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François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète's major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète's 'new algebra' relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of analysis based on the use of formal methods. However, Viète's algebraic analysis is not an analysis in the same sense as his cryptanalysis is. In Aristotelian terms, the first is a form of ' α , ν α ´ λ υ σ ι ς ', while the second is a form of δ ι α ι ´ ρ ε σ ι ς . While the first is a top-down argument from the point of view of the human subject, since it is an argument going from what is not actual to what is actual for such a subject, the second one is a bottom-up argument from this same point of view, since it starts from what is first for us and proceed towards what is first by nature.


NOTICE: this is the author’s version of a work that was accepted for publication in Studies in History and Philosophy of Science Part A. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Studies in History and Philosophy of Science Part A, volume 37, issue 2, in 2006.

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