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Symmetry and the Monster: One of the greatest quests of mathematics de Mark Ronan

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

Autor Mark Ronan
en Limba Engleză Paperback – 26 iul 2007
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, Poincare'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.
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Specificații

ISBN-13: 9780192807236
ISBN-10: 0192807234
Pagini: 264
Ilustrații: Line drawings & 12 halftones
Dimensiuni: 129 x 196 x 18 mm
Greutate: 0.2 kg
Ediția:Revised
Editura: Oxford University Press
Colecția OUP Oxford
Locul publicării:Oxford, United Kingdom

Descriere

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.

Recenzii

Ronan unfolds his story with admirable verve and clarity... [His] exposition includes entertaining glimpses of the personalities involved in this extraordinary quest, but best of all gives an admirabe amount of detail concerning the actual substance of their work.
...accessible, artfully written...it stresses the human side of the drama. Though I have been a long-time participant in the story, I found myself learning much in every chapter and not wanting to put the book down.
Ronan does a good job of describing the mathematics in broad strokes and giving a flavour of what is happening and - more importantly - why mathematicians get excited about these questions.
This book tells for the first time the fascinating story of the biggest theorem ever to have been proved. Mark Ronan graphically describes not only the last few decades of the chase and the intriguing characters who led it, but also some of the more interesting byways, including my personal favourite, the one I called 'Monstrous Moonshine'.
Ronan tells a good story, and in doing so he paints a convincing picture of how mathematicians conduct their research.

Notă biografică

Mark Ronan is a Professor at the University of Illinois at Chicago, and was Visiting Professor of Mathematics at University College London, having held previous academic positions in Berlin, in Braunschweig, and in Birmingham where he was Mason Professor of Mathematics in the late 1980s and early 1990s. In his early career he worked on the fringes of the Classification program and knew personally all the main people involved in the modern part of this story. His work is now on geometric structures exhibiting symmetry, on which he has written numerous research papers and a textbook published by Academic Press in 1989. Besides mathematics, Mark reads Babylonian cuneiform and has a great love for music. He has acted in more than a dozen operas at the Lyric Opera of Chicago and danced in The Nutcracker.

Cuprins

  • 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 Theorum
  • 11: Pandora's Box
  • 12: The Leech Lattice
  • 13: Fischer's Monsters
  • 14: The Atlas
  • 15: A Monstrous Mystery
  • 16: Construction
  • 17: Moonshine
  • Appendix 1: The Golden Section
  • Appendix 2: The Witt Design
  • Appendix 3: The Leech Lattice
  • Appendix4: The 26 Exceptions