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The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry

3.85  ·  Rating Details  ·  893 Ratings  ·  66 Reviews
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 ...more
Paperback, 368 pages
Published September 1st 2006 by Simon & Schuster (first published 2005)
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(showing 1-30 of 2,656)
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Feb 26, 2014 Nguyễn rated it really liked it  ·  review of another edition
Shelves: sciences, favorite
Được giới thiệu cuốn sách này từ lâu trước khi cầm trên tay và đọc bản thảo tiếng Việt, tôi đã cười thầm khi người giới thiệu cuốn sách nói về nó :"Đây là một trong những tài liệu đầy đủ và sâu sắc nhất về Galois, cậu biết chưa ?" Trước đó, cái tên Mario Livio đã mang đến cho tôi đủ thất vọng với "Chúa trời có phải là nhà toán học", ngoài ra, chuyện đối xứng và lịch sử việc giải các phương trình đối với tôi, từ lâu đã không còn là vấn đề xa lạ. Hơn thế, tôi vẫn vỗ ngực là mình có nhiều và đủ hiể ...more
Jan 10, 2014 Greg rated it really liked it
This is a book about a genius. Livio quotes George Bernard Shaw early and appropriately to describe Abel and Galois: “The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.” (3) It is a very, very true statement.

Livio traces the development in mathematics over the broad strokes of history. It is a history of brilliant minds solving progressively more difficult algebraic equatio
Ami Iida
Aug 17, 2015 Ami Iida rated it really liked it
Shelves: math
it is written about symmetry and group theory.
they had made impressive upon the human being from math. .
There are lots of games coming from symmetry.
ex. tetris


15 puzzle

Rubik's Cube
you can play every games coming from symmetry. LOL LOL LOL
May 10, 2008 Jessica rated it liked it
This was definitely more readable than most of the books about math I have read. There was plenty in it that I didn't understand, but it didn't take away from the point of the book. Any mathematician who gets killed in a duel over a girl at age 20 after spending a year in prison for revolutionary activities is worth reading about...especially if he made a discovery that revolutionized mathematics.
Feb 26, 2014 Nguyễn rated it really liked it
Shelves: sciences
This book is a comprehensive introduction to a very hard problem of mathematics : finding the general solution for a general equation, along with the story of two genius Niels Hendrik Abel and especially Evarist Galois. In my opinion, the author has spent much time to collect the documents related to Galois's life, so that he has described Galois's story truthfully in a very scientific way. That makes sense for the other books on Galois or the same topics always tried to describes Galois's story ...more
Oct 23, 2011 Amanda rated it liked it  ·  review of another edition
This book was a gift and I did not understand what I was about to read when I started it. It was not what I expected - a discussion of symmetry in nature. Instead, it was a history of symmetry, which heavy emphasis on the lives and theories of the mathematicians who perfected the theory. Written for a general audience, I struggled through some of the more challenging parts, but "click" of comprehension occurred when I resumed this book as it began a discussion on super string theory. Having just ...more
William Schram
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 b ...more
Maurizio Codogno
A dispetto del nome, Mario Livio di italiano ne parla ben poco, come dice lui stesso. Ma non è certo questo il problema in questa sua opera, dove racconta... Beh, non è così facile spiegarlo. Il tema principale è la storia dell'equazione di quinto grado e della sua non-risolvibilità, facendo la storia dei vari tentativi a partire da Scipione del Ferro, Tartaglia e Cardano per giungere alla definitiva dimostrazione da parte di Abel e Galois. Le biografie di questi due geni precocemente morti sono ...more
Jan 01, 2010 Natan rated it really liked it
Shelves: science-math
I have a BA in physics, and even though this book is not a physics book, I learned just how much I didn't learn in my degree and how awful my teachers were. Livio obviously doesn't go into equations and mathematical derivations, but instead explains the reasoning behind them and how different branches of physics are actually connected (something they don't bother teaching you).
Bryan Higgs
Apr 07, 2011 Bryan Higgs rated it really liked it
This was the first book I read about symmetry and its related mathematical topic, group theory, and it is excellent.

