CiNii 図書 - Symmetry and the monster : one of the greatest quests of mathematics

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, Poincare'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.

1. Theaetetus's Icosahedron
2. Galois: Death of a Genius
3. Irrational Solutions
4. Groups
5. Sophus Lie
6. Lie Groups and Physics
7. Going Finite
8. After the War
9. The Man from Uccle
10. The Big Theorum
11. Pandora's Box
12. The Leech Lattice
13. Fischer's Monsters
14. The Atlas
15. A Monstrous Mystery
16. Construction
17. Moonshine

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Symmetry and the monster : one of the greatest quests of mathematics

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