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.

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