This book takes the same approach as many other similar books, focusing on the history (tragic in the case of Galois and Abel) and personalities, rather than the details of the mathematics.

This is a delightful read!

Highly recommended!
May 20, 2015 David rated it it was amazing
Central to this book are the figures of Niels Henrik Abel (1802-29) and Évariste Galois (1811-32). These two young men tackled the curious problem of finding a solution to the quintic, a general equation of fifth degree. Arithmetic solutions to linear equations, and the quadratic could be reduced to arithmetic operations and extraction of roots, and so could many other equations involving cubes and fourth powers, but the quintic stubbornly refused to yield to such solutions. The two central char ...more
Ian Durham
Aug 03, 2011 Ian Durham rated it it was amazing
A truly remarkable book. It manages to convey the beauty of the mathematics while simultaneously telling a compelling story. One of the best books I've ever read. Honestly, my words just don't do it justice. I highly, highly recommend this book to anyone even if math isn't necessarily your cup of tea.
Jan 04, 2015 Paul rated it liked it
Shelves: non-fiction
Although this book has its good points, parts of it are rather weak. In particular, the first two chapters, presumably used to motivate the rest of the book, are of poor quality, which may dissuade some readers.

The author does well when he recounts history and biography, as in the middle chapters, but he has difficulty explaining things, mostly because he avoids details and elaboration. Topics that I wish he had spent pages on, he skims over in a mere paragraph. Topics he spends pages on deserve
Bill H
Jan 07, 2012 Bill H rated it really liked it
I really enjoyed reading this -- it's a bit scattershot, but in the way you can have a wide-ranging conversation with some stranger at a party and feel that the evening was well spent.
Charles Pearce
Jul 24, 2012 Charles Pearce rated it liked it
Slow and dry at first. But it really picked up. It was a biography of the guy who came up with set theory. Now the physicists use it to explain the natural world.
Eva Filoramo
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
Feb 22, 2010 Melissa rated it it was amazing
I enjoyed this book, and the glimpse of how many are involved in discovering a new equation.
Apr 12, 2013 Mirko rated it really liked it
Interesting book about mathematics.
Sep 29, 2015 Rossdavidh rated it liked it  ·  review of another edition
Shelves: black
This has got to be the geekiest book I've read in a long time. It's all about math, for goodness sake. How do you stay awake through a book on math? Well, the duel, and the murder mystery, and the tragic poverty, and the backstabbing, and the mental illness all helped.

Because it's not really a book about math, it's a book about mathematicians. Very different subject, really. There is the baffling tale, which I'm still not certain if I believe, that in 1500's Venice, mathematicians would face off
Bill Weaver
May 12, 2010 Bill Weaver rated it it was amazing
This is a fascinating book on symmetry written by an astro-physicist, Mario Livio. I fell in love with symmetry when I was in graduate school studying chemistry. I loved the concepts of reflection, rotation and inversion on simple molecules and how one could determine energy levels with these operations. As I moved from molecules I started to notice symmetry in Rachel's exquisite homemade quilts, in nature, in Bach's music, in art and architecture. So far this book is not about using symmetry in ...more
Chelsea M
Apr 10, 2013 Chelsea M rated it liked it  ·  review of another edition
Shelves: non-fiction
I have long been fascinated by the life story of Galois, but I wasn't able to understand group theory, and could not fully appreciate his genius. I chose this book in hopes of solving this problem.

It certainly wasn't bad, but it was written at a lower level than I would have liked. I had to read through explanations of terms and ideas that I was already familiar with, which was frustrating, and while I liked the variety of topics that the book explored, the author often didn't discuss each topic
Sep 27, 2013 Jocelyn rated it liked it
Another day, another dense book on mathematics, science, and what-have-you. The Equation That Couldn't Be Solved feels a bit unorganized, but what is is a decent read. The concepts are abstract and generally hard to grasp, but I found myself enjoying Livio's brief biographies of Galois and Abel more than the mathematical parts of the book themselves.

