Preface, Michael Atiyah vii
Number theory, transcendence and Diophantine geometry in the next
millennium, A. Baker and G. Wustholz 1
Harmonic analysis and combinatorics: How much may they contribute to
each other?, J. Bourgain 13
Back to Riemann, Shiing-Shen Chern 33
Noncommutative geometry and the Riemann zeta function, Alain Connes 35
Polynomials, vanishing cycles and Floer homology, S. K. Donaldson 55
The two cultures of mathematics, W. T. Gowers 65
Ten problems, V. F. R. Jones 79
An algebraic integration, David Kazhdan 93
Mathematics: The right choice?, Frances Kirwan 117
On some challenging problems in nonlinear partial differential equations, P.-L. Lions 121
Real world turbulence and modern applied mathematics, AndrewJ. Majda 137
Mathematics as profession and vocation, Yu. I. Manin 153
Problems and conjectures in rigidity theory, Gregory Margulis 161
A glimpse into symplectic geometry, Dusa McDuff 175
Rational curves on algebraic varieties, Shigefumi Mori 189
The dawning of the age of stochasticity, David Mumford 197
Mathematical physics on the 20th and 21st century, Roger Penrose 219
Limitations to regularity, K. F. Roth 235
Conversations on mathematics with a visitor from outer space, David Ruelle 251
Some problems in number theory, analysis and mathematical physics, Peter Sarnak 261
Mathematical problems for the next century, Steve Smale 271
Positivity problems and conjectures in algebraic combinatorics, Richard P. Stanley 295
On the future of mathematics/physics interaction, Cumrun Vafa 321
Twenty years of number theory, AndrewWiles 329
Magic, mystery, and matrix, Edward Witten 343
Review of geometry and analysis, S.-T. Yau 353
Polymathematics: Is mathematics a single science or a set of arts?, V. I. Arnold 403
Mathematics and computing, Peter D. Lax 417
The theme of p-adic variation, Barry Mazur 433
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