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Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics Paperback – September 4, 2007

by Mark Ronan (Author)
3.8 out of 5 stars 19 customer reviews
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Product Details

  • Paperback: 272 pages
  • Publisher: Oxford University Press; Revised ed. edition (September 4, 2007)
  • Language: English
  • ISBN-10: 0192807234
  • ISBN-13: 978-0192807236
  • Product Dimensions: 7.6 x 0.6 x 5 inches
  • Shipping Weight: 7.2 ounces (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (19 customer reviews)
  • Amazon Best Sellers Rank: #1,106,891 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

4.0 out of 5 starsSlightly too dumbed-down
By Nigel Seel on October 2, 2007
Format: Paperback
According to the blurb on the back, the American Mathematical Monthly described this book as "truly a page-turner". I have to say it is not.

Mark Ronan's task is to take us through the history of group theory culminating in the recently-completed project to classify the finite simple groups. This has taken decades of work by large numbers of highly-skilled mathematicians, with proofs so long and abstruse that there is a genuine concern that no future generation of mathematicians will be able to comprehend them.

How do you communicate this to a lay audience? The key decision for the writer is to gauge his audience. Ronan's view is a readership which knows no group theory. He therefore can't even define a simple group: "a simple group is a group which is not the trivial group and whose only normal subgroups are the trivial group and the group itself" - Wikipedia.

The reader, lacking help in engaging with the subject matter, is instead entertained by concise and amusing mini-biographies and anecdotes about the many participants in the quest. Ronan is a little dry as a writer, but in general this works well enough, although he is too indulgent of such monstrous personages as Sophus Lie. The final milestone in the classification project was confirmation of discovery of the mathematical Monster, the largest of the 26 sporadic groups. This was big news even on conventional news outlets, such as the BBC.

In conclusion, this book will work for mathematicians who know some group theory and who like the historical context spelled out. I don't think many people not educated in mathematics will make it through to the end.Read more ›
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5.0 out of 5 starsI couldn't put it down
By Peter Haggstrom on November 6, 2008
Format: Paperback Verified Purchase
This book is a ripping yarn - I couldn't put it down. My wife asked when I came to bed at midnight : "Maths porn again darling? " Although I have done some group theory, my knowledge was nowhere near enough to make any meaningful attempt to understand the detail of the Monster project and like many others, it remained an intractable beast that others were battling with. Ronan explains in a high level way the history to the Monster starting with Galois and working his way through the historical development. He peppers the account with all manner of interesting observations about the participants which are revealing in ways that one does not often find in maths books. For instance, there is a revealing comment on page 152 about someone of the stature of John H Conway who confessed he "felt like a fraud" in giving talks early on in his work on Monster. It seems a graduate student asked him the obvious question namely " How do you now that your new group can't be decomposed into something simpler?" Maths is an unforgiving business.

Mark Ronan who has worked with and/or knows most of the heavy hitters in the field has done a wonderful job explaining the history of what is an extraordinary undertaking not only in purely intellectual terms but also in personal terms. The sociological dimensions of this immense task are reflected in all manner of small and large stories. Thus John H Conway bargains with his wife to have blocks of time away from the 4 kids so he can crack some problems and he manages in 12 ½ hours to prove something important about the Leech Lattice. That set him up for life. The proofs in this field can be hundreds of pages long - one by Mason is 800 pages long and has not been published. This itself imposes huge strains on referees.Read more ›
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4.0 out of 5 starsThe Monster at the End of the Book
By mrliteral on March 4, 2008
Format: Paperback Verified Purchase
While it is simple enough to conceive an object in one, two or three dimensions, adding just one more dimension can be mind-bending. The four dimensional cube - or tesseract - cannot be truly perceived, but we can at least get a glimmer of it when we look at its projection, which appears like a cube within a cube. Five dimensions are even harder to perceive. The Monster, the subject of Mark Ronan's Symmetry and the Monster, has 196,884 dimensions. It seems appropriately named.

What is the Monster, however? This takes a while to describe, and it all begins with the brilliant Galois, a mathematical genius who would be dead by 20 after being on the losing side in a duel. Galois would make some major strides in the field of algebra known as group theory. A group is really just a self-contained set of numbers (or other components) with an operation (such as addition) and certain properties (such as closure, the idea that when you do the operation on two members of the set, you get another member of the set; for example, with the whole numbers and addition, adding any two positive integers gets you another positive integer).

Groups can be both finite and infinite, and among finite groups, there are so-called simple groups (or what Ronan calls atoms of symmetry). These are not simple as in easy, but simple as they cannot be deconstructed into simpler groups, just as when you factor a number, you cannot factor any further when you reach the prime factors. Most simple groups fit into certain families, but there also 26 exceptional groups (or sporadic groups). Determining that the number was 26 and finding all these groups is what Symmetry and the Monster is all about. The final group would be the biggest, by far: the Monster.Read more ›
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Most Recent Customer Reviews

3.0 out of 5 starsNot a real success

This book provides a nice introduction to group theory and its history but it fails as a book about the Monster group. Read more

Published 8 months ago by Scott Tillinghast
5.0 out of 5 starsExcelent book! Provides a beautiful exposition of the groups ...

Excelent book! Provides a beautiful exposition of the groups theory, and the fantastic role of the symmetry in mathematics. Awesome!

Published 9 months ago by Amazon Customer
4.0 out of 5 starsA Book Worth Reading.

The full significance of the Monster is not yet known. But it may turn out to be the most important development in mathematics, physics and philosophy made in the past 100 years. Read more

Published 11 months ago by Ozkar de Grump
4.0 out of 5 starsFour Stars

OK

Published 23 months ago by Kenneth A. Perko, Jr.
3.0 out of 5 starsDon't expect too much from this book

If you know not much about group theory, don't expect you can understand too much about what mathematicians are doing with all those discoveries about groups, symmetries, Monsters... Read more

Published on June 19, 2014 by Suncake58
5.0 out of 5 starsSuperb! Actually conveys the essence of the underlying mathematics

There has been no shortage of books attempting to explain major results and open problems in mathematics to a relatively lay audience, from Perelman's resolution of the Poincare... Read more

Published on February 27, 2014 by GrazziDad
5.0 out of 5 starsA Great Read

I really enjoyed reading the book, "Symmetry and the Monster: One of the great qusts of mathematics". Read more

Published on September 6, 2012 by Amazon Customer
2.0 out of 5 starsA subject simplified into incomprehensibility

This is a history book about the history of research into group theory and the discovery of the "Monster", not a book about that Monster. Read more

Published on March 6, 2012 by Dick Grune
3.0 out of 5 starssearching for what - complexity?

I did enjoy this book despite the fact that Galois - the reason for my picking it up - got left behind very quickly. Read more

Published on January 2, 2011 by A. G. Plumb
2.0 out of 5 starsOn why you should not buy this book

Far too many forward links, everything is to be seen later, while the Author spend time in describing why and why not someone went through a duel, or missed a train, or whatever,... Read more

Published on June 25, 2010 by ziobilly

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