Preface

Road map

Intersecting polynomials: Maxim Kontsevich 11 Patterns and permutations: Donald Knuth 

Separable permutations

Hipparchus and Schroeder

De methodis serierum et fluxionum: Newton's method De methodis serierum et fluxionum: Newton's series Some formal algebra

Gauss on algebraic curves

Proof of Gauss's claim on singularities

De seriebus divergentibus: Euler, Cauchy and Poincare´ Convergence: Cauchy

Moebius and his band

Moebius necklaces

Resolution of singularities

The 3-sphere and the Hopf fibration

The cusp and the trefoil

Victor Puiseux, at last!

Jack Milnor and his fibration

The Hipparchus-Schroeder-Tamari-Stasheff associahedron 191 Jim Stasheff and loop spaces

Operads

Singular operads

Gauss is back: curves in the plane

Analytic chord diagrams: an algorithm

Analytic chord diagrams: interlace graphs

Gauss and linking

Kontsevich is back: universal invariant

Postface

Acknowledgments

Image Credits