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

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 Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry."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__ 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 Galois, Who Spent The Night Before He Died Frantically Scribbling His Unpublished Discoveries, Used Symmetry To Understand Algebraic Equations, And He Discovered That There Were Building Blocks Or 'atoms Of Symmetry.'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.--pub. Desc. Theaetetus's Icosahedron -- Galois: Death Of A Genius -- Irrational Solutions -- Groups -- Sophus Lie -- Lie Groups And Physics --going Finite -- After The War -- The Man From Uccle -- The Big Theorem -- Pandora's Box -- The Leech Latice -- Fischer's Monsters -- The Atlas -- A Monstrous Mystery -- Construction -- Moonshine. Mark Ronan. Includes Bibliographical References (p. 230-237) And Index. 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, Poincar'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 . 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, Poincar'e'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 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. - ;Mathemat. Read more... Abstract: The hunt for the 'Monster' of symmetry is one of the great mathematical quests. The Monster is a giant snowflake in 196,884 dimensions, with a beautiful structure which may turn out to unlock our understanding of symmetry and the very fabric of our universe. The story of its discovery became the biggest joint mathematical project of all time. Read more... Imagine a giant snowflake in 196,884 dimensions... This is the story of a mathematical quest that began two hundred years ago in revolutionary France, led to the biggest collaboration ever between mathematicians across the world, and revealed the'Monster'- not monstrous at all, but a structure of exquisite beauty and complexity. Told here for the first time in accessible prose, it is a story that involves brilliant yet tragic characters, curious number'coincidences'that led to breakthroughs in the mathematics of symmetry, and strange crystals that reach into many dimensions. And it is a story that is not yet over, for we have yet to understand the deep significance of the Monster - and its tantalizing hints of connections with the physical structure of spacetime. Once we understand the full nature of the Monster, we may well have revealed a whole new and deeper understanding of the nature of our Universe. Content: Contents Prologue 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 Theorem 11 Pandora's Box 12 The Leech Lattice 13 Fischer's Monsters 14 The Atlas 15 A Monstrous Mystery 16 Construction 17 Moonshine Notes Appendix 1: The Golden Section Appendix 2: The Witt Design Appendix 3: The Leech Lattice Appendix 4: The 26 Exceptions Glossary Index.