The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry | 
 enlarge | Author: Mario Livio
Publisher: Simon & Schuster
Category: Book
List Price: $15.00
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Rating:  21 reviews
Sales Rank: 201668
Media: Paperback
Pages: 368
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 9.2 x 5.8 x 0.5
ISBN: 0743258215
Dewey Decimal Number: 512.209
EAN: 9780743258210
Publication Date: August 22, 2006
Availability: Usually ships in 1-2 business days
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Product Description
What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved.For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Evariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.
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| Customer Reviews: Read 16 more reviews...
 Better than his earlier book December 8, 2005
Bruce R. Gilson (Rockville, MD United States)
39 out of 43 found this review helpful
I've earlier reviewed Livio's book on the Golden Ratio and if you'll read my review of that book, you'll see that I found it somewhat disappointing, though liking parts of it enough to give an overall 4-star rating. This book is much better. Basically, it addresses two topics: the attempts made over the ages to use formulas (such as the one we learned in algebra in school for the quadratic equation) to solve higher degree equations, which failed when algebraists got to the fifth degree, and the mathematics that describes symmetry, called group theory. These two topics would seem to be unrelated, but in fact, when Evariste Galois proved that the formula could not be found for fifth degree equations, he did it by inventing group theory! This book explores this connection, while also giving a lot of biographical information about both Galois and Niels Abel, who duplicated Galois' result about fifth degree equations.
I found that this book reads very well, and I highly recommend it.
very accessible introduction to group theory and it's history September 5, 2006
Patrick Regan (Northampton, MA USA)
9 out of 11 found this review helpful
The equation that couldn't be solved is about the history of group theory. The stories of two of it's early contributors Abel and Galois is told in detail. In addition the author provides an accessible overview of group theory. The specific equation that couldn't be solved is the quintic, which cannot be factored in general. That means that while there are specific examples of polynomials with a factor of x raised to 5 or greater that can be factored there is no general formula like the quadratic eqauation that can factor all quintic or higher polynomials. Although originally used to study factoring, group theory has evolved to be about many other things including the mathematical concept of symmetry. Symmetry arises in many parts of mathematics and science so it is very imporant. I came away from this book with a knowledge of the history of group theory and a smattering of knowledge about group theory and it's applications. I highly recommend this book to those people, like me, who are interested in mathematics and would like to peek under the surface to see what it is all about.
The Captivating History of Symmetry November 8, 2005
Martin J. O'Neill (Bloomington IN)
12 out of 13 found this review helpful
This book represents an ambitious effort of Mario Livio to explain and describe the mathematical origen of group theory, the language of symmetry, in its historical context. The subject is developed to show the importance of the theory for some of the most important scientific achievements of the 20th century (the general theory of relativity). The author's account of the lives of the 2 young mathematicians who did the seminal work in this field presents a very gripping story and evokes the tragic sense that much was lost with their untimely deaths.
The research involved in writing this book is truly extraordinary, and the ability of the author to interrelate the resulting information in a meaningful way is impressive.
Mathematics as Beautiful as a Symphony October 28, 2005
John Matlock (Winnemucca, NV)
18 out of 21 found this review helpful
At some level mathematics becomes developes a beauty and a mystique not unlike a symphony or a poem or a painting. And like these, the most beautiful math is often done by very young men.
The story of the solving of the quintic equation is a tale worth telling. The mathematics of algebra began thousands of years ago. The Greek Pythagoras in the sixth century BC made a great advance with the solving of the quadratic equation. Over the next couple of thousand years further work got us to the solution of the quartic equation during the Renaissance. Then came the quintic, the subject of this book.
Two young mathematicians solved the problem Norwegian Niels Henrik Abel, and Frenchman Evariste Galois. The work they did was brilliant, and they both died very young. This book is a tale of what they did, and the implications of that work.
The results of their work lead to the concepts of symmetry. This book, written almost like a detective story then take symmetry into the musid of Bach, the basic forces of nature, and the selection of sexual partners. It's a delightful read.
Superb exploration of the mathematical, artistic, social and cultural significance of symmetry September 13, 2005
Josh Clark (Austin, TX)
18 out of 19 found this review helpful
I picked up this book not knowing anything about symmetry and, frankly, not being too interested in it. What I discovered was a brilliant, cerebral yet entertaining examination of both the mathematical foundations of this concept and its artistic, cultural, and social significance. Perfectly mixing mathematical analyses with fascinating biographical, historic and artistic information (as well as the occasional amusing anecdote), Livio's incredibly well-researched book is as illuminating as a great work of philosophy and as thrilling as a Sherlock Holmes mystery. Those with absolutely no knowledge of mathematics (like me) should not be deterred, because the author inventively elucidates any difficult concepts, leaving nothing unexplained yet never digressing unnecessarily from the central narrative. Above all, the haunting character of Evariste Galois will remain with readers for a long time after they have completed reading this masterful account.
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