Product Description

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.

Product Details

• Amazon Sales Rank: #14895 in Books
• Published on: 2007-07-26
• Original language: English
• Number of items: 1
• Binding: Paperback
• 272 pages

John H. Conway, F.R.S.
'Mark Ronan graphically describes not only the last few decades of the chase...but also some of the more interesting byways.'

Review
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 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. (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 )

The Mathematical Association of America
'Ronan does a good job of describing the mathematics in broad strokes and...why mathematicians get excited about these questions.'

Customer Reviews

Beauty and the Beast
They always say "mathematics is not a spectator sport", and this is true, but in reading this book, I felt I was as close as possible to being an enthralled spectator at a great game that I would have little or no idea how to play myself. I almost literally couldn't put the book down.

The author takes great pains to make the subject as simple as possible, but not simpler (to echo the quotation from Einstein which heads the penultimate chapter). Such a compromise cannot be perfect, and as someone who knows a little maths, I found it mildly irritating to have to replace each occurrence of the phrase "atom of symmetry" with "simple group", rather than have the metaphor explained once, and the correct term used thereafter. On the other hand, I was quite happy to keep reading about "cross-sections", rather than have to keep stumbling over the phrase "involution centralizer" and be thereby reminded of how little I know about group theory! If I would take issue with any of the author's choices of vocabulary, it is his use of the term "deconstruction" instead of "decomposition", which is an equally familiar word, with one less letter (but one more syllable), and it is one which doesn't cause the susceptible reader to imagine that Jacques Derrida was somehow involved in the project. (God forbid!)

Each reader, at whatever level of knowledge, will have his or her own preference as to the appropriate amount of technical vocabulary to use, and the author has clearly struck a considered balance in this respect. The result is, I think, an easy read even for complete non-mathematicians, but which still contains plenty to fascinate even the professional who is not a specialist in this most specialised of areas.

It is, indeed, a specialised field; the classification of finite simple groups is not your average piece of mathematical research. I was already aware of the length of the famous (notorious?) Feit-Thompson "odd order paper", but was not aware that, at 255 pages (occupying an entire issue of a mathematical journal), this was a mere bagatelle compared to some of the prodigiously (monstrously?) long papers and typescripts (some not yet published, and never likely to be) which played an essential role in this heroic project. One shivers when one reads of the fears of those involved that the dismayingly formidable techniques required for this area of mathematics - and apparently for it alone - would not be passed on orally to future generations, and the understanding of them would be lost, like that of hieroglyphics. (A second vast project, the Revision of the Classification, is still underway to try to ensure that this does not happen.)

But often the best way to understand something is to look at extreme cases, and I think it is no accident that this is the best popularisation of mathematics that I have read. Something of the soul of mathematics is laid bare here.

Too simplified?
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.

Aptly titled
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.