The Symposium on the Current State and Prospects ofMathematics was held in Barcelona from June 13 to June 18,1991. Seven invited Fields medalists gavetalks on thedevelopment of their respective research fields. Thecontents of all lectures were collected in the volume,together witha transcription of a round table discussionheld during the Symposium. All papers are expository. Someparts include precise technical statements of recentresults, but the greater part consists of narrative textaddressed to a very broad mathematical public.CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S.Novikov: Role of Integrable Models in the Development ofMathematics.- S.-T. Yau: The Current State and Prospects ofGeometry 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.