|
|
Title: Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics
Purchase
Item
Manufacturer: Oxford University Press, USA
List Price: $19.95
Our Price: $11.38
|
|
| Customer Reviews: |
| Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA Anecdotes and soft math | | 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. | | Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA The Monster at the End of the Book | 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.
Perhaps the best book dealing with the solution of a tough problem is Simon Singh's Fermat's Enigma, dealing with the proof of Fermat's Last Theorem. Ronan's book is not as easy of a read, but then again, he has a tougher row to hoe: while Fermat's Last Theorem is relatively easy to understand (though difficult to prove), the concept of symmetry groups is a bit more esoteric. Operating within this constraint, Ronan does a good job, writing clearly, with both a sense of history and sense of humor. This is not an easy subject to really grasp, but it may be ultimately rewarding to those who stick with it.
| | Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA Symmetry and the Monster | | 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. | | Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA Good but not enough example to illustrate ideas | | This is an interesting read in general but the author doesn't include enough examples to illustrate idea (e.g. some graphical examples of different rigid geometric transformaion of solids will be great at the beginning of the book). The author also introduce mathematical concepts without enough explanation. While some of the concepts are simple enough to be understood without clarification, some of the more complicated ones in the later chapters are not. So the readers who are not already familiar with the subjects might find it difficult to follow the author's arguments. | | Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA Slightly too dumbed-down | 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. With this in mind, Ronan could have profitably added a chapter at the beginning (or even an appendix) where he took the reader through normal subgroups, quotient groups and on to simple groups. He would then have been able to use correct terminology (his own merely irritates) and the journey would have been a lot more satisfying. Perhaps for the second edition?
| | Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics by Oxford University Press, USA 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. |
| |
