Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

by Paolo Mancosu

The seventeenth century saw more dramatic advances in mathematical theory and practice than any other era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Philosophy of mathematics and mathematical practice in the seventeenth century have often been studied independently of one another. In this groundbreaking work, Paolo Mancosu offers the first comprehensive account of the rich interaction between the two fields. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes's Geometrie, the relationship between empiricist epist