Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics

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Overview


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 ...

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Symmetry and the Monster: One of the greatest quests of mathematics

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Overview


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 Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry."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.

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Product Details

  • ISBN-13: 9780192807236
  • Publisher: Oxford University Press, USA
  • Publication date: 8/10/2007
  • Pages: 272
  • Sales rank: 1,007,400
  • Product dimensions: 7.72 (w) x 5.02 (h) x 0.75 (d)

Meet the Author

Mark Ronan is a Professor at the University of Illinois at Chicago, and a Visiting Professor of Mathematics at University College London.

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Table of Contents

1 Theaetetus's Icosahedron 5
2 Galois : death of a genius 11
3 Irrational solutions 27
4 Groups 42
5 Sophus lie 53
6 Lie groups and physics 71
7 Going finite 79
8 After the war 88
9 The man from Uccle 97
10 The big theorem 113
11 Pandora's box 127
12 The leech lattice 142
13 Fischer's monsters 157
14 The atlas 171
15 A monstrous mystery 190
16 Construction 205
17 Moonshine 216
App. 1 The golden section
App. 2 The Witt design
App. 3 The leech lattice
App. 4 The 26 exceptions
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Sort by: Showing 1 Customer Reviews
  • Posted April 9, 2011

    more from this reviewer

    The insigth into symmetry

    One of the greatest achievements of the 20th century mathematics has been the classification of the finite simple groups. Groups are mathematical objects that tells us about symmetries, and like many other mathematical objects they are relatively easy to describe, but can be fiendishly difficult to fully understand. Sometimes understanding comes from a single brilliant insights by an incredibly gifted individual, and these individuals become part of the mathematical lore that can even touch upon the popular imagination. However, most of the time these days the game of mathematics has become complex enough that it can become increasingly difficult for any individual to fully contribute to on its own to the full problem. Professional mathematicians don't mind this at all: they thrive in collaborations and feed off of each other's work and enthusiasm. The collaborative nature of mathematics is at full display when it comes to the classification of finite simple groups, an effort that spanned hundreds of articles in scientific journals between 1955 and 1983. I have always been curious to find out more about this enterprise, and this book does a remarkable job at presenting it to the general reader. It is comprehensive without becoming technically hard to follow. Anyone who has ever taken a college level mathematics course should be able to read it without much difficulty, although some basic understanding of group theory and modern algebra would be great bonus. The book also doesn't dumb down mathematics to the point that it becomes irritating for those who have some mathematical sophistication, so even professional scientists and mathematicians can find it very informative and a rewarding read.

    And if you are curious, the Monster from the title refers to the special simple finite group that has been one of the most fascinating mathematical objects discovered so far.

    2 out of 2 people found this review helpful.

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