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Symmetry and the Monster: One of the greatest quests of mathematics [Paperback]

Mark Ronan
3.7 out of 5 stars  See all reviews (7 customer reviews)
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Book Description

4 Sep 2007 0192807234 978-0192807236 New Ed
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.

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Symmetry and the Monster: One of the greatest quests of mathematics + Fearless Symmetry: Exposing the Hidden Patterns of Numbers + Elliptic Tales: Curves, Counting, and Number Theory
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Product details

  • Paperback: 272 pages
  • Publisher: OUP Oxford; New Ed edition (4 Sep 2007)
  • Language: English
  • ISBN-10: 0192807234
  • ISBN-13: 978-0192807236
  • Product Dimensions: 19.5 x 13.4 x 1.8 cm
  • Average Customer Review: 3.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Bestsellers Rank: 341,949 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description


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. (Peter Pesic. TLS)

...accessible, artfully 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. (Robert L. Griess Jr.)

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. (The Mathematical Association of America)

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'. (John H. Conway, F.R.S.)

Ronan tells a good story, and in doing so he paints a convincing picture of how mathematicians conduct their research. (Gareth Jones, London Mathematical Society Newsletter)

About the Author

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.

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Customer Reviews

Most Helpful Customer Reviews
26 of 28 people found the following review helpful
2.0 out of 5 stars Too simplified? 23 Mar 2008
Reading this book left me somewhat frustrated, as the need for popularisation of a very difficult subject leads the author to cover the maths too lightly, in my view. The maths in the book is very easy to follow but unfortunately the result is that you get very little insight into what this is really about. However, there are some very nice and elaborate descriptions of historic events and past mathematicians, so basically I think this book will cater for two types of readers: 1) Mathematicians with a good insight into group theory who know what this is all about and want a quick and entertaining recap of the history of the field, and 2) people who don't care about the maths, but enjoy the history of how scientists discover stuff. For the rest of us, who are after popular presentations of real science, I think there are much better alternatives.
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18 of 20 people found the following review helpful
5.0 out of 5 stars Aptly titled 1 Jan 2008
Popularisations of mathematics are difficult to do well because you need to have a fair amount of the language of maths under your belt before you can follow the arguments. To that end, putting across the ideas in a non-technical manner needs a skill that few possess.

Ronan does a sparkling job here. The basic concepts of group theory are glossed over without going into tedious detail (and despite my affection for this particular branch of maths, I consider a lot of the detail *extremely* tedious), and once the story gets under way, the ideas are brought forward in a flowing, almost breathlessly excited, style which is infectious.

The author himself was involved in this stupendous quest of classification, so he knows what he's talking about.

One of the aspects of such a popular account is the bringing to life of the people behind the name, many of whom I'd never heard, quite a few of whom I'd already encountered in my travels through an undergrad degree in mathematics. Neither does the author shrink from confronting the political circumstances in which certain of the mathematicians were working, which adds a further dimension of interest to the tale.

The first thing one wants to do having read this book is to go and find out the mathematics behind it all. Be warned: it is difficult area to get to grips with. The basics are simple but the detail is diabolical.
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2 of 2 people found the following review helpful
3.0 out of 5 stars Expounds the history, not the mathematics 2 Oct 2009
By M. Cann
This book describes the people, places and events that form the history of the classification of finite simple groups, with a particular emphasis on one finite simple group in particular - The Monster. Mark Ronan avoids attempting to explain too much detail of the mathematics involved, instead choosing to concentrate on describing the history of the matter. Consequently the book can be read by anyone with an interest in how long lived problems such as this can be solved by passionate people, and how perseverance and inspiration can produce results.

Those wishing to gain anything more than a superficial understanding of symmetry or the classification of finite groups should look elsewhere; this is not the aim of this book. This is not, as I was rather hoping it would be, a finite simple group equivalent of Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics.
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2 of 2 people found the following review helpful
5.0 out of 5 stars Excellent overview of a very technical subject 29 Sep 2009
There are many topics in science that have been successfully translated into the popular science literature. Time travel, black holes, quantum mechanics, the discovery of DNA, evolution are all covered on the popular science shelves. Mathematics, however, is a rather poor cousin. The queen of sciences has never sat comfortably on the bookshelves. The problem is usually twofold, the subject matter is too technical to be readily recast in language easily understood by the amateur and simultaneously the life of the research mathematician is rarely adaptable to a thrilling narrative.

In Symmetry and the Monster both problems are met head-on. The main topic of the book is the quest to classify the the finite simple groups of symmetries in mathematics. This is a subject of huge scope which has only reached completion at the end of the twentieth century and is an incredibly technical subject. Mark Ronan does an excellent job of describing the roller-coaster ride towards the completion of this quest with only the minimal use of mathematical jargon or equations. Indeed the reader has the marvellous sensation at the point of reading that the broad concepts have been well understood. However the expert reader may be disappointed to discover that every aspect of the story has not been covered in the fullest mathematical detail. However as an attempt to popularise an abstract area Mark Ronan has balanced the technical description carefully within the cradle of the human narrative. The characters involved in this story from Galois to Conway are towering figures in the mathematical community whose stories are rarely told in popular accounts.
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