The Origins of Algebra : From al-Khwarizmi to Descartes. International Workshop held at Bercelona, 27-29 March 2003

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Renaissance algebra, its relationship to medieval Arabic (or Islamic, to be more precise) algebra, and the ways in which algebraic knowledge traveled from one culture to another and was transformed by the journey have always been topics of considerable interest to historians of mathematics. Of course the focus of the historian’s interest has not always been the same. Decades ago, the stories regarding the early 16th-century discovery of general methods to solve third- and fourth-degree equations, including vicious quarrels between Italian mathematicians, commanded much attention. The generality of the methods and notations employed and the nonappearance of a notion of number broad enough to encompass negative and imaginary quantities, were also of much concern. The 'conflicts' between algebra and geometry were also prominent subjects of interest for historians of algebra in early modern Europe. It was generally understood—and this particular interpretation of the history of mathematical thought in the 16th and 17th centuries is somehow still alive today, at least in textbooks and popularizations of the history of mathematics—that algebra played a 'progressive' role against the 'conservative,' old-fashioned understanding of mathematical objects in geometrical terms."


This article was originally published in Historia Mathematica, volume 33, issue 1, in 2006.

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