The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations

Cambridge University Press (2004)
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Abstract

The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized solution we see a transition to a practice of mathematics based on the systematic approach. With three chapters ranging chronologically from Hellenistic mathematics, through late Antiquity, to the medieval world, Reviel Netz offers an alternate interpretation of the historical journey of pre-modern mathematics.

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Reviel Netz
Stanford University

Citations of this work

In defence of geometrical algebra.Viktor Blåsjö - 2016 - Archive for History of Exact Sciences 70 (3):325-359.
The natures of numbers in and around Bombelli’s L’algebra.Roy Wagner - 2010 - Archive for History of Exact Sciences 64 (5):485-523.
Medieval Arabic Algebra as an Artificial Language.Jeffrey A. Oaks - 2007 - Journal of Indian Philosophy 35 (5-6):543-575.

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