1 Introduction -- One Interviews and Reminiscences -- 1 An Interview with Michael Atiyah -- 2 On the Steps of Moscow University Steve Smale, -- 3 An Interview with Jean-Pierre Serre -- 4 Mathematical Anecdotes -- 5 My Collaboration with Julia Robinson -- 6 Contemporary Mathematics -- Two Algebra and Number Theory -- 7 The Proof of the Mordell Conjecture -- 8 Adventures in Arithmetick, or: How to Make Good Use of a Fourier Transform -- 9 Solving Polynomial Systems -- 10 Artin's Conjecture for Primitive Roots -- 11 Representation Theory of Finite Groups: From Frobenius to Brauer -- 12 Quaternionic Determinants -- Three Analysis -- 13 The Surfaces of Delaunay -- 14 The Banach-Tarski Theorem -- 15 Painleve's Conjecture -- 16 A Geometrization of Lebesgue's Space-Filling Curve -- 17 Sophus Lie and Harmony in Mathematical Physics, on the 150th Anniversary of His Birth -- 18 The Missing Link -- Four Applied mathematics -- 19 Yeast Oscillations, Belousov-Zhabotinsky Waves, and the Nonretraction Theorem -- Strings -- 21 Integrability in Mathematics and Theoretical Physics: Solitons -- 22 On Newton's Problem of Minimal Resistance -- 23 If Hamilton Had Prevailed: Quaternions in Physics -- Five Arrangements and Patterns -- 24 On the Problème des Ménages -- 25 Quasicrystals: The View from Les Houches -- 26 Celtic Knotwork: Mathematical Art -- 27 The Sacred Cut Revisited: The Pavement of the Baptistery of San Giovanni, Florence -- 28 Symmetrical Combinations of Three or Four Hollow Triangles -- Six Geometry and Topology -- 29 Instantons and the Topology of 4-Manifolds -- 30 The Computer-Aided Discovery of New Embedded Minimal Surfaces -- 31 What Is the Difference between a Parabola and a Hyperbola? -- 32 How to Build Minimal Polyhedral Models of the Boy Surface -- 33 Recent Developments in Braid and Link Theory -- 34 Hyperbolic Geometry and Spaces of Riemann Surfaces -- Seven History of Mathematics -- 35 Kurt Godel in Sharper Focus -- 36 Who Would Have Won the Fields Medals a Hundred Years Ago? -- 37 The Last 100 Days of the Bieberbach Conjecture -- 38 A Little-Known Chapter in the History of German Mathematics -- 39 The War of the Frogs and the Mice, or the Crisis of the Mathematische Annalen -- 40 Hilbert's Problems and Their Sequels -- Index of Names.