Bücher von Davide Crippa

This book explores the major historical phenomenon of the algebraization of mathematics in the second half of the 17th and 18th centuries, offering a broader understanding of the consolidation of analytic geometry and infinitesimal calculus as disciplines. The authors examine the external (intellectual, geographical, and political) factors that influenced these transformations and shed light on the process of acquisition and integration of analytical mathematics into traditional curricula. Drawing on new trends in historiography of science, this book emphasizes the importance of "dwarfs", that is mathematicians but also technicians, artisans, military personnel, engineers, and architects, often ignored or marginalized in traditional histories, in the circulation of original mathematical knowledge, and of peripheral countries such as Italy and Spain as important sites for the appropriation and production of such knowledge.

This book is about James Gregory¿s attempt to prove that the quadrature of the circle, the ellipse and the hyperbola cannot be found algebraically. Additonally, the subsequent debates that ensued between Gregory, Christiaan Huygens and G.W. Leibniz are presented and analyzed. These debates eventually culminated with the impossibility result that Leibniz appended to his unpublished treatise on the arithmetical quadrature of the circle.The author shows how the controversy around the possibility of solving the quadrature of the circle by certain means (algebraic curves) pointed to metamathematical issues, particularly to the completeness of algebra with respect to geometry. In other words, the question underlying the debate on the solvability of the circle-squaring problem may be thus phrased: can finite polynomial equations describe any geometrical quantity? As the study reveals, this question was central in the early days of calculus, when transcendental quantities and operations entered the stage.Undergraduate and graduate students in the history of science, in philosophy and in mathematics will find this book appealing as well as mathematicians and historians with broad interests in the history of mathematics.