Titlebook: Mathematical Research Today and Tomorrow; Viewpoints of Seven Carles Casacuberta,Manuel Castellet Conference proceedings 1992 Springer-Ver

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Recent progress in diophantine geometry,egel developed the method of Diophantine approximation to prove finiteness results for the number of rational or integral points on certain curves. However, they did not manage to prove the Mordell conjecture, which in some sense is the strongest possible statement of this kind. This has been achiev

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Conference proceedings 1992Role of Integrable Modelsin the Development ofMathematics.- S.-T. Yau: The Current State andProspects 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.

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Conference proceedings 1992talks 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. Allpapers are expository. Someparts include precise technical statements of recentresults, but the

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Leaving mathematics for philosophy,le played by different ideas from biology in catastrophe theory..The attitude adopted is critical towards experimentation with no underlying theory and towards an improper use of statistics as a justification of analogical thinking in science.

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Noncommutative geometry,how an analogous correspondence, in the domain of real analysis, between geometrical spaces and algebras of functional analysis, going beyond the commutative case. This theory is based on three essential points:

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