Supervisors info:
Παπασταυρίδης Σταύρος, Ομότιμος Καθηγητής
Λάππας Διονύσιος, Αν. Καθηγητής
Ράπτης Ευάγγελος. Καθηγητής
Summary:
The present paper attempts to shed light to the ideas that led to carving a new path, culminating in the transformation of Algebra from a process aiming at solving a problem or equation to an autonomous discipline, using universal symbols, relying on mathematical principles, and claiming overall application. At the core of these ideas lies the analytical method. The framework, however, was created by questioning founding conditions of Aristotelian philosophy and converting relevant methodology. Quantification of magnitudes that followed led to proclaiming mathematics as the touchstone of any theory. We focus on 16th c developments and the work of Francois Viete. To manifest the historic continuum reference ought to be made to the work of Diophantos, the mathematicians of Islam, Ramus, as well as, Cardano, Bombelli – prominent mathematicians of the 16th c Italian school. Such references are mainly comparative, adopting the views of Thomas Kuhn that a theory does not develop in linear or cumulative fashion, but through deviation, regression and breach. Subsequently, data regarding the diffusion of Viete’s theories in England are presented with reference to the work of Harriot, Oughtred, and finally the influence of these theories upon 17th c developments and the Cartesian semiotics in particular is investigated. Thus, Algebra emerges as the vehicle of transition to the scientific revolution in the field of mathematics, providing the required basis upon which groundbreaking branches such as Analytic Geometry and Calculus, are constructed.
