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The Reception of the Galilean Science of Motion in Seventeenth-Century Europe
This book collects contributions by some of the leading scholars working on seventeenth-century mechanics and the mechanical philosophy. Together, the articles provide a broad and accurate picture of the fortune of Galileo's theory of motion in Europe and of the various physical, mathematical, and ontological arguments that were used in favour and against it. Were Galileo's contemporaries really aware of what Westfall has described as "the incompatibility between the demands of mathematical mechanics and the needs of mechanical philosophy"? To what extent did Galileo's silence concerning the cause of free fall impede the acceptance of his theory of motion? Which methods were used, before the invention of the infinitesimal calculus, to check the validity of Galileo's laws of free fall and of parabolic motion? And what sort of experiments were invoked in favour or against these laws? These and related questions are addressed in this volume.
The Secret Formula
The legendary Renaissance math duel that ushered in the modern age of algebra The Secret Formula tells the story of two Renaissance mathematicians whose jealousies, intrigues, and contentious debates led to the discovery of a formula for the solution of the cubic equation. Niccolò Tartaglia was a talented and ambitious teacher who possessed a secret formula—the key to unlocking a seemingly unsolvable, two-thousand-year-old mathematical problem. He wrote it down in the form of a poem to prevent other mathematicians from stealing it. Gerolamo Cardano was a physician, gifted scholar, and notorious gambler who would not hesitate to use flattery and even trickery to learn Tartaglia's secret. S...
A Pure Soul
This biography illuminates the life of Ennio De Giorgi, a mathematical genius in parallel with John Nash, the Nobel Prize Winner and protagonist of A Beautiful Mind. Beginning with his childhood and early years of research, into his solution of the 19th problem of Hilbert and his professorship, this book pushes beyond De Giorgi’s rich contributions to the mathematics community, to present his work in human rights, including involvement in the fight for Leonid Plyushch’s freedom and the defense of dissident Uruguayan mathematician José Luis Massera. Considered by many to be the greatest Italian analyst of the twentieth century, De Giorgi is described in this volume in full through documents and direct interviews with friends, family, colleagues, and former students.
Conflicts Between Generalization, Rigor, and Intuition
This volume is, as may be readily apparent, the fruit of many years’ labor in archives and libraries, unearthing rare books, researching Nachlässe, and above all, systematic comparative analysis of fecund sources. The work not only demanded much time in preparation, but was also interrupted by other duties, such as time spent as a guest professor at universities abroad, which of course provided welcome opportunities to present and discuss the work, and in particular, the organizing of the 1994 International Graßmann Conference and the subsequent editing of its proceedings. If it is not possible to be precise about the amount of time spent on this work, it is possible to be precise about the date of its inception. In 1984, during research in the archive of the École polytechnique, my attention was drawn to the way in which the massive rupture that took place in 1811—precipitating the change back to the synthetic method and replacing the limit method by the method of the quantités infiniment petites—significantly altered the teaching of analysis at this first modern institution of higher education, an institution originally founded as a citadel of the analytic method.
Geometry and Complex Variables
This reference presents the proceedings of an international meeting on the occasion of theUniversity of Bologna's ninth centennial-highlighting the latest developments in the field ofgeometry and complex variables and new results in the areas of algebraic geometry,differential geometry, and analytic functions of one or several complex variables.Building upon the rich tradition of the University of Bologna's great mathematics teachers, thisvolume contains new studies on the history of mathematics, including the algebraic geometrywork of F. Enriques, B. Levi, and B. Segre ... complex function theory ideas of L. Fantappie,B. Levi, S. Pincherle, and G. Vitali ... series theory and logarithm theory contributions of P.Mengoli and S. Pincherle ... and much more. Additionally, the book lists all the University ofBologna's mathematics professors-from 1860 to 1940-with precise indications of eachcourse year by year.Including survey papers on combinatorics, complex analysis, and complex algebraic geometryinspired by Bologna's mathematicians and current advances, Geometry and ComplexVariables illustrates the classic works and ideas in the field and their influence on today'sresearch.
The Making of Measure and the Promise of Sameness
Measurement is all around us. Whether inches or miles, centimeters or kilometers, measures of distance stand at the very foundation of everything we do, so much so that we take them for granted. But this has not always been the case. This book reaches back to medieval Italy, where measurements were displayed in the open, showing how a simple innovation triggered a chain of cultural transformations whose consequences are visible today on a global scale. Drawing from literary works and frescoes, architectural surveys, and legal compilations, Emanuele Lugli offers a history of material practices widely overlooked by historians and explains how measurements work as powerful molds of ideas, affecting our notions of what we consider similar, accurate, and truthful.
Leibniz
This is the first full English translation, with a critical introduction and a comprehensive commentary, of the Dissertation on Combinatorial Art (1666), in which Leibniz introduces some of his most important ideas in philosophy, logic, and mathematics.
Seventeenth-Century Indivisibles Revisited
The tremendous success of indivisibles methods in geometry in the seventeenth century, responds to a vast project: installation of infinity in mathematics. The pathways by the authors are very diverse, as are the characterizations of indivisibles, but there are significant factors of unity between the various doctrines of indivisible; the permanence of the language used by all authors is the strongest sign. These efforts do not lead to the stabilization of a mathematical theory (with principles or axioms, theorems respecting these first statements, followed by applications to a set of geometric situations), one must nevertheless admire the magnitude of the results obtained by these methods a...
