Description
Book SynopsisProduced under the auspices of the International Mathematical Union (IMU), this volume was born as part of the activities observing the World Mathematical Year 2000. It consists of 30 articles that also offer reflections about the amazing mathematical progress we have witnessed in this century.
Table of ContentsNumber theory, transcendence and Diophantine geometry in the next millennium by A. Baker and G. Wustholz Harmonic analysis and combinatorics: How much may they contribute to each other? by J. Bourgain Back to Riemann by S.-S. Chern Noncommutative geometry and the Riemann zeta function by A. Connes Polynomials, vanishing cycles and Floer homology by S. K. Donaldson The two cultures of mathematics by W. T. Gowers Ten problems by V. F. R. Jones An algebraic integration by D. Kazhdan Mathematics: The right choice? by F. Kirwan On some challenging problems in nonlinear partial differential equations by P.-L. Lions Real world turbulence and modern applied mathematics by A. J. Majda Mathematics as profession and vocation by Yu. I. Manin Problems and conjectures in rigidity theory by G. Margulis A glimpse into symplectic geometry by D. McDuff Rational curves on algebraic varieties by S. Mori The dawning of the age of stochasticity by D. Mumford Mathematical physics of the 20 and 21 centuries by R. Penrose Limitations to regularity by K. F. Roth Conversations on mathematics with a visitor from outer space by D. Ruelle Some problems in number theory, analysis and mathematical physics by P. Sarnak Mathematical problems for the next century by S. Smale Positivity problems and conjectures in algebraic combinatorics by R. P. Stanley On the future of mathematics/physics interaction by C. Vafa Twenty years of number theory by A. Wiles Magic, mystery, and matrix by E. Witten Review of geometry and analysis by S.-T. Yau Polymathematics: Is mathematics a single science or a set of arts? by V. I. Arnold Mathematics and computing by P. D. Lax The theme of adic variation by B. Mazur.
