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. Individual members of mathematical societies of the IMU member countries can purchase this volume at the AMS member price when buying directly from the AMS.
Author(s): Arnold V.I., et al.
Publisher: AMS
Year: 2000
Language: English
Pages: 469
Tags: Математика;Прочие разделы математики;
Contents......Page all_25235_to_00469.cpc0003.djvu
Preface......Page all_25235_to_00469.cpc0005.djvu
Number theory, transcendence arid Diophantine geometry in the next millennium......Page all_25235_to_00469.cpc0011.djvu
Harmonic analysis and combinatorics: How much may they contribute to each other?......Page all_25235_to_00469.cpc0023.djvu
Back to Riemann......Page all_25235_to_00469.cpc0043.djvu
Noncommutative geometry and the Riemann zeta function......Page all_25235_to_00469.cpc0045.djvu
Polynomials, vanishing cycles and Floer homology......Page all_25235_to_00469.cpc0065.djvu
The two cultures of mathematics......Page all_25235_to_00469.cpc0075.djvu
Ten problems......Page all_25235_to_00469.cpc0089.djvu
An algebraic integration......Page all_25235_to_00469.cpc0103.djvu
Mathematics: The right choice? ......Page all_25235_to_00469.cpc0127.djvu
On some challenging problems in nonlinear partial differential equations......Page all_25235_to_00469.cpc0131.djvu
Real world turbulence and modern applied mathematics......Page all_25235_to_00469.cpc0147.djvu
Mathematics as profession and vocation......Page all_25235_to_00469.cpc0163.djvu
Problems and conjectures in rigidity theory......Page all_25235_to_00469.cpc0171.djvu
A glimpse into symplectic geometry......Page all_25235_to_00469.cpc0185.djvu
Rational curves on algebraic varieties......Page all_25235_to_00469.cpc0199.djvu
The dawning of the age of stochasticity......Page all_25235_to_00469.cpc0207.djvu
Mathematical physics on the 20th and 21st century......Page all_25235_to_00469.cpc0229.djvu
Limitations to regularity......Page all_25235_to_00469.cpc0245.djvu
Conversations on mathematics with a visitor from outer space......Page all_25235_to_00469.cpc0261.djvu
Some problems in number theory, analysis and mathematical physics......Page all_25235_to_00469.cpc0271.djvu
Mathematical problems for the next century......Page all_25235_to_00469.cpc0281.djvu
Positivity problems and conjectures in algebraic combinatorics......Page all_25235_to_00469.cpc0305.djvu
On the future of mathematics/physics interaction......Page all_25235_to_00469.cpc0331.djvu
Twenty years of number theory......Page all_25235_to_00469.cpc0339.djvu
Magic, mystery, and matrix......Page all_25235_to_00469.cpc0353.djvu
Review of geometry and analysis......Page all_25235_to_00469.cpc0363.djvu
Polymathematics: Is mathematics a single science or a set of arts? ......Page all_25235_to_00469.cpc0413.djvu
Mathematics and computing......Page all_25235_to_00469.cpc0427.djvu
The theme of p-adic variation......Page all_25235_to_00469.cpc0443.djvu
