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Philosophia Mathematica Advance Access published online on January 23, 2006
Philosophia Mathematica, doi:10.1093/philmat/nkj017
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© The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Article

The History of Algebra and the Development of the Form of its Language{dagger}

Ladislav Kvasz 1 *

1 Department of Algebra, Geometry and Mathematics Education, Comenius University, 84248 Bratislava, Slovakia

* To whom correspondence should be addressed.
Ladislav Kvasz, E-mail: kvasz{at}fmph.uniba.sk


  Abstract

This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwarizmi, Cardano, and Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language and analyzes the changes of this language in the course of history. It turns out that the most fundamental epistemological changes in the development of algebra can be interpreted as changes of the pictorial form (in the sense of Wittgenstein's Tractatus) of the symbolic language of algebra. Thus the paper develops further the method of reconstruction which the author introduced for the analysis of the development of geometry.

{dagger}I would like to thank Donald Gillies, Tána Jajcayová, Eberhard Knobloch, Paul Rusnock, and Pavol Zlatos for their comments and criticism of previous versions of this paper. I would like also to express my gratitude to the Alexander von Humboldt Foundation for a scholarship at the Technical University in Berlin, which made it possible to write this paper.
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