The equation that couldn't be solved: how mathematical genius discovered the language of symmetry

Abstract

Traces the four-thousand-year-old mathematical effort to discover and define the laws of symmetry, citing the achievements of doomed geniuses Niels Henrick Abel and Evariste Galois to solve the quintic equation and give birth to group theory.

Contents

Symmetry -- eye s'dnim eht ni yrtemmyS -- Never forget this in the midst of your equations -- The poverty-stricken mathematician -- The romantic mathematician -- Groups -- Symmetry rules -- Who's the most symmetrical of them all? -- Requiem for a romantic genius -- Appendix 1. Card puzzle -- Appendix 2. Solving a system of two linear equations -- Appendix 3. Diophantus's solution -- Appendix 4. A Diophantine equation -- Appendix 5. Tartaglia's verses and formula -- Appendix 6. Adriaan van Roomen's challenge -- Appendix 7. Properties of the roots of quadratic equations -- Appendix 8. The Galois family tree -- Appendix 9. The 14-15 puzzle -- Appendix 10. Solution to the matches problem.