Mathematics: frontiers and perspectives

Preface / Michael Atiyah

Number theory, transcendence and Diophantine geometry in the next millennium / A. Baker and G. Wustholz

Harmonic analysis and combinatorics: How much may they contribute to each other? / J. Bourgain

Back to Riemann / Shiing-Shen Chern

Noncommutative geometry and the Riemann zeta function / Alain Connes

Polynomials, vanishing cycles and Floer homology / S. K. Donaldson

two cultures of mathematics / W. T. Gowers

Ten problems / V. F. R. Jones

algebraic integration / David Kazhdan

Mathematics: The right choice? / Frances Kirwan

On some challenging problems in nonlinear partial differential equations / P.-L. Lions

Real world turbulence and modern applied mathematics / Andrew J. Majda

Mathematics as profession and vocation / Yu. I. Manin

Problems and conjectures in rigidity theory / Gregory Margulis

glimpse into symplectic geometry / Dusa McDuff

Rational curves on algebraic varieties / Shigefumi Mori

dawning of the age of stochasticity / David Mumford

Mathematical physics on the 20[superscript th] and 21[superscript st] century / Roger Penrose

Limitations to regularity / K. F. Roth

Conversations on mathematics with a visitor from outer space / David Ruelle

Some problems in number theory, analysis and mathematical physics / Peter Sarnak

Mathematical problems for the next century / Steve Smale

Positivity problems and conjectures in algebraic combinatorics / Richard P. Stanley

On the future of mathematics/physics interaction / Cumrun Vafa

Twenty years of number theory / Andrew Wiles

Magic, mystery, and matrix / Edward Witten

Review of geometry and analysis / S.-T. Yau

Polymathematics: Is mathematics a single science or a set of arts? / V. I. Arnold

Mathematics and computing / Peter D. Lax

theme of p-adic variation / Barry Mazur.