I would say that this isn't really for anyone without a decent mathematical background, but anyone considering reading the book is probably at least
Anand Gopal
Sep 23, 2008 Anand Gopal rated it liked it
Shelves: mathematics
The equation in the title refers to the quintic, a fifth-degree polynomial. Livio traces the history of attempts to solve this equation (and lower-order equations), culminating in Evariste Galois brilliant proof and remarkable life. Galois was an committed Republican in mid-19th century revolutionary Frace and spent time in prison for his political activities. He was killed just months after his 20th birthday, possibly in a duel over a woman.

Livio's unpacking of Galois's life and proofs make fo
Jun 13, 2011 May added it
Shelves: mathematics
Livio takes a subject that one would think was exceptionally dull, i.e. Symmetry/Group theory, and brings the historical perspective that makes suitable for those who are not math geeks. He expertly gives the generalities of mathematical theory, so that Laymen can follow along.

I really wish more teachers would assign historical works to help students better understand that while math has generally been advanced one person at a time, that it is not unattainable or even not useful at the higher l
Oct 21, 2011 Benjamin rated it really liked it  ·  review of another edition
I really liked this book. The historical tidbits were great; learning how self-important Cauchy was was especially fun. Unfortunately, Livio falls into the frequent popular-science trap of presenting horribly contrived analogies for some mathematical or scientific concept. Much worse is his example of the Play-Doh deformation group. It is not clear to me how one would define this in such a way that it is actually a group. For example, he needs to guarantee that no deformation sends two different ...more
Ed Terrell
Jul 19, 2014 Ed Terrell rated it it was amazing
Shelves: 2013, mathematics
Livio takes us on historical journey in the development of mathematics. Starting with Babylonia and moving gracefully into the Middle Ages of Europe, he traces the lives of characters and the societies as they uncover the hidden treasures and develop the mathematical tools we use today. In the post Napoleon Europe, he takes special care and interest in the child prodigies Abel and Galois. Especially Galois. The heated revolutionary was killed at twenty in a duel but not before he put to paper id ...more
So Hakim
Feb 09, 2015 So Hakim rated it liked it
A bit uneven. Some talk about the concept of symmetry, its history, and its examples, but somehow seems not tightly wrapped.

On the positive side there are nice biographies. I personally like the treatment of Abel and Galois. There is also historical overview including Renaissance Italy's Cardano and Tartaglia, but that's about it.
May 20, 2010 Seth rated it liked it
I mostly enjoyed this book, but like others have said, it's a mixed bag, with the book sort of going all over the place. I liked the digressions into the biographies of Galois and Abel, but by the time the book got to the last chapters, it was just too much of "and here's another example of symmetry!" for two pages, and then "here's another example of symmetry!" for another two pages. That said, I enjoyed large chunks of the book. A bit less breadth and a bit more depth would perhaps have been b ...more
Mario Grella
Se non sapete nulla della simmetria e non capite nulla di matematica, compratevi un giallo di Simenon perché dopo aver letto questo continuerete a non saper nulla di simmetria e a capir nulla di matematica...
Jimmy Ele
Aug 03, 2016 Jimmy Ele rated it it was amazing
This is a masterwork. It touches on the aspects of symmetry in Mathematics and takes it further into physics, art, and poetry. Tragic mathematicians are deftly painted under a loving hand. Highly recommended book, an instant favorite, especially for it's outpouring of ideas and subjects which have guided me to ever more abstract vistas of research and thought.
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“The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature's design.” 0 likes
“While composite faces tend, by construction, to also be more symmetric, Langlois found that even after the effects of symmetry have been controlled, averageness was still judged to be attractive. These findings argue for a certain level of prototyping in the mind, since averageness might well be coupled with a prototypical template.” 0 likes
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