Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics: Ronan, Mark: 9780192807229: Amazon.com: Books

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

by Mark Ronan (Author)

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

Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics
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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 Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry."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.

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ISBN-10

0192807226
ISBN-13

978-0192807229
Edition

First Edition
Publisher

Oxford University Press
Publication date

July 1, 2006
Language

English
Dimensions

5.25 x 1 x 8 inches
Print length

272 pages
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Editorial Reviews

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"Remarkable contribution to the pop-math genre."--SIAM Review

"Succeeds in bringing to the fore an aspect of mathematics that some popularizers miss--that math is not a science of monuments, but a living tradition as vibrant as physics or ethics or law, one in which new monuments pop up weekly and old ones are retrofitted for purposes inconceivable to their creators."--Seed Magazine

Book Description

The exciting story of one of the great mathematical quests, spiced with the stories of the many extraordinary people involved

Product details

Publisher ‏ : ‎ Oxford University Press; First Edition (July 1, 2006)
Language ‏ : ‎ English
Hardcover ‏ : ‎ 272 pages
ISBN-10 ‏ : ‎ 0192807226
ISBN-13 ‏ : ‎ 978-0192807229
Item Weight ‏ : ‎ 11.2 ounces
Dimensions ‏ : ‎ 5.25 x 1 x 8 inches

Best Sellers Rank: #679,385 in Books (See Top 100 in Books)
- #451 in Mathematics History
- #1,478 in Scientist Biographies
- #20,654 in Unknown

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Mark Ronan

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Dr. Lee D. Carlson

They created a Monster....

Reviewed in the United States on July 1, 2006

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The story of the `Monster Moonshine' is told eloquently and with great enthusiasm in this book, and gives to the curious reader the needed insight into both the relevance and the mathematical constructions needed to bring it about. To understand in-depth the Monster requires a highly advanced background in mathematics, and to understand its connection with physics requires even more. The book though is not written for professional mathematicians, but rather for the general reader, who may have heard about the Monster through the popular press. Even though the author explains the ideas very well, a general reader however may find the book tough going at times. Those readers who have at least a background in mathematics that could be obtained in a typical undergraduate curriculum could better appreciate it.

There are many parts of the book whether the author gives really good explanations and motivations for various mathematical concepts. One is where he introduces the concept of symmetry via solid geometry and the `Platonic solids', which allows a more straightforward comprehension for readers without extensive mathematical preparation. He also uses it to introduce the concept of `duality', which is actually something that even readers with a good background in mathematics will appreciate. Although he does not define what it means for objects to be dual to each other rigorously, he gives examples, and for the purposes of the book merely notes that such objects will have the same symmetries. Another one is the use of the Sam Loyd tile game to explain the difference between even and odd permutations. Still another is the introduction of Lie groups as being a generalization of Galois theory for differential equations.

The author also discusses briefly the life histories of the mathematicians involved in the relevant group theory including their idiosyncrasies and different methods for doing mathematical research (and also the famous fictional mathematician `Bourbaki' who in reality was a group of highly respected mathematicians). Readers curious about the publishing habits of mathematicians will find out, interestingly, that they usually publish alone, and when they do publish together there is no arguing about whose name comes first: the listing of names is done in alphabetical order. Also interesting is the discussion on the role of reviewers of the research papers that led to the Monster. Since only a tiny minority of individuals understood (or were interested in) the relevant constructions, the anonymity of the reviewers was essentially compromised. But this did not act as a retardant to the research, and these events are another strong argument against anonymous reviewing.

The author also makes strong commentary against the use of computers in doing proofs of mathematics. He insists on being able to check the papers by hand, and details a fascinating story about how complicated calculations that seemed to formidable to do without the assistance of a computing machine were actually accomplished by some of the mathematicians involved in research into the Monster. One can't help but be impressed by their achievements in this regard. However, proofs done by computing machines are just as good as those done by humans. In fact, one might argue that machine proofs are always better, since their logic is impeccable and the likelihood of committing mistakes is very small. In addition, the intermixture of colloquial language with mathematical symbolism that is typical of human proofs makes totally rigorous proof unattainable, if one insists on a strict interpretation of deduction.

