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.

Contributions by: A. Connes, G. Faltings, V. Jones, S. Novikov, S. Smale, R. Thom, S.-T. Yau