gingras mathematics document

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Hist. Sci., xxxix (2001)WHAT DID MATHEMATICS DO TO PHYSICS?Yves GingrasUniversit du Qubec MontralINTRODUCTIONThe question of the relationships between physics and mathematics is as old asphilosophy. In his Physics and his Posterior analytics Aristotle xed the frameworkfor discussions on the relations and distinctions between physics and mathematicsas well as the nature of the mixed sciences right up to the Renaissance and wellinto the seventeenth century. It could even be argued that the basic impulse towardthe mathematization of natural philosophy in the seventeenth century owes less tothe platonism of Galileo and others invoked by Koyr than to the long traditionof discussions on the mixed sciences. These discussions tended to extend the useof mathematics to domains beyond those considered by Aristotle as the morephysical among the mathematical sciences, 1 that is, Astronomy, Optics andHarmonics. Mechanics was to be added following the Renaissance recovery of thePseudo-Aristotelian Mechanical problems.2 Without concern for what Aristotlereally meant, or for the fact that his physics was not mathematical, philosophersoffered different interpretations of his views on mixed sciences, some stressing theincompatibility of physics and mathematics, others pointing to their compatibilityusing examples taken from the mixed sciences. Renaissance discussions of themixed sciences thus contributed to extending the latters domain

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