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65 of 65 people found the following review helpful:
5.0 out of 5 stars
Terrific book for both interested layperson and professional mathematician, November 16, 2006
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.
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51 of 51 people found the following review helpful:
5.0 out of 5 stars
They created a Monster...., June 30, 2006
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.
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16 of 16 people found the following review helpful:
4.0 out of 5 stars
A mystery in 196,883 dimensions, April 10, 2007
"The Monster" is an abstract mathematical object, dimly seen even by its discoverers. It sits at the heart of the Classification Theorem (the "Enormous" theorem), a proof in 15,000 pages with contributions from over 100 mathematicians. The Monster has tantalizing connections to algebra, number theory, and seemingly every other field that people have examined closely enough. It's driven an amazing amount of innovation in many areas, and has arguably changed the definition of mathematical proof. Since it exists only in such rarefied atmospheres, The Monster itself is accessible to only the most diligent of seekers. Still, Ronan has done a fair job of explaining what this beast is, and why this unique object deserves researchers' attention, all in non- (or slightly-) mathematical language. More than that, Ronan has given biographical sketches of some of the remarkable characters that contributed to its study. Evariste Galois was one, that hot-headed, romantic, and tragic figure who spent the last night of his life scribbling his thoughts, before dying in a duel. Ronan also sketches the life of Sophus Lie (rhymes with "bee," not "buy"), a brooding Norwegian giant, and others from the earliest records of mathematics to the current day. Along the way, Ronan touches on so many fields of mathematics that it's a wonder the Enormous Theorem could ever have been written: combinatorial design theory, finite fields, geometry, number theory, and lots more. Even more fascinating is how the fields morph into one another at their least-understood edges. In any objective sense, it's a story of bookish people, each working quietly to create one of the bricks or beams that went into the Enormous edifice. Mathematicians are human, though, and as passionate as anyone else when they've devoted their lives to something. The words of this book are about mathematicians and their math. The spirit of this book, however, is about that passion, about the towering achievements that characterized what's known about The Monster, and about the thrill of discovery that so clearly remains to future researchers. //wiredweird
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