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.)