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
Buy Used: $1.60
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Rating:  22 reviews
Sales Rank: 173192
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 17 more reviews...
 Better than his earlier book December 8, 2005
Bruce R. Gilson (Rockville, MD United States)
38 out of 42 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.
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.
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.
Brilliant September 19, 2005
Bryan
11 out of 12 found this review helpful
Dr. Livio has followed up his last smash, The Golden Ratio, with yet another fascinating, deep and enjoyable book. The sweep from mathematics to group theory and symmetry to history and art is simply mindboggling. This book is so well researched that it ends up solving a longstanding mystery: Livio identifies who probably killed Evariste Galois, the brilliant young mathematician who laid out the proofs that became the foundation for the entire science of group theory the night before he died in a dawn pistol duel at the age of 20. Evariste's death has been a mystery for nearly 200 years. The Equation That Couldn't Be Solved ironically solves that mystery.
Besides identifying a killer, this book is the first science book for the layman that attempts to tackle group theory and its related fields. It may well be the last. It will be very hard to top.
A Fascinating Tale September 21, 2005
The Quiet Eye
14 out of 16 found this review helpful
In this book Mario Livio tells, in his typically clear and gripping style, the
story of the quintic (5th degree) equation, which resisted solution till the
early 19th century, in spite of enormous efforts by many gifted and well-known
mathematicians. It was finally solved independently by
two young and brilliant mathematicians, Niels Henrik Abel from Norway and
Evariste Galois from France, both of whom died tragic deaths at a very young
age, Abel at the age of 27, and Galois at the age of 20. The approach taken by
Galois, who had unusual mathematical abilities, is truly brilliant and
revolutionary, and opened the door to a whole new branch in mathematics, the
group theory, the "official language" of symmetry. The social views of Galois
were equally revolutionary, who died at the tender young age 20 in a duel
resulting from a love fight, with his final words to his brother, "Don't cry
for me, I need all my courage to die at 20."
Ironically, the circumstances leading to the tragic and spectacular death of
Galois were themselves shrouded in mystery. No doubt there are many conspiracy
theories, but most of them do not explain many known facts about the incidence.
Mario Livio has put an enormous amount of effort in solving this mystery, which
coherently explains most of the known facts, which he has presented in this
book.
The book combines the fascinating life stories of the great two mathematicians
told in the style of a modern thriller, with amazing insights into the purpose
and meaning of their discoveries expressed in a language easily accessible by
the general public. The book is replete with fascinating details on art,
history, science and mathematics coming, as it does, from a uniquely gifted
expert in all these subjects. The book makes for a truly fascinating and
inspiring reading.
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