This remarkable book is a celebration of the state of mathematics at the end of the millennium. Produced under the auspices of the International Mathematical Union (IMU), the volume was born as part of the activities observing the World Mathematical Year 2000. The volume consists of 30 articles written by some of the most influential mathematicians of our time. Authors of 15 contributions were recognized in various years by the IMU as recipients of the Fields Medal, from K. F. Roth (Fields Medalist, 1958) to W. T. Gowers (Fields Medalist, 1998). The articles offer valuable reflections about the amazing mathematical progress we have witnessed in this century and insightful speculations about the possible development of mathematics over the next century.Some articles formulate important problems, challenging future mathematicians. Others pay explicit homage to the famous set of Hilbert Problems posed one hundred years ago, giving enlightening commentary. Yet other papers offer a deeply personal perspective, allowing singular insight into the minds and hearts of people doing mathematics today."" Mathematics: Frontiers and Perspectives"" is a unique volume that pertains to a broad mathematical audience of various backgrounds and levels of interest. It offers readers true and unequaled insight into the wonderful world of mathematics at this important juncture: the turn of the millennium. The work is one of those rare volumes that can be browsed, and if you do simply browse through it, you get a wonderful sense of mathematics today. Yet it also can be intensely studied on a detailed technical level for gaining insight into some of the great problems on which mathematicians are currently working. Editors Michael Atiyah and Peter Lax were winners of the famous Abel Prize awarded by The Norwegian Academy of Science and Letters for outstanding work in mathematics.
Number 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.