Mathematical Research Today and Tomorrow: Viewpoints of Seven Fields Medalists Lectures given at the Institut d’Estudis Catalans, Barcelona, Spain, June 1991

René Thom (auth.), Carles Casacuberta, Manuel Castellet (eds.)3540560114, 9783540560111

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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Table of contents :
Leaving mathematics for philosophy….Pages 1-12
Rôle of integrable models in the development of mathematics….Pages 13-28
The current state and prospects of geometry and nonlinear differential equations….Pages 29-39
Noncommutative geometry….Pages 40-58
Theory of computation….Pages 59-69
Knots in mathematics and physics….Pages 70-77
Recent progress in diophantine geometry….Pages 78-86
Round-table discussion….Pages 87-108