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Mathematical Research Today and Tomorrow

Viewpoints of Seven Fields Medalists. Lectures given at the Institut d'Estudis Catalans, Barcelona, Spain, June 1991

  • Conference proceedings
  • © 1992

Overview

Editors:
  1. Carles Casacuberta
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  2. Manuel Castellet
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1525)

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Table of contents (8 papers)

  1. Front Matter

    Pages I-V
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  2. Leaving mathematics for philosophy

    • René Thom
    Pages 1-12

  3. Rôle of integrable models in the development of mathematics

    • Sergei Novikov
    Pages 13-28

  4. The current state and prospects of geometry and nonlinear differential equations

    • Shing-Tung Yau
    Pages 29-39

  5. Noncommutative geometry

    • Alain Connes
    Pages 40-58

  6. Theory of computation

    • Stephen Smale
    Pages 59-69

  7. Knots in mathematics and physics

    • Vaughan F. R. Jones
    Pages 70-77

  8. Recent progress in diophantine geometry

    • Gerd Faltings
    Pages 78-86

  9. Round-table discussion

    • Carles Casacuberta, Manuel Castellet
    Pages 87-108

  10. Back Matter

    Pages 109-112
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About this book

The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.

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