Ideas and Their Reception

Ideas and Their Reception

Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989

1st Edition - December 28, 1989

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  • Editors: David E. Rowe, John McCleary
  • eBook ISBN: 9781483266213

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The History of Modern Mathematics, Volume I: Ideas and their Reception documents the proceedings of the Symposium on the History of Modern Mathematics held at Vassar College in Poughkeepsie, New York on June 20-24, 1989. This book is concerned with the emergence and reception of major ideas in fields that range from foundations and set theory, algebra and invariant theory, and number theory to differential geometry, projective and algebraic geometry, line geometry, and transformation groups. Other topics include the theory of reception for the history of mathematics and British synthetic vs. French analytic styles of algebra in the early American Republic. The early geometrical works of Sophus Lie and Felix Klein, background to Gergonne's treatment of duality, and algebraic geometry in the late 19th century are also elaborated. This volume is intended for students and researchers interested in developments in pure mathematics.

Table of Contents

  • Table of Contents for Volume II

    Contributors List


    The Context of Reception

    A Theory of Reception for the History of Mathematics

    Riemann's Habilitationsvortrag and the Synthetic A Priori Status of Geometry

    Foundations of Mathematics

    Cantor's Views on the Foundations of Mathematics

    Kronecker's Views on the Foundations of Mathematics

    Toward a History of Cantor's Continuum Problem

    National Styles in Algebra

    British Synthetic vs. French Analytic Styles of Algebra in the Early American Republic

    Toward a History of Nineteenth-Century Invariant Theory

    Geometry and the Emergence of Transformation Groups

    The Early Geometrical Works of Sophus Lie and Felix Klein

    Line Geometry, Differential Equations, and the Birth of Lie's Theory of Groups

    Projective and Algebraic Geometry

    The Background to Gergonne's Treatment of Duality: Spherical Trigonometry in the Late 18th Century

    Algebraic Geometry in the Late Nineteenth Century

    Abel's Theorem

    Abel's Theorem

    Number Theory

    Heinrich Weber and the Emergence of Class Field Theory

    Notes on the Contributors

Product details

  • No. of pages: 470
  • Language: English
  • Copyright: © Academic Press 1989
  • Published: December 28, 1989
  • Imprint: Academic Press
  • eBook ISBN: 9781483266213

About the Editors

David E. Rowe

John McCleary

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