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. Language: English