Mathematics : frontiers and perspectives
著者
書誌事項
Mathematics : frontiers and perspectives
American Mathematical Society, c2000
- : [hbk.]
- : pbk
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注記
At head of title: IMU; International Mathematical Union
Includes bibliographical references
内容説明・目次
内容説明
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 28 articles written by some of the most influential mathematicians of our time. Authors of 14 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.
目次
- A. Baker and G. W stholz, Number theory, transcendence and Diophantine geometry in the next millennium
- J. Bourgain, Harmonic analysis and combinatorics - How much may they contribute to each other?
- S.-S. Chern, Back to Riemann
- A. Connes, Noncommutative geometry and the Riemann zeta function
- S.K. Donaldson, Polynomials, vanishing cycles and Floer homology
- W.T. Gowers, The two cultures of mathematics
- V.F R. Jones, Ten problems
- D. Kazhdan, An algebraic integration
- F. Kirwan, Mathematics - The right choice?
- P.-L. Lions, On some challenging problems in nonlinear partial differential equations
- A.J. Majda, Real world turbulence and modern applied mathematics
- Yu. I. Manin, Mathematics as profession and vocation
- G. Margulis, Problems and conjectures in rigidity theory
- D. McDuff, A glimpse into symplectic geometry
- S. Mori, Rational curves on algebraic varieties
- D. Mumford, The dawning of the age of stochasticity
- R. Penrose, Mathematical physics of the 20th and 21st centuries
- K F. Roth, Limitations to regularity
- D. Ruelle, Conversations on mathematics with a visitor from outer space
- P. Sarnak, Some problems in number theory, analysis and mathematical physics
- S. Smale, Mathematical problems for the next century
- R.P. Stanley, Positivity problems and conjectures in algebraic combinatorics
- C. Vafa, On the future of mathematics/physics interaction
- A. Wiles, Twenty years of number theory
- E. Witten, Magic, mystery, and matrix
- S.-T. Yau, Review of geometry and analysis. (Part contents.)
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