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 (and grounded in the polemical practices of
early Greek science) we see a transition to a practice of
mathematics based on the systematic approach (and grounded in the
deuteronomic practices of Late Antiquity and the Middle Ages). 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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