geometrization of algebra is considered fundamental to progress in the area-calculation problem which later takes place. However, as Rashed (2012, 2013) systematically shows, Muslim scholars between the 9th and 12th centuries had already addressed these questions thoroughly as part of a broader scientific research program, even without symbolic algebra or Cartesian representation.

The individual contributed paper seeks to contest traditional Western-centric narratives by integrating marginalized voices into the existing canon of calculus through a specific case study: the interplay between the emergence of algebra and the evolution of techniques for area and volume calculation among professional Muslim scholars of the 9th–12th centuries.

Bressoud, D. M. (2019). Calculus Reordered: A History of the Big Ideas. Princeton University Press. https://doi.org/10.2307/j.ctvc778s8
Kline, M. (1985). Matemáticas: la pérdida de la certidumbre. Siglo XXI Editores. España.
Rashed, R. (2013). Ibn al-Haytham and analytical mathematics: A history of Arabic sciences and mathematics (Vol. 2) (S. Glynn & R. Wareham, Trads.). Routledge.
Rashed, R. (2012). Founding figures and commentators in Arabic mathematics: A history of Arabic sciences and mathematics (Vol. 1) (R. Wareham, C. Allen & M. Barany, Trads.; N. El-Bizri, Ed.). Routledge

Author

• NICOLAS ELIAS DANIEL IGOLNIKOV, Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales, Centro de Formación e Investigación en Enseñanza de las Ciencias (CEFIEC)