Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

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.