I thought it was pretty good, if a bit odd at times. It didn't seem to get to the point until chapter 6 or so. The book itself is split into Nine chapters followed by ten appendices and notes on the text. Initially, the first two chapters talk about symmetry in different ways. For instance, human beings tend to find things that are symmetrical in some way to be more aesthetically pleasing to the eye. The book talks about such things as M.C. Escher etchings and drawings, musical pieces composed by J.S. Bach and Mozart, Latin Squares, Roulette, and the Pauli Exclusion Principle.

So then it gets into the Ancient Babylonians and how they discovered a technique to solve a quadratic equation. This isn't improved on until sometime in the Middle Ages on the cusp of the Renaissance when a series of unfortunate events happen to a number of greedy and self serving mathematicians. The Cubic is solved and some people find solutions independently, but some go and steal the technique I guess. This raises bitter feelings and resentment in terms of priority and University Positions. So with that, people moved on to a general solution of an equation have a 4th power, a quartic. Not sure if that spelling is right, but oh well. So they had at it for many years and this was all happening when Abel and Galois came into the picture.

Abel's biography is included and it is sad. I guess that is what happens when people don't appreciate genius. He dies young, but leaves some fantastic mathematics behind him. The same can be said of Galois. He got too caught up in politics back in the day and endangered himself. At least in my opinion.

Chapter six leads to groups. It talks about the 15-puzzle, the Rubik's Cube and a discussion on geometries that ignore the Parallel Postulate. Chapter seven discusses symmetry in nature. No more needs to be said. Chapter eight talks about such things as why men find women with hourglass figures to be attractive and other things. Chapter nine summarizes the input of Galois and Abel to modern mathematics.

All in all it was pretty good. It seemed to take some time to build up to a point, and that is my only problem with it. The language is accessible, and it doesn't get into heavy mathematics. Four out of five. ( )

Decisamente meno bello de "La Sezione aurea"; un po' affrettato, a volte privo di un vero e proprio filo conduttore che non sia quello della simmetria - spesso ho avuto l'impressione che tale concetto fosse usato in modo pretestuoso, e che alcuni argomenti fossero affrontati soltanto per esigenze di completezza.
La storia di Evariste Galois, in compenso, è raccontata con dovizia di particolari, lasciando spazio alle varie ipotesi sulle cause della sua morte.
Tutto sommato, è un libro interessante, ricco di spunti di riflessione; lascia però il sapore di una grande occasione che l'autore non ha sfruttato appieno. ( )

Like reading five books , so much information. I keep picturing Galois ( group theory ) as being Elric from Full Metal Alchemist. ( Probably not far off really ) " ANYTHING can be transformed ! " ( )

Like reading five books , so much information. I keep picturing Galois ( group theory ) as being Elric from Full Metal Alchemist. ( Probably not far off really ) " ANYTHING can be transformed ! " ( )

While the concept of symmetry is fascinating I think that it's application to particle physics may be like applying circles to planetary motions. Nature just isn't symmetric. This book includes a great history of the mathematics of Group Theory. ( )

This book would make a good biography of Abel and Galois but is really a book about maths and not a maths book (if you can see the distinction). We get the intimate details of the two mathematicians' lives but their actual discoveries seem to be an addendum to the book as a whole. If you want a popular history and have a basic mathematical knowledge this is for you but I wouldn't recommend it if you want to exit the process knowing something about Galois theory. ( )

In Chapter One, Mario Livio promises to open our eyes to the magic of symmetry through the language of mathematics. To do so, he first acquaints us with group theory of modern algebra. A group is any collection of elements (they need not be numbers) that have the properties of (1) closure, (2) associativity, (3) an identity element, and (4) an inverse operation. The fact that this simple definition leads to a theory that unifies all symmetries amazes even mathematicians.

Livio give us a little of the history of algebra, beginning with the ancient Greeks and Hindus, who solved the general quadratic. The story of the solution of the general cubic is a fascinating one involving allegations of cheating and libel among 16th century Italian mathematicians. Moreover, the solution required the invention of imaginary numbers. Once the cubic was solved, the solution or the quadratic quickly followed, but the quintic remained a mystery.

Even Euler and Gauss were stumped by the quintic, and they began to think the problem was insoluble. In fact, the work of two very young mathematicians, Niels Henrik Abel and Evariste Galois, proved that there could be no general solution to the general form of the quintic equation. The solution proved to be a surprise in that it depended on the relations among the coefficients of the variables. Only those quintics with a proper symmetry among the coefficients can be solved by purely algebraic operations. Livio does not actually show why the previous statement is true, probably because it requires real math. Nevertheless, the conclusion is pretty startling even to a math tyro like me.

The book gets a bit bogged down in its biographical sections, devoting more time to Galois’s life than I found interesting. Nevertheless, it is worth reading.

(JAB) ( )

I read picked this book because I have since my early algebra days been interested in the quintic (e.g. x^5 + 2x^4 + … + 1). It presented a very good explanation of the history that led up to its ultimate proof that it’s impossible to solve in the general case using standard arithmetic operators and extraction of roots.

Although it covered that well, it kind of went off on many tangents to fields that sort of had to do with symmetry. Perhaps I should have got a book focused more — but all around it was interesting. ( )

The story of group theory (Abel, Galois, et al) -- another good pop-math book.

First 5 chapters give a general history of mathematics centered around the solution to the quintic. It took a proof based on group theory to show it couldn’t be solved using basic operations. In depth focus on Abel and Galois. Chapters 6-8 much more interesting and includes a nice discussion of groups and symmetry in quantum physics.

Some quotes:

"The theory of groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing." Pg. 180 (actually quoting James R. Newman)

"The unexpected link between permutations and icosahedral rotations allowed Klein to weave a magnificent tapestry in which the quintic equation, rotation groups, and elliptic functions were all interwoven." – pg. 197

"Simple groups are the basic building blocks of group theory in the same sense that prime numbers are the building blocks of all the integer numbers" – pg. 224 ( )

How ignorant I am.