Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics | 
 enlarge | Author: Mark Ronan
Publisher: Oxford University Press, USA
Category: Book
List Price: $27.00
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Rating:  16 reviews
Sales Rank: 599533
Media: Hardcover
Pages: 272
Number Of Items: 1
Shipping Weight (lbs): 0.7
Dimensions (in): 7.8 x 4.9 x 1.1
ISBN: 0192807226
Dewey Decimal Number: 516.1
EAN: 9780192807229
Publication Date: July 1, 2006
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Product Description
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.
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 Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or "atoms of symmetry."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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| Customer Reviews: Read 11 more reviews...
 They created a Monster.... July 1, 2006
Dr. Lee D. Carlson (Saint Louis, Missouri USA)
47 out of 47 found this review helpful
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.
Terrific book for both interested layperson and professional mathematician November 16, 2006
Daz (Berkeley, CA USA)
47 out of 47 found this review helpful
As a mathematician, I did not need to read the first half of the book, which explains very clearly some of the concepts used in the meatier second half. But I was very impressed with the clarity of Ronan's exposition. One valuable bit of terminology that he uses is calling a group (a technical mathematical concept that is the central subject of the book, and which he explains with great lucidity) an "atom of symmetry". This is a perfect way to convey the meaning of a group, and give the lay reader an easy way to conceptualize it.
Besides explaining things in terms that any intelligent reader can understand without getting lost in details -- AND without blurring the truth, either (quite a feat!) -- Ronan gives an engrossing account of which mathematician had which insight, and discussed it with which other mathematician, etc., so that the way progress in math occurs is elucidated. I'm a mathematician who doesn't know a great deal about the main subject of this book, and can honestly say that I learned a lot of intriguing stuff by reading it.
The math described is very pretty. For those who understand the terminology, I'll mention that this book's main subject is the classification of the finite sporadic simple groups (and it is now known that there are exactly 26 of them in all). The largest and most complicated of these 26 is enormous, and known as The Monster, whence the title of the book.
Ronan also describes several loose ends -- bits of mathematics that are not well understood -- to further give the lay reader an accurate picture of how mathematicians and mathematics works.
Do not walk or run, but *skip* to your nearest book emporium and buy this book.
Disclaimer: I have never met the author, have no financial interest in the sale of this book, and the above is entirely my personal opinion.
Monster Reveals Mathematics June 18, 2006
Chrisjfarrell
18 out of 20 found this review helpful
The beauty of this book lies in its revelations about the world of mathematics. The Monster is a super-large `group' and the theory behind it appears to be a perfect vehicle for the revelatory purpose. Its arithmetic involves multiplying and dividing rows of numbers differing by one from each other, or others raised to simple powers. Such simplicity immediately disarms those who might think that mathematics is just ever more complicated arithmetic, as most past schooling might have suggested. Instead Ronan thrusts us into a realm where concepts of spatial relationships are explored. Forget three dimensions, how about six or eight or more? I confess I didn't understand every paragraph, but that doesn't matter. It is the journey that counts. And when you get to the end look at the glossary and the utter simplicity of the definition of a `group'. It should give you a sense of wonder that something so apparently straightforward has led human minds on the fantastic journeys laid out in this marvelous little pocket-sized monograph - and that that is mathematics.
A most beautiful book July 6, 2007
Franklin Juarez (Chicago, IL, USA)
2 out of 2 found this review helpful
Since the first page up to the last, this extraordinary book keeps you in suspense.
It start telling about an extraordinary coincidence, found by two matematicians, that keeps you reading and interested; and in the last page ends with the same coincidence... But this time you know that this "coincidence" could be one of the most important misteries of the universe....of the human mind...and humankind.
It is a history about the questioning in the aparently game-like properties of space.
it is a history of the findings of many people, from ancient history, passing through all the years and up to the present time. From many cultures and languages. All trying to get answers to the riddles of form and symmetry.
You just need to have the knowledge of high school mathematics in order to understand the book. And to have an inquiring or philosophical mind.
The only formula that appears in the book is the solution of an equation of grade two. Also there are big numbers written as products of other numbers with exponents.
Also you have to know what is the meaning of a prime number.
Abstract mathematics will take now a new outlook to you.
Perhaps it is not so "abstract" after all.
Anecdotes and soft math April 12, 2008
Lee P. Neuwirth (princeton, nj usa)
1 out of 1 found this review helpful
Full of stories and simplified explanations of very deep material, this is one of the best math books I have read. One needn't be a professional mathematician to enjoy or understand it.
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