Mathematics is driven forward by the quest to solve a small number of major problems—the four most famous challenges being Fermat's Last Theorem, the Riemann Hypothesis, Poincaré's Conjecture, and the quest for the "Monster" of Symmetry. Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest.
Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry." Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed "the Monster"—a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe.
This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science—and especially readers of such books as Fermat's Last Theorem.
ISBN-13: 9780192807236
Media Type: Paperback
Publisher: Oxford University Press
Publication Date: 09-04-2007
Pages: 272
Product Dimensions: 7.72(w) x 5.02(h) x 0.75(d)
Mark Ronan is a Professor at the University of Illinois at Chicago, and a Visiting Professor of Mathematics at University College London.
Table of Contents
Prologue1. Theaetetus's Icosahedron2. Galois: Death of a Genius3. Irrational Solutions4. Groups5. Sophus Lie6. Lie Groups and Physics7. Going Finite8. After the War9. The Man from Uccle10. The Big Theorum11. Pandora's Box12. The Leech Lattice13. Fischer's Monsters14. The Atlas15. A Monstrous Mystery16. Construction17. MoonshineAppendix 1: The Golden SectionAppendix 2: The Witt DesignAppendix 3: The Leech LatticeAppendix 4: The 26 Exceptions
