Great currents of mathematical thought 伟大的数学思想
内容提要 :
Years in the making, this feast of mathematical ideas comprises works by 50 eminent French scholars. The first book of the two-volume set embraces "Mathematics: Concepts and Development," with several essays each under the categories of "Structures," Disciplines," "Space," "Function," "Group," "Probability," and "The Mathematical Epic." The second volume, "Mathematics in the Arts and Sciences," comprises essays on "Mathematics and the Human Intellect," "Mathematics and Technology," and "Mathematics and Civilization." 1962 edition.
目录 :
Preface to the Second Edition
Foreword An Unpublished Letter of Paul Valery Introduction Part Ⅰ, The Temple of Mathematics 1.Definitions in Mathematics by Nicolas Borel 2.The Architecture of Mathematics by Nicolas Bourbaki 3.Analogy in Mathematics by Robert Dehheil 4.Symmetry and Dissymmetry in Mathematics and Physics by Albert Lautman 5.Intuitive Approaches Toward some Vital Organs of Mathematics by Georges Bouligand 6.The Natural Number and its Generalizations by Mauriee Freehet 7.A Mathematical Enigma: Fermat's Last Theorem by Theophile Got 8.The History of the Mysterious Numbers by Paul Dubreil 9.The Problem of the Infinite: Transfinite Numbers and Alephs by Henri Eyraud 10.From Three-Dimensional Space to the Abstract Spaces by Maurice Freehet 11.A Journey into the Fourth Dimension by Andre Sainte-Lagtie 12.On the Curvature of Space and the Possibility of Forming a Conception of it by Elementary Means by Rene Thiry 13.The Origin and the Evolution of the Notion of an Analytic Function of One Variable by Georges Valiron 14.The Role of Families of Functions in Mathematical Analysis by Paul Montel 15.From Cauchy to Riemann, or the Birth of the Theory of Real Functions by Jean T. Desanti 16.The Innateness of the Transfinite by Arnoud Denjoy D. GRouP 17.The Notion of Group its Power and its Limitations by Andr6 Lentin 18.Modern Opinions on the Foundations of the Theory of Probability by Robert Fortet 19.Chance and Mathematics by Pius Servien Part Ⅱ, The Mathematical Epic 20.A General View of the Evolution of Mathematics by Paul Germain 21.Views on Newton's Mathematical Thought by Pierre Brunet 22.A Centenary: Sophus Lie by ]~lie Cartan 23.Women Mathematicians by Mme. Marie-Louise Dubreil-Jacodn …… |