Symmetry and the Monster: One of the greatest quests of mathematics (Google eBook)

Front Cover
Oxford University Press, May 18, 2006 - Science - 272 pages
2 Reviews
The hunt for the 'Monster' of symmetry is one of the great mathematical quests, alongside Fermat's Last Theorem, the Riemann Hypothesis, and Poincar--eacute--; Conjecture. The Monster is a giant snowflake in 196,884 dimensions - the largest exception to our neat classifications of symmetry, with a beautiful structure which may turn out to unlock our understanding of symmetry, string theory, and the very fabric of our universe. The story of its discovery became the biggest joint mathematical project of all time - involving determination, luck, and some very extraordinary characters. - ;Mathematics is being driven forward by the quest to solve a small number of major problems - generating excitement in the mathematical world and beyond. Four famous challenges have been Fermat's Last Theorem, the Riemann Hypothesis, Poincar--eacute--;'s Conjecture, and, now, the quest for the 'Monster' of Symmetry. It is this latter that forms the topic of this book. Although its roots go back much further, the quest to understand symmetry really begins with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. He used symmetry to understand algebraic equations, and he discovered that there were building blocks or 'atoms of symmetry'. Most fit into a table, rather like the periodic table of elements, but there are 26 exceptions. The biggest of these was dubbed 'the Monster' - a giant snowflake in 196,884 dimensions. At first the Monster was only dimly seen. Did it really exist, or was it a mirage? Many mathematicians became involved. The Monster became clearer, and it was no longer monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe. The story of the discovery involves some extraordinary characters, and Mark Ronan brings these people to life, and recreates in accessible language the growing excitement of what became the biggest joint project ever in the field of mathematics - the hunt for the Monster. - ;...includes entertaining glimpses of the personalities involved ...but best of all gives an admirable amount of detail... - TLS;a fascinating book that will appeal to anyone with an appetite for exploration and discovery, and which is accessble to all. -
  

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An excellent book, historically and mathematically, can be read as a novel, I read it in one day which is exceptional for the arduous topic. With more books like this Math anxiety would disappear.

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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.
 

Contents

Prologue
1Theaetetuss Icosahedron
Death of a Genius
3Irrational Solutions
4Groups
5Sophus Lie
6Lie Groups and Physics
7Going Finite
13Fischers Monsters
14The Atlas
15A Monstrous Mystery
16Construction
17Moonshine
Notes
Appendix 1The Golden Section
Appendix 2The Witt Design

8After the War
9The Man from Uccle
10The Big Theorem
11Pandoras Box
12The Leech Lattice
Appendix 3The Leech Lattice
Appendix 4The 26 Exceptions
Glossary
Index
Copyright

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