Everything in this book is therefore interesting, but the author does not want to leave the reader with the impression that there is no further work to be done on the Monster. This work he says involves obtaining a real understanding of the mathematical constructions behind the Monster. Also, there are further "coincidences" of a number-theoretic nature that need elucidation (one of these, interestingly, involves the integer 163). These issues will no doubt motivate a few young mathematicians to investigate the Monster in even more detail. It will be interesting to see what they find.

55 people found this helpful

A gripping read for those of us who are math squibs

Reviewed in the United States on October 2, 2013

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I came back to math 20 years after my BSc when a friend lent me a book in a similar style to this one. I was so blown away by how beautiful mathematics can be when explained well and went on a binge of reading these books. This one was a gripping read, both illustrating and explaining the ideas of the taxonomy of groups as well as giving a real feeling as to the excitement that must have been felt by those working at the frontier of this research. I hope the author writes more like this.

Symmetry and the Monster

Reviewed in the United States on February 29, 2008

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Interesting reading. The description of the lives of the mathematicians who contributed to the development of group theory helps create a basis of understanding for the topic. As a student, I wanted a different point of view than that of the text, and this book has done just that.

One person found this helpful

Reviewed in the United States on November 6, 2013

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For those who enjoy these types of history within the world of mathematics and logic, this is really a good one.

Edgar H. Bristol

Reviewed in the United States on August 31, 2015

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Andres Corradaemmanuel

Good outline of the history of the discovery of the exceptional finite groups

Reviewed in the United States on August 5, 2006

The book outlines the players and events that lead to the "Classification Theorem" -- a 'collective' proof by various mathematicians that identified all the finite groups. The theorem is estimated to span 15,000 pages of dense technical writing over various journal articles. The surprise in the classification effort was that there exist 26 exceptional groups and Ronan titled his book after the largest of these -- the Monster group.

The book was a good short read. It took me a day to finish it. The people involved in the classification along with some hints on the technical issues involved form the backbone of the story. I found it entertaining but wish that it had covered the mathematics in greater depth (at the level of an undergraduate) and had a better bibliography to guide future readings of a curious reader.

29 people found this helpful

Amazon Customer

Reviewed in the United States on September 17, 2014

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instructive and entertaining

Leonti H. Thompson

Reviewed in the United States on June 18, 2007

Humans have shown a fascination for symmetry from the earliest times--from cave drawings to universal symmetric symbols as crosses, spirals, etc.. Symmetry is seen in ancient designs, architecture, calligraphy. From the developments in understanding the mathematics of symmetry seen in ancient civilizations--Egyptians, Greeks, Chinese, Hindus--the trend has grown with a greater understanding provided thru mathematical descriptions. "Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics" by Professor Ronan outlines in graphic clarity and drama the development of mathematical group theory, starting with Galois in the 19th century to the most recent, stunning achievement of those brilliant mathematicians who reached their crowning success in decoding "The Monster"--a group of near-unbelievable complexity. If one wishes to find intellectual stimulation and a glimpse into what may be the farther reaches of reality, I recommend highly that you obtain a copy. The writing is superbly clear and spare in its use of technical terms--all of which are clearly explained when they are used. Understanding the concepts helps, in my opinion, to develop ones rigor of thinking. As a psychiatrist, I am interested in the possible role that understanding of "The Monster" may play in giving us more expanded ideas about consciounsess itself. There are other applications of this knowledge to such areas as string theory. Professor Ronan is to be highly commended for having provided us with the means not only of understanding the essence of what may be the greatest intellecutal achievement known, but, also, the means of understanding more about those remarkable mathematicians in their humanity as well as in their brilliance and diligence.

Leonti H. Thompson, M.D.

4 people found this helpful

Top reviews from other countries

A. Rodgers

Beauty and the Beast

Reviewed in the United Kingdom on April 19, 2007

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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.

33 people found this helpful

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